diff --git a/.Rbuildignore b/.Rbuildignore index 613562f..ebd26be 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -3,3 +3,5 @@ ChangeLog ^\.travis\.yml$ ^docs$ .github +.git +_pkgdown.yml diff --git a/DESCRIPTION b/DESCRIPTION index b14db9d..8ccbf79 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -20,6 +20,7 @@ Authors@R: c(person("Roger", "Bivand", role = c("cre", "aut"), email = "Roger.Bi person("Abhirup", "Mallik", role = c("ctb", "trl")), person("Giovanni", "Millo", role = "ctb"), person("Kelley", "Pace", role = "ctb"), + person("Josiah", "Parry", role = "ctb", comment = c(ORCID = "0000-0001-9910-865X")), person("Pedro", "Peres-Neto", role = "ctb"), person("Tobias", "Rüttenauer", role = "ctb"), person(given = "Mauricio", family = "Sarrias", role = c("ctb"), email = "mauricio.sarrias@ucn.cl"), @@ -30,7 +31,7 @@ Imports: spdep (>= 1.3-1), coda, methods, MASS, boot, splines, LearnBayes, nlme, multcomp Suggests: parallel, RSpectra, tmap, foreign, spam, knitr, lmtest, expm, sandwich, rmarkdown, igraph (>= 2.0.0), tinytest -Description: A collection of all the estimation functions for spatial cross-sectional models (on lattice/areal data using spatial weights matrices) contained up to now in 'spdep'. These model fitting functions include maximum likelihood methods for cross-sectional models proposed by 'Cliff' and 'Ord' (1973, ISBN:0850860369) and (1981, ISBN:0850860814), fitting methods initially described by 'Ord' (1975) . The models are further described by 'Anselin' (1988) . Spatial two stage least squares and spatial general method of moment models initially proposed by 'Kelejian' and 'Prucha' (1998) and (1999) are provided. Impact methods and MCMC fitting methods proposed by 'LeSage' and 'Pace' (2009) are implemented for the family of cross-sectional spatial regression models. Methods for fitting the log determinant term in maximum likelihood and MCMC fitting are compared by 'Bivand et al.' (2013) , and model fitting methods by 'Bivand' and 'Piras' (2015) ; both of these articles include extensive lists of references. A recent review is provided by 'Bivand', 'Millo' and 'Piras' (2021) . 'spatialreg' >= 1.1-* corresponded to 'spdep' >= 1.1-1, in which the model fitting functions were deprecated and passed through to 'spatialreg', but masked those in 'spatialreg'. From versions 1.2-*, the functions have been made defunct in 'spdep'. +Description: A collection of all the estimation functions for spatial cross-sectional models (on lattice/areal data using spatial weights matrices) contained up to now in 'spdep'. These model fitting functions include maximum likelihood methods for cross-sectional models proposed by 'Cliff' and 'Ord' (1973, ISBN:0850860369) and (1981, ISBN:0850860814), fitting methods initially described by 'Ord' (1975) . The models are further described by 'Anselin' (1988) . Spatial two stage least squares and spatial general method of moment models initially proposed by 'Kelejian' and 'Prucha' (1998) and (1999) are provided. Impact methods and MCMC fitting methods proposed by 'LeSage' and 'Pace' (2009) are implemented for the family of cross-sectional spatial regression models. Methods for fitting the log determinant term in maximum likelihood and MCMC fitting are compared by 'Bivand et al.' (2013) , and model fitting methods by 'Bivand' and 'Piras' (2015) ; both of these articles include extensive lists of references. A recent review is provided by 'Bivand', 'Millo' and 'Piras' (2021) . 'spatialreg' >= 1.1-* corresponded to 'spdep' >= 1.1-1, in which the model fitting functions were deprecated and passed through to 'spatialreg', but masked those in 'spatialreg'. From versions 1.2-*, the functions have been made defunct in 'spdep'. From version 1.3-6, add Anselin-Kelejian (1997) test to `stsls` for residual spatial autocorrelation . License: GPL-2 URL: https://github.com/r-spatial/spatialreg/, https://r-spatial.github.io/spatialreg/ BugReports: https://github.com/r-spatial/spatialreg/issues/ diff --git a/NEWS.md b/NEWS.md index 87577c0..fd189e9 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,7 +1,10 @@ -# Version 1.3-5 (development) +# Version 1.3-6 (development) +* #56 add Anselin-Kelejian (1997) test to `stsls`, reported in its summary method, analogous to the reporting in the summary method of `lagsarlm` of the Lagrange multiplier test, both for residual spatial autocorrelation * adding missing man page anchors +# Version 1.3-5 (2024-08-19) + * conforming with STRICT_R_HEADERS=1 * Condition on forthcoming `tmap` 4 diff --git a/R/s2sls.R b/R/s2sls.R index 0f7ed10..1284a2b 100644 --- a/R/s2sls.R +++ b/R/s2sls.R @@ -156,9 +156,10 @@ print.summary.Stsls <- function(x, digits = max(5, .Options$digits - 3), else cat("Residual variance (sigma squared): ") cat(format(signif(x$sse/x$df, digits)), ", (sigma: ", format(signif(sqrt(x$sse/x$df), digits)), ")\n", sep="") - cat("Anselin-Kelejian (1997) test for residial autocorrelation: ") - cat(format(signif(x$AK, digits)), "\n p-value: ", - format.pval(pchisq(x$AK, 1, lower.tail=FALSE), digits), sep="") + cat("Anselin-Kelejian (1997) test for residual autocorrelation\n") + cat("test value: ", format(signif(x$AK, digits)), ", p-value: ", + format.pval(pchisq(x$AK, 1, lower.tail=FALSE), digits), + "\n", sep="") if (!is.null(correl)) { p <- NCOL(correl) @@ -299,6 +300,7 @@ htsls <- function(y,Z,Q,e) { # sebiv <- sqrt(diag(vi)) # tbiv <- biv / sebiv # pbiv <- pnorm(abs(tbiv),lower.tail=FALSE) * 2 + colnames(vi) <- rownames(vi) <- names(biv) result <- list(coefficients=biv, # se=sebiv,t=tbiv,p=pbiv, var=vi,sse=sse,residuals=c(e),df=df) @@ -364,7 +366,7 @@ tsls <- function(y,yend,X,Zinst,robust=FALSE, HC="HC0", legacy=FALSE, sig2n_k=FA else stop("invalid HC choice") ZoZ<-crossprod(Zp,(Zp*omega)) varb<-ZpZpi%*%ZoZ%*%ZpZpi - + colnames(varb) <- rownames(varb) <- names(biv) result <- list(coefficients=biv, var=varb, sse=sse, @@ -376,6 +378,7 @@ tsls <- function(y,yend,X,Zinst,robust=FALSE, HC="HC0", legacy=FALSE, sig2n_k=FA sse <- c(crossprod(e,e)) s2 <- sse / df varb <- ZpZpi * s2 + colnames(varb) <- rownames(varb) <- names(biv) # sebiv <- sqrt(diag(varb)) # tbiv <- biv / sebiv # pbiv <- pnorm(abs(tbiv),lower.tail=FALSE) * 2 diff --git a/README.md b/README.md index c60a1b6..17e0da2 100644 --- a/README.md +++ b/README.md @@ -5,6 +5,6 @@ ### spatialreg: spatial models estimation and testing -A collection of all the estimation functions for spatial cross-sectional models (on lattice/areal data using spatial weights matrices) contained up to now in **spdep**. These model fitting functions include maximum likelihood methods for cross-sectional models proposed by Cliff and Ord (1973, ISBN: 0850860369) and (1981, ISBN: 0850860814), fitting methods initially described by Ord (1975) https://doi.org/10.1080/01621459.1975.10480272. The models are further described by Anselin (1988) https://doi.org/10.1007/978-94-015-7799-1. Spatial two stage least squares and spatial general method of moment models initially proposed by Kelejian and Prucha (1998) https://doi.org/10.1023/A:1007707430416 and (1999) https://doi.org/10.1111/1468-2354.00027 are provided. Impact methods and MCMC fitting methods proposed by LeSage and Pace (2009) https://doi.org/10.1201/9781420064254 are implemented for the family of cross-sectional spatial regression models. Methods for fitting the log determinant term in maximum likelihood and MCMC fitting are compared by Bivand et al. (2013) https://doi.org/10.1111/gean.12008, and model fitting methods by Bivand and Piras (2015) https://doi.org/10.18637/jss.v063.i18; both of these articles include extensive lists of references. A recent review is provided by Bivand, Millo and Piras (2021) https://doi.org/10.3390/math9111276. **spatialreg** >= 1.1-1 corresponds to **spdep** = 1.1-1, in which the model fitting functions are deprecated and pass through to **spatialreg**, but will mask those in **spatialreg**. From versions 1.2-1, the functions have been made defunct in **spdep**. +A collection of all the estimation functions for spatial cross-sectional models (on lattice/areal data using spatial weights matrices) contained up to now in **spdep**. These model fitting functions include maximum likelihood methods for cross-sectional models proposed by Cliff and Ord (1973, ISBN: 0850860369) and (1981, ISBN: 0850860814), fitting methods initially described by Ord (1975) https://doi.org/10.1080/01621459.1975.10480272. The models are further described by Anselin (1988) https://doi.org/10.1007/978-94-015-7799-1. Spatial two stage least squares and spatial general method of moment models initially proposed by Kelejian and Prucha (1998) https://doi.org/10.1023/A:1007707430416 and (1999) https://doi.org/10.1111/1468-2354.00027 are provided. Impact methods and MCMC fitting methods proposed by LeSage and Pace (2009) https://doi.org/10.1201/9781420064254 are implemented for the family of cross-sectional spatial regression models. Methods for fitting the log determinant term in maximum likelihood and MCMC fitting are compared by Bivand et al. (2013) https://doi.org/10.1111/gean.12008, and model fitting methods by Bivand and Piras (2015) https://doi.org/10.18637/jss.v063.i18; both of these articles include extensive lists of references. A recent review is provided by Bivand, Millo and Piras (2021) https://doi.org/10.3390/math9111276. **spatialreg** >= 1.1-1 corresponds to **spdep** = 1.1-1, in which the model fitting functions are deprecated and pass through to **spatialreg**, but will mask those in **spatialreg**. From versions 1.2-1, the functions have been made defunct in **spdep**. From version 1.3-6, add Anselin-Kelejian (1997) test to `stsls` for residual spatial autocorrelation https://doi.org/10.1177/016001769702000109. Default branch now `main`. diff --git a/_pkgdown.yml b/_pkgdown.yml new file mode 100644 index 0000000..d709461 --- /dev/null +++ b/_pkgdown.yml @@ -0,0 +1,3 @@ +template: + bootstrap: 5 +url: https://r-spatial.github.io/spatialreg/ diff --git a/docs/404.html b/docs/404.html index 62e0300..37246c9 100644 --- a/docs/404.html +++ b/docs/404.html @@ -4,118 +4,80 @@ - + Page not found (404) • spatialreg - - - - - - - + + + + + - - - -
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Page not found (404)

+
Content not found. Please use links in the navbar. -
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- -
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-

Developed by Roger Bivand, Gianfranco Piras.

+
+

Developed by Roger Bivand, Gianfranco Piras.

-
-

-

Site built with pkgdown 2.0.9.

+
+

Site built with pkgdown 2.1.1.

-
+
- - + diff --git a/docs/articles/SpatialFiltering.html b/docs/articles/SpatialFiltering.html index 07818e2..82009c5 100644 --- a/docs/articles/SpatialFiltering.html +++ b/docs/articles/SpatialFiltering.html @@ -4,100 +4,77 @@ - + Moran Eigenvectors • spatialreg - - - - - - - - + + + + + - - + + Skip to contents -
-
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-

Moran Eigenvectors

+ + +
+
+ +

Moran Eigenvectors

Roger Bivand

Source: vignettes/SpatialFiltering.Rmd - - +
SpatialFiltering.Rmd
-

Introduction 1 +

Introduction 1

The Moran eigenvector approach (Dray, Legendre, and Peres-Neto 2006; Griffith and Peres-Neto @@ -106,16 +83,23 @@

Introduction \(\mathbf{M W M}\), where

-

\[\mathbf{M} = \mathbf{I} - +𝐌𝐖𝐌\mathbf{M W M}, +where

+

$$\mathbf{M} = \mathbf{I} - \mathbf{X}(\mathbf{X}^{\rm T} -\mathbf{X})^{-1}\mathbf{X}^{\rm T}\] is a symmetric and -idempotent projection matrix and \(\mathbf{W}\) are the spatial weights. In -the spatial lag form of SpatialFiltering and -in the GLM ME form below, \(\mathbf{X}\) is an \(n\)-vector of ones, that is the intercept -only.

+\mathbf{X})^{-1}\mathbf{X}^{\rm T}$$ is a symmetric and +idempotent projection matrix and +𝐖\mathbf{W} +are the spatial weights. In the spatial lag form of +SpatialFiltering and in the GLM +ME form below, +𝐗\mathbf{X} +is an +nn-vector +of ones, that is the intercept only.

In its general form, SpatialFiltering -chooses the subset of the \(n\) +chooses the subset of the +nn eigenvectors that reduce the residual spatial autocorrelation in the error of the model with covariates. The lag form adds the covariates in assessment of which eigenvectors to choose, but does not use them in @@ -137,13 +121,13 @@

Introduction sf::st_crs(NY8) <- "EPSG:32618" NY8$Cases <- NY8$TRACTCAS }

-
## Reading layer `sf_bna2_utm18' from data source 
-##   `/home/rsb/lib/r_libs/spData/shapes/NY8_bna_utm18.gpkg' using driver `GPKG'
-## Simple feature collection with 281 features and 12 fields
-## Geometry type: MULTIPOLYGON
+
## Reading layer `NY8_utm18' from data source 
+##   `/home/rsb/lib/r_libs/spData/shapes/NY8_utm18.gpkg' using driver `GPKG'
+## Simple feature collection with 281 features and 17 fields
+## Geometry type: POLYGON
 ## Dimension:     XY
-## Bounding box:  xmin: 357628 ymin: 4649538 xmax: 480360.3 ymax: 4808317
-## Projected CRS: UTM Zone 18, Northern Hemisphere

+## Bounding box:  xmin: 358241.9 ymin: 4649755 xmax: 480393.1 ymax: 4808545
+## Projected CRS: WGS 84 / UTM zone 18N
 NY_nb <- read.gal(system.file("weights/NY_nb.gal", package="spData"), override.id=TRUE)
##   Eigenvector ZI pr(ZI)
 ## 0          NA NA   0.31
-## 1          24 NA   0.46
-## 2         164 NA   0.41
-## 3         113 NA   0.44
-## 4          60 NA   0.50
+## 1 24 NA 0.44 +## 2 223 NA 0.42 +## 3 206 NA 0.43 +## 4 169 NA 0.48 
 NY8$eigen_1 <- fitted(nyME)[,1]
 NY8$eigen_2 <- fitted(nyME)[,2]
@@ -239,23 +225,23 @@

Introduction ## glm(formula = Cases ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME + offset(log(POP8)) + ## fitted(nyME), family = "poisson", data = NY8) ## -## Coefficients: (1 not defined because of singularities) -## Estimate Std. Error z value Pr(>|z|) -## (Intercept) -8.123408 0.184525 -44.023 < 2e-16 *** -## PEXPOSURE 0.144595 0.031469 4.595 4.33e-06 *** -## PCTAGE65P 4.072265 0.607725 6.701 2.07e-11 *** -## PCTOWNHOME -0.392118 0.193313 -2.028 0.0425 * -## fitted(nyME)vec24 1.548573 0.725355 2.135 0.0328 * -## fitted(nyME)vec164 -0.166982 0.767258 -0.218 0.8277 -## fitted(nyME)vec113 NA NA NA NA -## fitted(nyME)vec60 -0.001836 0.769811 -0.002 0.9981 +## Coefficients: +## Estimate Std. Error z value Pr(>|z|) +## (Intercept) -8.13431 0.18388 -44.237 < 2e-16 *** +## PEXPOSURE 0.14136 0.03134 4.511 6.45e-06 *** +## PCTAGE65P 4.16875 0.60149 6.931 4.19e-12 *** +## PCTOWNHOME -0.39290 0.19222 -2.044 0.04096 * +## fitted(nyME)vec24 1.62658 0.72243 2.252 0.02435 * +## fitted(nyME)vec223 0.92941 0.70391 1.320 0.18671 +## fitted(nyME)vec206 -0.11559 0.68987 -0.168 0.86693 +## fitted(nyME)vec169 -1.82674 0.68142 -2.681 0.00735 ** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## (Dispersion parameter for poisson family taken to be 1) ## -## Null deviance: 428.84 on 280 degrees of freedom -## Residual deviance: 349.30 on 274 degrees of freedom +## Null deviance: 428.25 on 280 degrees of freedom +## Residual deviance: 340.08 on 273 degrees of freedom ## AIC: Inf ## ## Number of Fisher Scoring iterations: 5 @@ -267,25 +253,27 @@

Introduction ## Model 1: Cases ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME + offset(log(POP8)) ## Model 2: Cases ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME + offset(log(POP8)) + ## fitted(nyME) -## Resid. Df Resid. Dev Df Deviance Pr(>Chi) -## 1 277 354.0 -## 2 274 349.3 3 4.6969 0.1954 -

Figure \[fig:geigen2\] shows the -spatial patterns chosen to match the very small amount of spatial -autocorrelation remaining in the model. As with the other Poisson -regressions, the closeness to TCE sites is highly significant. Since, -however, many TCE sites are also in or close to more densely populated -urban areas with the possible presence of both point-source and -non-point-source pollution, it would be premature to take such results -simply at their face value. There is, however, a potentially useful -contrast between the cities of Binghamton in the south of the study area -with several sites in its vicinity, and Syracuse in the north without -TCE sites in this data set.

+## Resid. Df Resid. Dev Df Deviance Pr(>Chi) +## 1 277 353.35 +## 2 273 340.08 4 13.269 0.01003 * +## --- +## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 +

Figure fig:geigen2fig:geigen2 +shows the spatial patterns chosen to match the very small amount of +spatial autocorrelation remaining in the model. As with the other +Poisson regressions, the closeness to TCE sites is highly significant. +Since, however, many TCE sites are also in or close to more densely +populated urban areas with the possible presence of both point-source +and non-point-source pollution, it would be premature to take such +results simply at their face value. There is, however, a potentially +useful contrast between the cities of Binghamton in the south of the +study area with several sites in its vicinity, and Syracuse in the north +without TCE sites in this data set.

References

-
+
Dray, S., P. Legendre, and P. R. Peres-Neto. 2006. “Spatial Modeling: A Comprehensive Framework for Principle Coordinate Analysis of @@ -304,45 +292,27 @@

References -
-
    -

  1. This vignette formed pp. 302–305 of the first edition of -Bivand, R. S., Pebesma, E. and Gómez-Rubio V. (2008) Applied Spatial -Data Analysis with R, Springer-Verlag, New York. It was retired from the -second edition (2013) to accommodate material on other topics, and is -made available in this form with the understanding of the publishers.↩︎

    2. -
-

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- - +
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-

Developed by Roger Bivand, Gianfranco Piras.

+
+

Developed by Roger Bivand, Gianfranco Piras.

-
-

-

Site built with pkgdown 2.0.9.

+
+

Site built with pkgdown 2.1.1.

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- - + diff --git a/docs/articles/SpatialFiltering_files/figure-html/unnamed-chunk-6-1.png b/docs/articles/SpatialFiltering_files/figure-html/unnamed-chunk-6-1.png index a4a1129..ccf59c3 100644 Binary files a/docs/articles/SpatialFiltering_files/figure-html/unnamed-chunk-6-1.png and b/docs/articles/SpatialFiltering_files/figure-html/unnamed-chunk-6-1.png differ diff --git a/docs/articles/index.html b/docs/articles/index.html index c47f993..e879264 100644 --- a/docs/articles/index.html +++ b/docs/articles/index.html @@ -1,70 +1,45 @@ -Articles • spatialreg - - -
-
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+
  • Changelog
    • +
      • +
      • +
    + + +
    +
    +
    +
    +

    Articles

    All vignettes

    -

    +
    Spatial weights objects as sparse matrices and graphs
    @@ -73,24 +48,22 @@

    All vignettes

    Moran Eigenvectors
    -
    -
    +
    -
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    Developed by Roger Bivand, Gianfranco Piras.

    +
    +

    Developed by Roger Bivand, Gianfranco Piras.

    -
    -

    Site built with pkgdown 2.0.9.

    +
    +

    Site built with pkgdown 2.1.1.

    -
    +
    + - - diff --git a/docs/articles/nb_igraph.html b/docs/articles/nb_igraph.html index 72aa149..a6d43e0 100644 --- a/docs/articles/nb_igraph.html +++ b/docs/articles/nb_igraph.html @@ -4,95 +4,67 @@ - + Spatial weights objects as sparse matrices and graphs • spatialreg - - - - - - - - + + + + + - - + + Skip to contents -
    -
    -
    -
    -

    Spatial weights objects as sparse matrices and -graphs

    + +
    +
    + +

    Spatial weights objects as sparse matrices and graphs

    Roger Bivand

    Source: vignettes/nb_igraph.Rmd - - +
    nb_igraph.Rmd
    @@ -162,7 +134,7 @@ 

    ## Loading required package: spData
    ## Loading required package: Matrix
    ## Loading required package: sf
    -
    ## Linking to GEOS 3.12.2, GDAL 3.9.0, PROJ 9.4.1; sf_use_s2() is TRUE
    +
    ## Linking to GEOS 3.13.0, GDAL 3.10.0, PROJ 9.5.0; sf_use_s2() is TRUE

    Getting some data @@ -181,9 +153,9 @@

    Getting some datasf_extSoftVersion() }

    ##           GEOS           GDAL         proj.4 GDAL_with_GEOS     USE_PROJ_H 
-##       "3.12.2"        "3.9.0"        "9.4.1"         "true"         "true" 
+##       "3.13.0"       "3.10.0"        "9.5.0"         "true"         "true" 
 ##           PROJ 
-##        "9.4.1"
    +## "9.5.0" 
     library(sf)
 columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1])
    @@ -225,13 +197,16 @@
    +
    ## Warning in spdep::droplinks(nb_q, 21): some observations have no neighbours
    +
    ## Warning in spdep::droplinks(nb_q, 21): neighbour object has 3 sub-graphs
    +
    +nb_q[[21]]
    ## [1] 24 30 34
    -
    +
     col2[[21]]
    
 
    ## [1] 0
    
-
    +
     col2
    
 
    ## Neighbour list object:
 ## Number of regions: 49 
@@ -241,10 +216,10 @@ 
    
-
    +
     spdep::is.symmetric.nb(col2)
    
 
    ## [1] TRUE
    
-
    +
     coords <- st_coordinates(st_centroid(st_geometry(columbus)))
 plot(nb_q, coords, col="grey")
 plot(col2, coords, add=TRUE)
    
@@ -263,7 +238,7 @@ 
    Using sparse matrice
 neighbours with the zero.policy argument (default false).
 The matrix and graph representations of no-neighbour entities are not
 obvious.
    
-
    +
     nb_B <- spdep::nb2listw(col2, style="B", zero.policy=TRUE)
 nb_B$style
    
 
    ## [1] "B"
    
@@ -282,13 +257,13 @@ 
    Symmetric sparse matricesi-j and
 j-i weights. The coercion method does check
 whether symmetry is present before proceeding:
    
-
    +
     library(spatialreg)
 library(Matrix)
 B <- as(nb_B, "CsparseMatrix")
 all(B == t(B))
    
 
    ## [1] TRUE
    
-
    +
     str(B)
    
 
    ## Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
 ##   ..@ i       : int [1:230] 1 2 0 2 3 0 1 3 4 1 ...
@@ -299,7 +274,7 @@ 
    Symmetric sparse matrices##   .. ..$ : chr [1:49] "1" "2" "3" "4" ...
 ##   ..@ x       : num [1:230] 1 1 1 1 1 1 1 1 1 1 ...
 ##   ..@ factors : list()
    
-
    +
     rownames(B)[1:10]
    
 
    ##  [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10"
    
 
    Let us now try to retreive the list of neighbours from the symmetric
@@ -310,18 +285,22 @@ 
    Symmetric sparse matrices"dsTMatrix". The style is not retreived automatically, but
 is set to "M" to indicate conversion from a matrix. The
 neighbour links are retreived correctly, as are the IDs:
    
-
    +
     nb_B1 <- spdep::mat2listw(as(as(B, "TsparseMatrix"), "CsparseMatrix"),
     style="B", zero.policy=TRUE)
    
 
    ## Warning in sn2listw(df, style = style, zero.policy = zero.policy, from_mat2listw = TRUE): no-neighbour observations found, set zero.policy to TRUE;
 ## this warning will soon become an error
    
-
    +
    ## Warning in sn2listw(df, style = style, zero.policy = zero.policy,
+## from_mat2listw = TRUE): neighbour object has 3 sub-graphs
    
+
    ## Warning in spdep::mat2listw(as(as(B, "TsparseMatrix"), "CsparseMatrix"), :
+## neighbour object has 3 sub-graphs
    
+
     nb_B1$style
    
 
    ## [1] "B"
    
-
    +
     all.equal(nb_B1$neighbours, col2, check.attributes=FALSE)
    
 
    ## [1] TRUE
    
-
    +
     all.equal(attr(nb_B1$neighbours, "region.id"), attr(nb_B$neighbours, "region.id"))
    
 
    ## [1] TRUE
    
 
    
@@ -334,7 +313,7 @@ 
    Log deter
 the eigenvalue approach with for example spatialreg::eigenw
 is limited by the need to operate on dense matrices in memory to solve
 the eigenproblem:
    
-
    +
     rho <- 0.1
 do_spatialreg <- FALSE
 if (requireNamespace("spatialreg", quietly=TRUE)) do_spatialreg <- TRUE
@@ -342,29 +321,31 @@ 
    Log deter
 
    ## [1] -1.44787
    
 
    When n is large, this may become impractical and/or
 time-consuming, but does permit the rapid calculation of values of the
-log determinant for differing values of the spatial coefficient \(\rho\). The Matrix package
-provides many determinant methods, here for a
-"dsCMatrix" resulting from subtracting a
-"dsCMatrix", the product of a scalar and a
-"dsTMatrix", from a "ddiMatrix". The value of
-the log determinant follows, calling a sparse Cholesky decomposition
-internally for suitable input matrices.
    
-
    +log determinant for differing values of the spatial coefficient
+ρ\rho.
+The Matrix package provides many
+determinant methods, here for a "dsCMatrix"
+resulting from subtracting a "dsCMatrix", the product of a
+scalar and a "dsTMatrix", from a "ddiMatrix".
+The value of the log determinant follows, calling a sparse Cholesky
+decomposition internally for suitable input matrices.
    
+
     n <- nrow(B)
 I <- Diagonal(n)
 class(I - rho * B)
    
 
    ## [1] "dgCMatrix"
 ## attr(,"package")
 ## [1] "Matrix"
    
-
    +
     c(determinant(I - rho * B, logarithm=TRUE)$modulus)
    
 
    ## [1] -1.44787
    
 
    The computation of a sparse Cholesky decomposition for each value of
-the spatial coefficient \(\rho\) may be
-avoided by updating a pre-computed object; this approach provides fast
-and accurate log determinants for larger (but not very large) data
+the spatial coefficient
+ρ\rho
+may be avoided by updating a pre-computed object; this approach provides
+fast and accurate log determinants for larger (but not very large) data
 sets:
    
-
    +
     nW <- -B
 nChol <- Cholesky(nW, Imult=8)
 n * log(rho) + (2 * c(determinant(update(nChol, nW, 1/rho), sqrt=TRUE)$modulus))
    
@@ -376,7 +357,7 @@ 
    Asymmetric sparse matricesThe use of row-standardisation leads to asymmetry even if the
 underlying neighbours are symmetric, unless all entities have matching
 numbers of neighbours (for example a regular grid on a torus):
    
-
    +
     nb_W <- spdep::nb2listw(col2, style="W", zero.policy=TRUE)
 W <- as(nb_W, "CsparseMatrix")
 str(W)
    
@@ -389,7 +370,7 @@ 
    Asymmetric sparse matrices##   .. ..$ : chr [1:49] "1" "2" "3" "4" ...
 ##   ..@ x       : num [1:230] 0.333 0.25 0.5 0.25 0.25 ...
 ##   ..@ factors : list()
    
-
    +
     all(W == t(W))
    
 
    ## [1] FALSE
    
 
    The lag method for listw objects is often
@@ -398,17 +379,17 @@ 
    Asymmetric sparse matriceszero.policy to
 TRUE, the spatial lag of entity 21, which has no
 neighbours, is zero by construction:
    
-
    +
     set.seed(1)
 x <- runif(n)
 r1 <- as.numeric(W %*% x)
 r2 <- lag(nb_W, x, zero.policy=TRUE)
 all.equal(r1, r2, check.attributes=FALSE)
    
 
    ## [1] TRUE
    
-
    +
     plot(x, r1, ylim=c(0,1))
    
 
    
-
    +
     c(x[21], r1[21])
    
 
    ## [1] 0.9347052 0.0000000
    
 
    
@@ -422,20 +403,20 @@ 
    Log dete
 result may be a complex vector (here it is not, as discussed below). The
 appropriate determinant method for "dgCMatrix"
 objects uses an LU decomposition internally:
    
-
    +
     rho <- 0.5
 sum(log(1 - rho * eigenw(nb_W)))
    
 
    ## [1] -1.594376
    
-
    +
     class(I - rho * W)
    
 
    ## [1] "dgCMatrix"
 ## attr(,"package")
 ## [1] "Matrix"
    
-
    +
     c(determinant(I - rho * W, logarithm=TRUE)$modulus)
    
 
    ## [1] -1.594376
    
 
    We can show the internal workings of the method as:
    
-
    +
     LU <- lu(I - rho * W)
 sum(log(abs(diag(slot(LU, "U")))))
    
 
    ## [1] -1.594376
    
@@ -449,7 +430,7 @@ 
    Log determinants: symmetric by
 less costly numerical methods. The "W" style used the
 cardinalities of neighbour sets (row sums) to introduce row
 standardisation, and they are stored as an attribute:
    
-
    +
     d <- attr(nb_W$weights, "comp")$d
 all.equal(d, spdep::card(col2))
    
 
    ## [1] TRUE
    
@@ -457,24 +438,24 @@ 
    Log determinants: symmetric by
 (which must be symmetric), we can pre- and post-multiply by the square
 roots of the inverted neighbour counts, yielding a symmetric matrix with
 the appropriate properties:
    
-
    +
     dW <- Diagonal(n, d) %*% W
 all(dW == t(dW))
    
 
    ## [1] TRUE
    
-
    +
     isd <- Diagonal(n, 1/sqrt(d))
 isd[21,21]
    
 
    ## [1] Inf
    
-
    +
     Ws <- as(isd %*% dW %*% isd, "symmetricMatrix")
 rowSums(Ws)[21]
    
 
    ## [1] 0
    
-
    +
     class(Ws)
    
 
    ## [1] "dsCMatrix"
 ## attr(,"package")
 ## [1] "Matrix"
    
-
    +
     c(determinant(I - rho * Ws, logarithm=TRUE)$modulus)
    
 
    ## [1] -1.594376
    
 
    As can be seen, the division by the square root of zero for entity 21
@@ -495,19 +476,19 @@ 
    Using eigsn is somewhat larger, use may be made of the
 eigs function in RSpectra:
    
-
    +
     1/range(spatialreg::eigenw(nb_B))
    
 
    ## [1] -0.3212551  0.1638329
    
-
    +
     if (!require("RSpectra", quietly=TRUE)) dothis <- FALSE
    
-
    +
     1/c(eigs(B, k=1, which="SR")$values, eigs(B, k=1, which="LR")$values)
    
 
    ## [1] -0.3212551  0.1638329
    
 
    In this case, the results are trivial with small k.
    
-
    +
     1/range(eigenw(nb_W))
    
 
    ## [1] -1.544645  1.000000
    
-
    +
     1/Re(c(eigs(W, k=1, which="SR")$values, eigs(W, k=1, which="LR")$values))
    
 
    ## [1] -1.544645  1.000000
    
 
    Using row-standardisation has the nice feature of setting the upper
@@ -523,15 +504,15 @@ 
    Converting from sym
 
    
 
    First we’ll see how to get from sparse matrices to graphs. The mode
 of a symmetric matrix is "undirected" by definition:
    
-
    +
     class(B)
    
 
    ## [1] "dgCMatrix"
 ## attr(,"package")
 ## [1] "Matrix"
    
-
    +
 
    ## 10824 bytes
    
-
    +
     if (!require("igraph", quietly=FALSE)) dothis <- FALSE
    
 
    ## Loading required package: igraph
    
 
    ## 
@@ -542,22 +523,22 @@ 
    Converting from sym
 
    ## The following object is masked from 'package:base':
 ## 
 ##     union
    
-
    +
     g1 <- graph_from_adjacency_matrix(B, mode="undirected")
 class(g1)
    
 
    ## [1] "igraph"
    
-
    +
 
    ## 6544 bytes
    
 
    
 
    
 
    Converting from graph to symmetric adjacency matrix
 
    
-
    We can also convert this graph pack to the same matrix, but note that
-get.adjacency chooses a particular class of sparse matrix
-to be returned, so that the conversion process typically leads many
-matrices to fewer graph types, and back to fewer matrix types:
    
-
    +
    We can also convert this graph back to the same matrix, but note that
+as_adjacency_matrix chooses a particular class of sparse
+matrix to be returned, so that the conversion process typically leads
+many matrices to fewer graph types, and back to fewer matrix types:
    
+
     # Matrix 1.4-2 vulnerability work-around
 ow <- options("warn")$warn
 options("warn"=2L)
@@ -566,13 +547,13 @@ 
    Converting from gra
 
    ## [1] "dgCMatrix"
 ## attr(,"package")
 ## [1] "Matrix"
    
-
    +
     if (!inherits(B1, "try-error")) print(object.size(B1))
    
 
    ## 10824 bytes
    
-
    +
     if (!inherits(B1, "try-error")) print(all.equal(B, as(B1, "CsparseMatrix")))
    
 
    ## [1] TRUE
    
-
    +
     options("warn"=ow)
    
 
    
 
    
@@ -583,7 +564,7 @@ 
    Graph components in spdepn.comp.nb from the early days of the package. It is useful
 to know whether an nb object is divided up into separate
 subgraphs, and which entities are members of which such subgraph.
    
-
    +
     res <- spdep::n.comp.nb(col2)
 table(res$comp.id)
    
 
    ## 
@@ -595,18 +576,18 @@ 
    Graph components in igraph<
 
    
 
    The same result can be obtained using the clusters
 function in igraph:
    
-
    +
     c1 <- components(g1)
 c1$no == res$nc
    
 
    ## [1] TRUE
    
-
    +
     all.equal(c1$membership, res$comp.id)
    
 
    ## [1] "names for target but not for current"
    
-
    +
     all.equal(c1$csize, c(table(res$comp.id)), check.attributes=FALSE)
    
 
    ## [1] TRUE
    
 
    The same holds for the row-standardised variant:
    
-
    +
     W <- as(spdep::nb2listw(col2, style="W", zero.policy=TRUE), "CsparseMatrix")
 g1W <- graph_from_adjacency_matrix(W, mode="directed", weighted="W")
 c1W <- components(g1W)
@@ -625,14 +606,14 @@ 
    Shortest paths in weights mat
 above. The diameter measure is then the diameter of the largest
 component subgraph. Note that this generates an n x
 n matrix:
    
-
    +
 
    ## [1] FALSE
    
-
    +
     dg1 <- diameter(g1)
 dg1
    
 
    ## [1] 7
    
-
    +
     sp_mat <- distances(g1)
 str(sp_mat)
    
 
    ##  num [1:49, 1:49] 0 1 1 2 2 3 4 3 3 4 ...
@@ -648,9 +629,30 @@ 
    Shortest paths in weights matr
 in advance (the largest lag order for which the number of links is
 greater than zero), we run into the problem of how to represent missing
 neighbour information.
    
-
    -nbl10 <- spdep::nblag(col2, maxlag=10)
-vals <- sapply(nbl10, function(x) sum(spdep::card(x)))
+
    +nbl10 <- spdep::nblag(col2, maxlag=10)
    
+
    ## Warning in spdep::nblag(col2, maxlag = 10): lag 1 neighbour object has 3
+## sub-graphs
    
+
    ## Warning in spdep::nblag(col2, maxlag = 10): lag 2 neighbour object has 4
+## sub-graphs
    
+
    ## Warning in spdep::nblag(col2, maxlag = 10): lag 3 neighbour object has 8
+## sub-graphs
    
+
    ## Warning in spdep::nblag(col2, maxlag = 10): lag 4 neighbour object has 8
+## sub-graphs
    
+
    ## Warning in spdep::nblag(col2, maxlag = 10): lag 5 neighbour object has 14
+## sub-graphs
    
+
    ## Warning in spdep::nblag(col2, maxlag = 10): lag 6 neighbour object has 29
+## sub-graphs
    
+
    ## Warning in spdep::nblag(col2, maxlag = 10): lag 7 neighbour object has 43
+## sub-graphs
    
+
    ## Warning in spdep::nblag(col2, maxlag = 10): lag 8 neighbour object has 49
+## sub-graphs
    
+
    ## Warning in spdep::nblag(col2, maxlag = 10): lag 9 neighbour object has 49
+## sub-graphs
    
+
    ## Warning in spdep::nblag(col2, maxlag = 10): lag 10 neighbour object has 49
+## sub-graphs
    
+
    +vals <- sapply(nbl10, function(x) sum(spdep::card(x)))
 zero <- which(vals == 0)
 zero[1]-1
    
 
    ## [1] 7
    
@@ -660,7 +662,7 @@ 
    Shortest paths in weights matr
 produced by shortest.paths, we need to set all these
 non-structural zeros to infinity (the length of the path between
 unconnected nodes), and re-instate structural zeros on the diagonal:
    
-
    +
     lmat <- lapply(nbl10[1:(zero[1]-1)], spdep::nb2mat, style="B", zero.policy=TRUE)
 mat <- matrix(0, n, n)
 for (i in seq(along=lmat)) mat = mat + i*lmat[[i]]
@@ -694,23 +696,23 @@ 
    Smirnov/Anselin (2009) cyclical m
 this for each block/subgraph by testing the condition until it meets
 w[j,k] > 0, at which point it breaks. Smirnov and Anselin (2009)
 state that rook neighbours on a regular grid meet the condition:
    
-
    +
     nb_r <- spdep::cell2nb(7, 7, type="rook")
 nb_rW <- spdep::nb2listw(nb_r, style="W")
 spdep:::find_q1_q2(nb_rW)
    
 
    ## [1] 1 1
    
 
    One block/graph component is found, and this one meets the cyclical
 matrix condition, as also shown by the domain:
    
-
    +
 
    ## [1] -1  1
    
 
    This does not apply to the spatial weights we have been using above,
 with two non-singleton components, neither meeting the cyclical matrix
 condition:
    
-
    +
     spdep:::find_q1_q2(nb_W)
    
 
    ## [1] 2 0
    
-
    +
 
    ## [1] -1.544645  1.000000
    
 
    By construction, all two-node connected graph components also meet
@@ -718,35 +720,26 @@ 
    Smirnov/Anselin (2009) cyclical m
 so the minimum must be -1.
    
 
    
 
    
-  
    
-
-  
-
+  
 
    
 
 
 
-      
    
-  
    
-
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    
-
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
 
    
 
-  
 
 
-  
+
 
   
 
diff --git a/docs/articles/sids_models.html b/docs/articles/sids_models.html
index 6365375..73ad9e4 100644
--- a/docs/articles/sids_models.html
+++ b/docs/articles/sids_models.html
@@ -4,94 +4,67 @@
 
 
 
-
+
 North Carolina SIDS data set (models) • spatialreg
-
-
-
-
-
-
-
-
+
+
+
+
+
 
-
-    
+
+    Skip to contents
 
-    
    
-      
    
-  
    
-    
    
-      
    North Carolina SIDS data set (models)
    
+
+
+
    
+  
    
+
+      
    North Carolina SIDS data set (models)
    
                         
    Roger
 Bivand
    
             
       
       Source: vignettes/sids_models.Rmd
-      
-
+      
    sids_models.Rmd
    
     
    
 
     
@@ -121,13 +94,15 @@ 
    Getting the data into R
 
    We will be using the spdep and
 spatialreg packages, here version: spdep, version
-1.3-5, 2024-06-02, the sf package and the
+1.3-7.1, 2024-10-13, the sf package and the
 tmap package. The data from the sources referred to
 above is documented in the help
 page for the nc.sids data set in
 spData. The actual data, included in a shapefile of the
 county boundaries for North Carolina were made available in the
-maptools package 1. These data are known to be geographical
+maptools package 1. These data are known to be geographical
 coordinates (longitude-latitude in decimal degrees) and are assumed to
 use the NAD27 datum.
    
 
    @@ -143,7 +118,7 @@ 
    Getting the data into RspData (formerly in
 spdep), and add the neighbour relationships used in
 Cressie and Chan (1989) to the background map as
-a graph shown in Figure \(\ref{plot-CC89.nb}\):
    
+a graph shown in Figure :
    
 
     gal_file <- system.file("weights/ncCC89.gal", package="spData")[1]
 ncCC89 <- read.gal(gal_file, region.id=nc$FIPSNO)
    
@@ -197,7 +172,9 @@ 
    CAR model fittingCressie and
 Chan (1989), also given in
 Cressie (1991). We now try to replicate them
-for the null weighted CAR model (Cressie has intercept 2.838, \(\hat{\theta}\) 0.833, for k=1):
    
+for the null weighted CAR model (Cressie has intercept 2.838,
+θ̂\hat{\theta}
+0.833, for k=1):
    
 
    
 
     nc2$fitIV <- fitted.values(ecarIVaw)
-sf_use_s2(FALSE)
-tm_shape(nc2) + tm_fill("fitIV")
    
+if (tmap4) {
+  tm_shape(nc2) + tm_polygons(fill="fitIV", fill.scale=tm_scale(values="brewer.yl_or_br"), fill.legend=tm_legend(position=tm_pos_in("left", "bottom"), frame=FALSE, item.r = 0), lwd=0.01)
+} else {
+tm_shape(nc2) + tm_fill("fitIV")
+}
    
 
    
 
    The final figure shows the value of the log likelihood function for
 the null model (I):
    
@@ -306,7 +291,7 @@ 
    CAR model fitting
 
    References
 
    
-
    
+
    
 
    
 Cressie, N. 1991. Statistics for Spatial Data. New York: Wiley.
 
    
@@ -331,43 +316,27 @@ 
    References
-
    
-
      
-
    1. These data were taken with permission from a now-offline
-link: [sal.agecon.uiuc.edu/datasets/sids.zip]; see also GeoDa Center for
-a contemporary source.↩︎
      2. 
-
    
-
    
-  
    
-
-  
 
+  
 
    
 
 
 
-      
    
-  
    
-
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    
-
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
 
    
 
-  
 
 
-  
+
 
   
 
diff --git a/docs/authors.html b/docs/authors.html
index 9c22ae4..eb8025e 100644
--- a/docs/authors.html
+++ b/docs/authors.html
@@ -1,172 +1,149 @@
 
-Authors and Citation • spatialreg
-    
+Authors and Citation • spatialreg
+    Skip to contents
 
-    
    
-      
    
+
    
+
    
+  
    
+
+      
    Authors and Citation
    
+    
    
 
-      
    
-  
    
-    
    
-      
    
-        
    Authors and Citation
    
-      
    
+    
    
+      
    Authors
    
 
-      
       
    • 
           
      Roger Bivand. Maintainer, author. 
           
      
         
      • 
         
    • 
-          
      Gianfranco Piras. Author. 
+          
      Gianfranco Piras. Author.
           
      
         
      • 
         
    • 
-          
      Luc Anselin. Contributor. 
+          
      Luc Anselin. Contributor.
           
      
         
      • 
         
    • 
-          
      Andrew Bernat. Contributor. 
+          
      Andrew Bernat. Contributor.
           
      
         
      • 
         
    • 
-          
      Eric Blankmeyer. Contributor. 
+          
      Eric Blankmeyer. Contributor.
           
      
         
      • 
         
    • 
-          
      Yongwan Chun. Contributor. 
+          
      Yongwan Chun. Contributor.
           
      
         
      • 
         
    • 
-          
      Virgilio Gómez-Rubio. Contributor. 
+          
      Virgilio Gómez-Rubio. Contributor.
           
      
         
      • 
         
    • 
-          
      Daniel Griffith. Contributor. 
+          
      Daniel Griffith. Contributor.
           
      
         
      • 
         
    • 
-          
      Martin Gubri. Contributor. 
+          
      Martin Gubri. Contributor.
           
      
         
      • 
         
    • 
-          
      Rein Halbersma. Contributor. 
+          
      Rein Halbersma. Contributor.
           
      
         
      • 
         
    • 
-          
      James LeSage. Contributor. 
+          
      James LeSage. Contributor.
           
      
         
      • 
         
    • 
-          
      Angela Li. Contributor. 
+          
      Angela Li. Contributor.
           
      
         
      • 
         
    • 
-          
      Hongfei Li. Contributor. 
+          
      Hongfei Li. Contributor.
           
      
         
      • 
         
    • 
-          
      Jielai Ma. Contributor. 
+          
      Jielai Ma. Contributor.
           
      
         
      • 
         
    • 
-          
      Abhirup Mallik. Contributor, translator. 
+          
      Abhirup Mallik. Contributor, translator.
           
      
         
      • 
         
    • 
-          
      Giovanni Millo. Contributor. 
+          
      Giovanni Millo. Contributor.
           
      
         
      • 
         
    • 
-          
      Kelley Pace. Contributor. 
+          
      Kelley Pace. Contributor.
           
      
         
      • 
         
    • 
-          
      Pedro Peres-Neto. Contributor. 
+          
      Josiah Parry. Contributor. 
           
      
         
      • 
         
    • 
-          
      Tobias Rüttenauer. Contributor. 
+          
      Pedro Peres-Neto. Contributor.
           
      
         
      • 
         
    • 
-          
      Mauricio Sarrias. Contributor. 
+          
      Tobias Rüttenauer. Contributor.
           
      
         
      • 
         
    • 
-          
      JuanTomas Sayago. Contributor. 
+          
      Mauricio Sarrias. Contributor.
           
      
         
      • 
         
    • 
-          
      Michael Tiefelsdorf. Contributor. 
+          
      JuanTomas Sayago. Contributor.
+          
      
+        
      • 
+        
    • 
+          
      Michael Tiefelsdorf. Contributor.
           
      
         
      • 
       
    
-    
    
-    
    
-      
    Citation
    
-      Source: inst/CITATION
-    
    
-    
    
 
+    
    
+      
    Citation
    
+      
    Source: inst/CITATION
    
 
-    
    Bivand R, Millo G, Piras G (2021).
+      
    Bivand R, Millo G, Piras G (2021).
 “A Review of Software for Spatial Econometrics in R.”
 Mathematics, 9(11).
-doi:10.3390/math9111276, https://www.mdpi.com/2227-7390/9/11/1276. 
+doi:10.3390/math9111276, https://www.mdpi.com/2227-7390/9/11/1276.
 
    
-    
    @Article{,
+      
    @Article{,
   title = {A Review of Software for Spatial Econometrics in {R}},
   author = {Roger Bivand and Giovanni Millo and Gianfranco Piras},
   journal = {Mathematics},
@@ -176,12 +153,12 @@ 
    Citation
    
   url = {https://www.mdpi.com/2227-7390/9/11/1276},
   doi = {10.3390/math9111276},
 }
    
-    
    Bivand R, Piras G (2015).
+      
    Bivand R, Piras G (2015).
 “Comparing Implementations of Estimation Methods for Spatial Econometrics.”
 Journal of Statistical Software, 63(18), 1–36.
-doi:10.18637/jss.v063.i18. 
+doi:10.18637/jss.v063.i18.
 
    
-    
    @Article{,
+      
    @Article{,
   title = {Comparing Implementations of Estimation Methods for Spatial Econometrics},
   author = {Roger Bivand and Gianfranco Piras},
   journal = {Journal of Statistical Software},
@@ -191,12 +168,12 @@ 
    Citation
    
   pages = {1--36},
   doi = {10.18637/jss.v063.i18},
 }
    
-    
    Bivand R, Hauke J, Kossowski T (2013).
+      
    Bivand R, Hauke J, Kossowski T (2013).
 “Computing the Jacobian in Gaussian spatial autoregressive models: An illustrated comparison of available methods.”
 Geographical Analysis, 45(2), 150–179.
-doi:10.1111/gean.12008. 
+doi:10.1111/gean.12008.
 
    
-    
    @Article{,
+      
    @Article{,
   title = {Computing the Jacobian in Gaussian spatial autoregressive models: An illustrated comparison of available methods},
   author = {Roger Bivand and Jan Hauke and Tomasz Kossowski},
   journal = {Geographical Analysis},
@@ -206,51 +183,49 @@ 
    Citation
    
   pages = {150--179},
   doi = {10.1111/gean.12008},
 }
    
-    
    Bivand R, Pebesma E, Gómez-Rubio V (2013).
+      
    Bivand R, Pebesma E, Gómez-Rubio V (2013).
 Applied spatial data analysis with R, Second edition.
 Springer, NY.
-https://asdar-book.org/. 
+https://asdar-book.org/.
 
    
-    
    @Book{,
+      
    @Book{,
   author = {Roger S. Bivand and Edzer Pebesma and Virgilio Gómez-Rubio},
   title = {Applied spatial data analysis with {R}, Second edition},
   year = {2013},
   publisher = {Springer, NY},
   url = {https://asdar-book.org/},
 }
    
-    
    Pebesma E, Bivand R (2023).
+      
    Pebesma E, Bivand R (2023).
 Spatial Data Science With Applications in R.
 Chapman & Hall.
-https://r-spatial.org/book/. 
+https://r-spatial.org/book/.
 
    
-    
    @Book{,
+      
    @Book{,
   author = {Edzer Pebesma and Roger S. Bivand},
   title = {Spatial Data Science With Applications in {R}},
   year = {2023},
   publisher = {Chapman & Hall},
   url = {https://r-spatial.org/book/},
 }
    
+    
    
 
-  
    
-
-
    
-
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/deps/bootstrap-5.3.1/bootstrap.bundle.min.js b/docs/deps/bootstrap-5.3.1/bootstrap.bundle.min.js
new file mode 100644
index 0000000..e8f21f7
--- /dev/null
+++ b/docs/deps/bootstrap-5.3.1/bootstrap.bundle.min.js
@@ -0,0 +1,7 @@
+/*!
+  * Bootstrap v5.3.1 (https://getbootstrap.com/)
+  * Copyright 2011-2023 The Bootstrap Authors (https://github.com/twbs/bootstrap/graphs/contributors)
+  * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)
+  */
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s(t){i.add(t.name),[].concat(t.requires||[],t.requiresIfExists||[]).forEach((function(t){if(!i.has(t)){var n=e.get(t);n&&s(n)}})),n.push(t)}return t.forEach((function(t){e.set(t.name,t)})),t.forEach((function(t){i.has(t.name)||s(t)})),n}var fi={placement:"bottom",modifiers:[],strategy:"absolute"};function pi(){for(var t=arguments.length,e=new Array(t),i=0;iNumber.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"offset",options:{offset:this._getOffset()}}]};return(this._inNavbar||"static"===this._config.display)&&(F.setDataAttribute(this._menu,"popper","static"),t.modifiers=[{name:"applyStyles",enabled:!1}]),{...t,...g(this._config.popperConfig,[t])}}_selectMenuItem({key:t,target:e}){const i=z.find(".dropdown-menu 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e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Ei,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ii)?this:z.prev(this,Ii)[0]||z.next(this,Ii)[0]||z.findOne(Ii,t.delegateTarget.parentNode),o=qi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}N.on(document,Si,Ii,qi.dataApiKeydownHandler),N.on(document,Si,Pi,qi.dataApiKeydownHandler),N.on(document,Li,qi.clearMenus),N.on(document,Di,qi.clearMenus),N.on(document,Li,Ii,(function(t){t.preventDefault(),qi.getOrCreateInstance(this).toggle()})),m(qi);const Vi="backdrop",Ki="show",Qi=`mousedown.bs.${Vi}`,Xi={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},Yi={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class Ui extends H{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Xi}static get DefaultType(){return Yi}static get NAME(){return Vi}show(t){if(!this._config.isVisible)return void g(t);this._append();const e=this._getElement();this._config.isAnimated&&d(e),e.classList.add(Ki),this._emulateAnimation((()=>{g(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ki),this._emulateAnimation((()=>{this.dispose(),g(t)}))):g(t)}dispose(){this._isAppended&&(N.off(this._element,Qi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=r(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),N.on(t,Qi,(()=>{g(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){_(t,this._getElement(),this._config.isAnimated)}}const Gi=".bs.focustrap",Ji=`focusin${Gi}`,Zi=`keydown.tab${Gi}`,tn="backward",en={autofocus:!0,trapElement:null},nn={autofocus:"boolean",trapElement:"element"};class sn extends H{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return en}static get DefaultType(){return nn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),N.off(document,Gi),N.on(document,Ji,(t=>this._handleFocusin(t))),N.on(document,Zi,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,N.off(document,Gi))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=z.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===tn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?tn:"forward")}}const on=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",rn=".sticky-top",an="padding-right",ln="margin-right";class cn{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,an,(e=>e+t)),this._setElementAttributes(on,an,(e=>e+t)),this._setElementAttributes(rn,ln,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,an),this._resetElementAttributes(on,an),this._resetElementAttributes(rn,ln)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&F.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=F.getDataAttribute(t,e);null!==i?(F.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(o(t))e(t);else for(const i of z.find(t,this._element))e(i)}}const hn=".bs.modal",dn=`hide${hn}`,un=`hidePrevented${hn}`,fn=`hidden${hn}`,pn=`show${hn}`,mn=`shown${hn}`,gn=`resize${hn}`,_n=`click.dismiss${hn}`,bn=`mousedown.dismiss${hn}`,vn=`keydown.dismiss${hn}`,yn=`click${hn}.data-api`,wn="modal-open",An="show",En="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},Cn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class On extends W{constructor(t,e){super(t,e),this._dialog=z.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new cn,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return Cn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||N.trigger(this._element,pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(wn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(N.trigger(this._element,dn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(An),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){N.off(window,hn),N.off(this._dialog,hn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Ui({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=z.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),d(this._element),this._element.classList.add(An),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,N.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){N.on(this._element,vn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),N.on(window,gn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),N.on(this._element,bn,(t=>{N.one(this._element,_n,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(wn),this._resetAdjustments(),this._scrollBar.reset(),N.trigger(this._element,fn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(N.trigger(this._element,un).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(En)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(En),this._queueCallback((()=>{this._element.classList.remove(En),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=p()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=p()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const 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W{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return zn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||N.trigger(this._element,Nn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new cn).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Dn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(Sn),this._element.classList.remove(Dn),N.trigger(this._element,Pn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(N.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add($n),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(Sn,$n),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new cn).reset(),N.trigger(this._element,Fn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Ui({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():N.trigger(this._element,jn)}:null})}_initializeFocusTrap(){return new sn({trapElement:this._element})}_addEventListeners(){N.on(this._element,Bn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():N.trigger(this._element,jn))}))}static jQueryInterface(t){return this.each((function(){const e=qn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}N.on(document,Wn,'[data-bs-toggle="offcanvas"]',(function(t){const e=z.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this))return;N.one(e,Fn,(()=>{a(this)&&this.focus()}));const i=z.findOne(In);i&&i!==e&&qn.getInstance(i).hide(),qn.getOrCreateInstance(e).toggle(this)})),N.on(window,Ln,(()=>{for(const t of z.find(In))qn.getOrCreateInstance(t).show()})),N.on(window,Hn,(()=>{for(const t of z.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&qn.getOrCreateInstance(t).hide()})),R(qn),m(qn);const Vn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Kn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Qn=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Kn.has(i)||Boolean(Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Yn={allowList:Vn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"
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i=this._getTipElement();this._element.setAttribute("aria-describedby",i.getAttribute("id"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),N.trigger(this._element,this.constructor.eventName("inserted"))),this._popper=this._createPopper(i),i.classList.add(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.on(t,"mouseover",h);this._queueCallback((()=>{N.trigger(this._element,this.constructor.eventName("shown")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!N.trigger(this._element,this.constructor.eventName("hide")).defaultPrevented){if(this._getTipElement().classList.remove(es),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))N.off(t,"mouseover",h);this._activeTrigger.click=!1,this._activeTrigger[os]=!1,this._activeTrigger[ss]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute("aria-describedby"),N.trigger(this._element,this.constructor.eventName("hidden")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(ts,es),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return e.setAttribute("id",i),this._isAnimated()&&e.classList.add(ts),e}setContent(t){this._newContent=t,this._isShown()&&(this._disposePopper(),this.show())}_getTemplateFactory(t){return this._templateFactory?this._templateFactory.changeContent(t):this._templateFactory=new Jn({...this._config,content:t,extraClass:this._resolvePossibleFunction(this._config.customClass)}),this._templateFactory}_getContentForTemplate(){return{".tooltip-inner":this._getTitle()}}_getTitle(){return this._resolvePossibleFunction(this._config.title)||this._element.getAttribute("data-bs-original-title")}_initializeOnDelegatedTarget(t){return this.constructor.getOrCreateInstance(t.delegateTarget,this._getDelegateConfig())}_isAnimated(){return this._config.animation||this.tip&&this.tip.classList.contains(ts)}_isShown(){return this.tip&&this.tip.classList.contains(es)}_createPopper(t){const e=g(this._config.placement,[this,t,this._element]),i=rs[e.toUpperCase()];return 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if("manual"!==e){const t=e===ss?this.constructor.eventName("mouseenter"):this.constructor.eventName("focusin"),i=e===ss?this.constructor.eventName("mouseleave"):this.constructor.eventName("focusout");N.on(this._element,t,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusin"===t.type?os:ss]=!0,e._enter()})),N.on(this._element,i,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusout"===t.type?os:ss]=e._element.contains(t.relatedTarget),e._leave()}))}this._hideModalHandler=()=>{this._element&&this.hide()},N.on(this._element.closest(is),ns,this._hideModalHandler)}_fixTitle(){const t=this._element.getAttribute("title");t&&(this._element.getAttribute("aria-label")||this._element.textContent.trim()||this._element.setAttribute("aria-label",t),this._element.setAttribute("data-bs-original-title",t),this._element.removeAttribute("title"))}_enter(){this._isShown()||this._isHovered?this._isHovered=!0:(this._isHovered=!0,this._setTimeout((()=>{this._isHovered&&this.show()}),this._config.delay.show))}_leave(){this._isWithActiveTrigger()||(this._isHovered=!1,this._setTimeout((()=>{this._isHovered||this.hide()}),this._config.delay.hide))}_setTimeout(t,e){clearTimeout(this._timeout),this._timeout=setTimeout(t,e)}_isWithActiveTrigger(){return Object.values(this._activeTrigger).includes(!0)}_getConfig(t){const e=F.getDataAttributes(this._element);for(const t of Object.keys(e))Zn.has(t)&&delete e[t];return t={...e,..."object"==typeof t&&t?t:{}},t=this._mergeConfigObj(t),t=this._configAfterMerge(t),this._typeCheckConfig(t),t}_configAfterMerge(t){return t.container=!1===t.container?document.body:r(t.container),"number"==typeof t.delay&&(t.delay={show:t.delay,hide:t.delay}),"number"==typeof t.title&&(t.title=t.title.toString()),"number"==typeof t.content&&(t.content=t.content.toString()),t}_getDelegateConfig(){const t={};for(const[e,i]of Object.entries(this._config))this.constructor.Default[e]!==i&&(t[e]=i);return t.selector=!1,t.trigger="manual",t}_disposePopper(){this._popper&&(this._popper.destroy(),this._popper=null),this.tip&&(this.tip.remove(),this.tip=null)}static jQueryInterface(t){return this.each((function(){const e=cs.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}}m(cs);const hs={...cs.Default,content:"",offset:[0,8],placement:"right",template:'',trigger:"click"},ds={...cs.DefaultType,content:"(null|string|element|function)"};class us extends cs{static get Default(){return hs}static get DefaultType(){return ds}static get 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e=this._observableSections.get(t.target.hash);if(e){t.preventDefault();const i=this._rootElement||window,n=e.offsetTop-this._element.offsetTop;if(i.scrollTo)return void i.scrollTo({top:n,behavior:"smooth"});i.scrollTop=n}})))}_getNewObserver(){const t={root:this._rootElement,threshold:this._config.threshold,rootMargin:this._config.rootMargin};return new IntersectionObserver((t=>this._observerCallback(t)),t)}_observerCallback(t){const e=t=>this._targetLinks.get(`#${t.target.id}`),i=t=>{this._previousScrollData.visibleEntryTop=t.target.offsetTop,this._process(e(t))},n=(this._rootElement||document.documentElement).scrollTop,s=n>=this._previousScrollData.parentScrollTop;this._previousScrollData.parentScrollTop=n;for(const o of t){if(!o.isIntersecting){this._activeTarget=null,this._clearActiveClass(e(o));continue}const t=o.target.offsetTop>=this._previousScrollData.visibleEntryTop;if(s&&t){if(i(o),!n)return}else s||t||i(o)}}_initializeTargetsAndObservables(){this._targetLinks=new Map,this._observableSections=new Map;const t=z.find(bs,this._config.target);for(const e of t){if(!e.hash||l(e))continue;const t=z.findOne(decodeURI(e.hash),this._element);a(t)&&(this._targetLinks.set(decodeURI(e.hash),e),this._observableSections.set(e.hash,t))}}_process(t){this._activeTarget!==t&&(this._clearActiveClass(this._config.target),this._activeTarget=t,t.classList.add(_s),this._activateParents(t),N.trigger(this._element,ps,{relatedTarget:t}))}_activateParents(t){if(t.classList.contains("dropdown-item"))z.findOne(".dropdown-toggle",t.closest(".dropdown")).classList.add(_s);else for(const e of z.parents(t,".nav, .list-group"))for(const t of z.prev(e,ys))t.classList.add(_s)}_clearActiveClass(t){t.classList.remove(_s);const e=z.find(`${bs}.${_s}`,t);for(const t of e)t.classList.remove(_s)}static jQueryInterface(t){return this.each((function(){const e=Es.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t]()}}))}}N.on(window,gs,(()=>{for(const t of z.find('[data-bs-spy="scroll"]'))Es.getOrCreateInstance(t)})),m(Es);const Ts=".bs.tab",Cs=`hide${Ts}`,Os=`hidden${Ts}`,xs=`show${Ts}`,ks=`shown${Ts}`,Ls=`click${Ts}`,Ss=`keydown${Ts}`,Ds=`load${Ts}`,$s="ArrowLeft",Is="ArrowRight",Ns="ArrowUp",Ps="ArrowDown",Ms="Home",js="End",Fs="active",Hs="fade",Ws="show",Bs=":not(.dropdown-toggle)",zs='[data-bs-toggle="tab"], [data-bs-toggle="pill"], [data-bs-toggle="list"]',Rs=`.nav-link${Bs}, .list-group-item${Bs}, [role="tab"]${Bs}, ${zs}`,qs=`.${Fs}[data-bs-toggle="tab"], .${Fs}[data-bs-toggle="pill"], .${Fs}[data-bs-toggle="list"]`;class Vs extends W{constructor(t){super(t),this._parent=this._element.closest('.list-group, .nav, [role="tablist"]'),this._parent&&(this._setInitialAttributes(this._parent,this._getChildren()),N.on(this._element,Ss,(t=>this._keydown(t))))}static get NAME(){return"tab"}show(){const t=this._element;if(this._elemIsActive(t))return;const e=this._getActiveElem(),i=e?N.trigger(e,Cs,{relatedTarget:t}):null;N.trigger(t,xs,{relatedTarget:e}).defaultPrevented||i&&i.defaultPrevented||(this._deactivate(e,t),this._activate(t,e))}_activate(t,e){t&&(t.classList.add(Fs),this._activate(z.getElementFromSelector(t)),this._queueCallback((()=>{"tab"===t.getAttribute("role")?(t.removeAttribute("tabindex"),t.setAttribute("aria-selected",!0),this._toggleDropDown(t,!0),N.trigger(t,ks,{relatedTarget:e})):t.classList.add(Ws)}),t,t.classList.contains(Hs)))}_deactivate(t,e){t&&(t.classList.remove(Fs),t.blur(),this._deactivate(z.getElementFromSelector(t)),this._queueCallback((()=>{"tab"===t.getAttribute("role")?(t.setAttribute("aria-selected",!1),t.setAttribute("tabindex","-1"),this._toggleDropDown(t,!1),N.trigger(t,Os,{relatedTarget:e})):t.classList.remove(Ws)}),t,t.classList.contains(Hs)))}_keydown(t){if(![$s,Is,Ns,Ps,Ms,js].includes(t.key))return;t.stopPropagation(),t.preventDefault();const e=this._getChildren().filter((t=>!l(t)));let 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"${t}"`);e[t]()}}))}}N.on(document,Ls,zs,(function(t){["A","AREA"].includes(this.tagName)&&t.preventDefault(),l(this)||Vs.getOrCreateInstance(this).show()})),N.on(window,Ds,(()=>{for(const t of z.find(qs))Vs.getOrCreateInstance(t)})),m(Vs);const Ks=".bs.toast",Qs=`mouseover${Ks}`,Xs=`mouseout${Ks}`,Ys=`focusin${Ks}`,Us=`focusout${Ks}`,Gs=`hide${Ks}`,Js=`hidden${Ks}`,Zs=`show${Ks}`,to=`shown${Ks}`,eo="hide",io="show",no="showing",so={animation:"boolean",autohide:"boolean",delay:"number"},oo={animation:!0,autohide:!0,delay:5e3};class ro extends W{constructor(t,e){super(t,e),this._timeout=null,this._hasMouseInteraction=!1,this._hasKeyboardInteraction=!1,this._setListeners()}static get Default(){return oo}static get DefaultType(){return so}static get NAME(){return"toast"}show(){N.trigger(this._element,Zs).defaultPrevented||(this._clearTimeout(),this._config.animation&&this._element.classList.add("fade"),this._element.classList.remove(eo),d(this._element),this._element.classList.add(io,no),this._queueCallback((()=>{this._element.classList.remove(no),N.trigger(this._element,to),this._maybeScheduleHide()}),this._element,this._config.animation))}hide(){this.isShown()&&(N.trigger(this._element,Gs).defaultPrevented||(this._element.classList.add(no),this._queueCallback((()=>{this._element.classList.add(eo),this._element.classList.remove(no,io),N.trigger(this._element,Js)}),this._element,this._config.animation)))}dispose(){this._clearTimeout(),this.isShown()&&this._element.classList.remove(io),super.dispose()}isShown(){return this._element.classList.contains(io)}_maybeScheduleHide(){this._config.autohide&&(this._hasMouseInteraction||this._hasKeyboardInteraction||(this._timeout=setTimeout((()=>{this.hide()}),this._config.delay)))}_onInteraction(t,e){switch(t.type){case"mouseover":case"mouseout":this._hasMouseInteraction=e;break;case"focusin":case"focusout":this._hasKeyboardInteraction=e}if(e)return void this._clearTimeout();const i=t.relatedTarget;this._element===i||this._element.contains(i)||this._maybeScheduleHide()}_setListeners(){N.on(this._element,Qs,(t=>this._onInteraction(t,!0))),N.on(this._element,Xs,(t=>this._onInteraction(t,!1))),N.on(this._element,Ys,(t=>this._onInteraction(t,!0))),N.on(this._element,Us,(t=>this._onInteraction(t,!1)))}_clearTimeout(){clearTimeout(this._timeout),this._timeout=null}static jQueryInterface(t){return this.each((function(){const e=ro.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}return R(ro),m(ro),{Alert:Q,Button:Y,Carousel:xt,Collapse:Bt,Dropdown:qi,Modal:On,Offcanvas:qn,Popover:us,ScrollSpy:Es,Tab:Vs,Toast:ro,Tooltip:cs}}));
+//# sourceMappingURL=bootstrap.bundle.min.js.map
\ No newline at end of file
diff --git a/docs/deps/bootstrap-5.3.1/bootstrap.bundle.min.js.map b/docs/deps/bootstrap-5.3.1/bootstrap.bundle.min.js.map
new file mode 100644
index 0000000..3863da8
--- /dev/null
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Bound instance: ${Array.from(instanceMap.keys())[0]}.`)\n      return\n    }\n\n    instanceMap.set(key, instance)\n  },\n\n  get(element, key) {\n    if (elementMap.has(element)) {\n      return elementMap.get(element).get(key) || null\n    }\n\n    return null\n  },\n\n  remove(element, key) {\n    if (!elementMap.has(element)) {\n      return\n    }\n\n    const instanceMap = elementMap.get(element)\n\n    instanceMap.delete(key)\n\n    // free up element references if there are no instances left for an element\n    if (instanceMap.size === 0) {\n      elementMap.delete(element)\n    }\n  }\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/index.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nconst MAX_UID = 1_000_000\nconst MILLISECONDS_MULTIPLIER = 1000\nconst TRANSITION_END = 'transitionend'\n\n/**\n * Properly escape IDs selectors to handle weird IDs\n * @param {string} selector\n * @returns {string}\n */\nconst parseSelector = selector => {\n  if (selector && window.CSS && window.CSS.escape) {\n    // document.querySelector needs escaping to handle IDs (html5+) containing for instance /\n    selector = selector.replace(/#([^\\s\"#']+)/g, (match, id) => `#${CSS.escape(id)}`)\n  }\n\n  return selector\n}\n\n// Shout-out Angus Croll (https://goo.gl/pxwQGp)\nconst toType = object => {\n  if (object === null || object === undefined) {\n    return `${object}`\n  }\n\n  return Object.prototype.toString.call(object).match(/\\s([a-z]+)/i)[1].toLowerCase()\n}\n\n/**\n * Public Util API\n */\n\nconst getUID = prefix => {\n  do {\n    prefix += Math.floor(Math.random() * MAX_UID)\n  } while (document.getElementById(prefix))\n\n  return prefix\n}\n\nconst getTransitionDurationFromElement = element => {\n  if (!element) {\n    return 0\n  }\n\n  // Get transition-duration of the element\n  let { transitionDuration, transitionDelay } = window.getComputedStyle(element)\n\n  const floatTransitionDuration = Number.parseFloat(transitionDuration)\n  const floatTransitionDelay = Number.parseFloat(transitionDelay)\n\n  // Return 0 if element or transition duration is not found\n  if (!floatTransitionDuration && !floatTransitionDelay) {\n    return 0\n  }\n\n  // If multiple durations are defined, take the first\n  transitionDuration = transitionDuration.split(',')[0]\n  transitionDelay = transitionDelay.split(',')[0]\n\n  return (Number.parseFloat(transitionDuration) + Number.parseFloat(transitionDelay)) * MILLISECONDS_MULTIPLIER\n}\n\nconst triggerTransitionEnd = element => {\n  element.dispatchEvent(new Event(TRANSITION_END))\n}\n\nconst isElement = object => {\n  if (!object || typeof object !== 'object') {\n    return false\n  }\n\n  if (typeof object.jquery !== 'undefined') {\n    object = object[0]\n  }\n\n  return typeof object.nodeType !== 'undefined'\n}\n\nconst getElement = object => {\n  // it's a jQuery object or a node element\n  if (isElement(object)) {\n    return object.jquery ? object[0] : object\n  }\n\n  if (typeof object === 'string' && object.length > 0) {\n    return document.querySelector(parseSelector(object))\n  }\n\n  return null\n}\n\nconst isVisible = element => {\n  if (!isElement(element) || element.getClientRects().length === 0) {\n    return false\n  }\n\n  const elementIsVisible = getComputedStyle(element).getPropertyValue('visibility') === 'visible'\n  // Handle `details` element as its content may falsie appear visible when it is closed\n  const closedDetails = element.closest('details:not([open])')\n\n  if (!closedDetails) {\n    return elementIsVisible\n  }\n\n  if (closedDetails !== element) {\n    const summary = element.closest('summary')\n    if (summary && summary.parentNode !== closedDetails) {\n      return false\n    }\n\n    if (summary === null) {\n      return false\n    }\n  }\n\n  return elementIsVisible\n}\n\nconst isDisabled = element => {\n  if (!element || element.nodeType !== Node.ELEMENT_NODE) {\n    return true\n  }\n\n  if (element.classList.contains('disabled')) {\n    return true\n  }\n\n  if (typeof element.disabled !== 'undefined') {\n    return element.disabled\n  }\n\n  return element.hasAttribute('disabled') && element.getAttribute('disabled') !== 'false'\n}\n\nconst findShadowRoot = element => {\n  if (!document.documentElement.attachShadow) {\n    return null\n  }\n\n  // Can find the shadow root otherwise it'll return the document\n  if (typeof element.getRootNode === 'function') {\n    const root = element.getRootNode()\n    return root instanceof ShadowRoot ? root : null\n  }\n\n  if (element instanceof ShadowRoot) {\n    return element\n  }\n\n  // when we don't find a shadow root\n  if (!element.parentNode) {\n    return null\n  }\n\n  return findShadowRoot(element.parentNode)\n}\n\nconst noop = () => {}\n\n/**\n * Trick to restart an element's animation\n *\n * @param {HTMLElement} element\n * @return void\n *\n * @see https://www.charistheo.io/blog/2021/02/restart-a-css-animation-with-javascript/#restarting-a-css-animation\n */\nconst reflow = element => {\n  element.offsetHeight // eslint-disable-line no-unused-expressions\n}\n\nconst getjQuery = () => {\n  if (window.jQuery && !document.body.hasAttribute('data-bs-no-jquery')) {\n    return window.jQuery\n  }\n\n  return null\n}\n\nconst DOMContentLoadedCallbacks = []\n\nconst onDOMContentLoaded = callback => {\n  if (document.readyState === 'loading') {\n    // add listener on the first call when the document is in loading state\n    if (!DOMContentLoadedCallbacks.length) {\n      document.addEventListener('DOMContentLoaded', () => {\n        for (const callback of DOMContentLoadedCallbacks) {\n          callback()\n        }\n      })\n    }\n\n    DOMContentLoadedCallbacks.push(callback)\n  } else {\n    callback()\n  }\n}\n\nconst isRTL = () => document.documentElement.dir === 'rtl'\n\nconst defineJQueryPlugin = plugin => {\n  onDOMContentLoaded(() => {\n    const $ = getjQuery()\n    /* istanbul ignore if */\n    if ($) {\n      const name = plugin.NAME\n      const JQUERY_NO_CONFLICT = $.fn[name]\n      $.fn[name] = plugin.jQueryInterface\n      $.fn[name].Constructor = plugin\n      $.fn[name].noConflict = () => {\n        $.fn[name] = JQUERY_NO_CONFLICT\n        return plugin.jQueryInterface\n      }\n    }\n  })\n}\n\nconst execute = (possibleCallback, args = [], defaultValue = possibleCallback) => {\n  return typeof possibleCallback === 'function' ? possibleCallback(...args) : defaultValue\n}\n\nconst executeAfterTransition = (callback, transitionElement, waitForTransition = true) => {\n  if (!waitForTransition) {\n    execute(callback)\n    return\n  }\n\n  const durationPadding = 5\n  const emulatedDuration = getTransitionDurationFromElement(transitionElement) + durationPadding\n\n  let called = false\n\n  const handler = ({ target }) => {\n    if (target !== transitionElement) {\n      return\n    }\n\n    called = true\n    transitionElement.removeEventListener(TRANSITION_END, handler)\n    execute(callback)\n  }\n\n  transitionElement.addEventListener(TRANSITION_END, handler)\n  setTimeout(() => {\n    if (!called) {\n      triggerTransitionEnd(transitionElement)\n    }\n  }, emulatedDuration)\n}\n\n/**\n * Return the previous/next element of a list.\n *\n * @param {array} list    The list of elements\n * @param activeElement   The active element\n * @param shouldGetNext   Choose to get next or previous element\n * @param isCycleAllowed\n * @return {Element|elem} The proper element\n */\nconst getNextActiveElement = (list, activeElement, shouldGetNext, isCycleAllowed) => {\n  const listLength = list.length\n  let index = list.indexOf(activeElement)\n\n  // if the element does not exist in the list return an element\n  // depending on the direction and if cycle is allowed\n  if (index === -1) {\n    return !shouldGetNext && isCycleAllowed ? list[listLength - 1] : list[0]\n  }\n\n  index += shouldGetNext ? 1 : -1\n\n  if (isCycleAllowed) {\n    index = (index + listLength) % listLength\n  }\n\n  return list[Math.max(0, Math.min(index, listLength - 1))]\n}\n\nexport {\n  defineJQueryPlugin,\n  execute,\n  executeAfterTransition,\n  findShadowRoot,\n  getElement,\n  getjQuery,\n  getNextActiveElement,\n  getTransitionDurationFromElement,\n  getUID,\n  isDisabled,\n  isElement,\n  isRTL,\n  isVisible,\n  noop,\n  onDOMContentLoaded,\n  parseSelector,\n  reflow,\n  triggerTransitionEnd,\n  toType\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/event-handler.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport { getjQuery } from '../util/index.js'\n\n/**\n * Constants\n */\n\nconst namespaceRegex = /[^.]*(?=\\..*)\\.|.*/\nconst stripNameRegex = /\\..*/\nconst stripUidRegex = /::\\d+$/\nconst eventRegistry = {} // Events storage\nlet uidEvent = 1\nconst customEvents = {\n  mouseenter: 'mouseover',\n  mouseleave: 'mouseout'\n}\n\nconst nativeEvents = new Set([\n  'click',\n  'dblclick',\n  'mouseup',\n  'mousedown',\n  'contextmenu',\n  'mousewheel',\n  'DOMMouseScroll',\n  'mouseover',\n  'mouseout',\n  'mousemove',\n  'selectstart',\n  'selectend',\n  'keydown',\n  'keypress',\n  'keyup',\n  'orientationchange',\n  'touchstart',\n  'touchmove',\n  'touchend',\n  'touchcancel',\n  'pointerdown',\n  'pointermove',\n  'pointerup',\n  'pointerleave',\n  'pointercancel',\n  'gesturestart',\n  'gesturechange',\n  'gestureend',\n  'focus',\n  'blur',\n  'change',\n  'reset',\n  'select',\n  'submit',\n  'focusin',\n  'focusout',\n  'load',\n  'unload',\n  'beforeunload',\n  'resize',\n  'move',\n  'DOMContentLoaded',\n  'readystatechange',\n  'error',\n  'abort',\n  'scroll'\n])\n\n/**\n * Private methods\n */\n\nfunction makeEventUid(element, uid) {\n  return (uid && `${uid}::${uidEvent++}`) || element.uidEvent || uidEvent++\n}\n\nfunction getElementEvents(element) {\n  const uid = makeEventUid(element)\n\n  element.uidEvent = uid\n  eventRegistry[uid] = eventRegistry[uid] || {}\n\n  return eventRegistry[uid]\n}\n\nfunction bootstrapHandler(element, fn) {\n  return function handler(event) {\n    hydrateObj(event, { delegateTarget: element })\n\n    if (handler.oneOff) {\n      EventHandler.off(element, event.type, fn)\n    }\n\n    return fn.apply(element, [event])\n  }\n}\n\nfunction bootstrapDelegationHandler(element, selector, fn) {\n  return function handler(event) {\n    const domElements = element.querySelectorAll(selector)\n\n    for (let { target } = event; target && target !== this; target = target.parentNode) {\n      for (const domElement of domElements) {\n        if (domElement !== target) {\n          continue\n        }\n\n        hydrateObj(event, { delegateTarget: target })\n\n        if (handler.oneOff) {\n          EventHandler.off(element, event.type, selector, fn)\n        }\n\n        return fn.apply(target, [event])\n      }\n    }\n  }\n}\n\nfunction findHandler(events, callable, delegationSelector = null) {\n  return Object.values(events)\n    .find(event => event.callable === callable && event.delegationSelector === delegationSelector)\n}\n\nfunction normalizeParameters(originalTypeEvent, handler, delegationFunction) {\n  const isDelegated = typeof handler === 'string'\n  // TODO: tooltip passes `false` instead of selector, so we need to check\n  const callable = isDelegated ? delegationFunction : (handler || delegationFunction)\n  let typeEvent = getTypeEvent(originalTypeEvent)\n\n  if (!nativeEvents.has(typeEvent)) {\n    typeEvent = originalTypeEvent\n  }\n\n  return [isDelegated, callable, typeEvent]\n}\n\nfunction addHandler(element, originalTypeEvent, handler, delegationFunction, oneOff) {\n  if (typeof originalTypeEvent !== 'string' || !element) {\n    return\n  }\n\n  let [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction)\n\n  // in case of mouseenter or mouseleave wrap the handler within a function that checks for its DOM position\n  // this prevents the handler from being dispatched the same way as mouseover or mouseout does\n  if (originalTypeEvent in customEvents) {\n    const wrapFunction = fn => {\n      return function (event) {\n        if (!event.relatedTarget || (event.relatedTarget !== event.delegateTarget && !event.delegateTarget.contains(event.relatedTarget))) {\n          return fn.call(this, event)\n        }\n      }\n    }\n\n    callable = wrapFunction(callable)\n  }\n\n  const events = getElementEvents(element)\n  const handlers = events[typeEvent] || (events[typeEvent] = {})\n  const previousFunction = findHandler(handlers, callable, isDelegated ? handler : null)\n\n  if (previousFunction) {\n    previousFunction.oneOff = previousFunction.oneOff && oneOff\n\n    return\n  }\n\n  const uid = makeEventUid(callable, originalTypeEvent.replace(namespaceRegex, ''))\n  const fn = isDelegated ?\n    bootstrapDelegationHandler(element, handler, callable) :\n    bootstrapHandler(element, callable)\n\n  fn.delegationSelector = isDelegated ? handler : null\n  fn.callable = callable\n  fn.oneOff = oneOff\n  fn.uidEvent = uid\n  handlers[uid] = fn\n\n  element.addEventListener(typeEvent, fn, isDelegated)\n}\n\nfunction removeHandler(element, events, typeEvent, handler, delegationSelector) {\n  const fn = findHandler(events[typeEvent], handler, delegationSelector)\n\n  if (!fn) {\n    return\n  }\n\n  element.removeEventListener(typeEvent, fn, Boolean(delegationSelector))\n  delete events[typeEvent][fn.uidEvent]\n}\n\nfunction removeNamespacedHandlers(element, events, typeEvent, namespace) {\n  const storeElementEvent = events[typeEvent] || {}\n\n  for (const [handlerKey, event] of Object.entries(storeElementEvent)) {\n    if (handlerKey.includes(namespace)) {\n      removeHandler(element, events, typeEvent, event.callable, event.delegationSelector)\n    }\n  }\n}\n\nfunction getTypeEvent(event) {\n  // allow to get the native events from namespaced events ('click.bs.button' --> 'click')\n  event = event.replace(stripNameRegex, '')\n  return customEvents[event] || event\n}\n\nconst EventHandler = {\n  on(element, event, handler, delegationFunction) {\n    addHandler(element, event, handler, delegationFunction, false)\n  },\n\n  one(element, event, handler, delegationFunction) {\n    addHandler(element, event, handler, delegationFunction, true)\n  },\n\n  off(element, originalTypeEvent, handler, delegationFunction) {\n    if (typeof originalTypeEvent !== 'string' || !element) {\n      return\n    }\n\n    const [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction)\n    const inNamespace = typeEvent !== originalTypeEvent\n    const events = getElementEvents(element)\n    const storeElementEvent = events[typeEvent] || {}\n    const isNamespace = originalTypeEvent.startsWith('.')\n\n    if (typeof callable !== 'undefined') {\n      // Simplest case: handler is passed, remove that listener ONLY.\n      if (!Object.keys(storeElementEvent).length) {\n        return\n      }\n\n      removeHandler(element, events, typeEvent, callable, isDelegated ? handler : null)\n      return\n    }\n\n    if (isNamespace) {\n      for (const elementEvent of Object.keys(events)) {\n        removeNamespacedHandlers(element, events, elementEvent, originalTypeEvent.slice(1))\n      }\n    }\n\n    for (const [keyHandlers, event] of Object.entries(storeElementEvent)) {\n      const handlerKey = keyHandlers.replace(stripUidRegex, '')\n\n      if (!inNamespace || originalTypeEvent.includes(handlerKey)) {\n        removeHandler(element, events, typeEvent, event.callable, event.delegationSelector)\n      }\n    }\n  },\n\n  trigger(element, event, args) {\n    if (typeof event !== 'string' || !element) {\n      return null\n    }\n\n    const $ = getjQuery()\n    const typeEvent = getTypeEvent(event)\n    const inNamespace = event !== typeEvent\n\n    let jQueryEvent = null\n    let bubbles = true\n    let nativeDispatch = true\n    let defaultPrevented = false\n\n    if (inNamespace && $) {\n      jQueryEvent = $.Event(event, args)\n\n      $(element).trigger(jQueryEvent)\n      bubbles = !jQueryEvent.isPropagationStopped()\n      nativeDispatch = !jQueryEvent.isImmediatePropagationStopped()\n      defaultPrevented = jQueryEvent.isDefaultPrevented()\n    }\n\n    const evt = hydrateObj(new Event(event, { bubbles, cancelable: true }), args)\n\n    if (defaultPrevented) {\n      evt.preventDefault()\n    }\n\n    if (nativeDispatch) {\n      element.dispatchEvent(evt)\n    }\n\n    if (evt.defaultPrevented && jQueryEvent) {\n      jQueryEvent.preventDefault()\n    }\n\n    return evt\n  }\n}\n\nfunction hydrateObj(obj, meta = {}) {\n  for (const [key, value] of Object.entries(meta)) {\n    try {\n      obj[key] = value\n    } catch {\n      Object.defineProperty(obj, key, {\n        configurable: true,\n        get() {\n          return value\n        }\n      })\n    }\n  }\n\n  return obj\n}\n\nexport default EventHandler\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/manipulator.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nfunction normalizeData(value) {\n  if (value === 'true') {\n    return true\n  }\n\n  if (value === 'false') {\n    return false\n  }\n\n  if (value === Number(value).toString()) {\n    return Number(value)\n  }\n\n  if (value === '' || value === 'null') {\n    return null\n  }\n\n  if (typeof value !== 'string') {\n    return value\n  }\n\n  try {\n    return JSON.parse(decodeURIComponent(value))\n  } catch {\n    return value\n  }\n}\n\nfunction normalizeDataKey(key) {\n  return key.replace(/[A-Z]/g, chr => `-${chr.toLowerCase()}`)\n}\n\nconst Manipulator = {\n  setDataAttribute(element, key, value) {\n    element.setAttribute(`data-bs-${normalizeDataKey(key)}`, value)\n  },\n\n  removeDataAttribute(element, key) {\n    element.removeAttribute(`data-bs-${normalizeDataKey(key)}`)\n  },\n\n  getDataAttributes(element) {\n    if (!element) {\n      return {}\n    }\n\n    const attributes = {}\n    const bsKeys = Object.keys(element.dataset).filter(key => key.startsWith('bs') && !key.startsWith('bsConfig'))\n\n    for (const key of bsKeys) {\n      let pureKey = key.replace(/^bs/, '')\n      pureKey = pureKey.charAt(0).toLowerCase() + pureKey.slice(1, pureKey.length)\n      attributes[pureKey] = normalizeData(element.dataset[key])\n    }\n\n    return attributes\n  },\n\n  getDataAttribute(element, key) {\n    return normalizeData(element.getAttribute(`data-bs-${normalizeDataKey(key)}`))\n  }\n}\n\nexport default Manipulator\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/config.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Manipulator from '../dom/manipulator.js'\nimport { isElement, toType } from './index.js'\n\n/**\n * Class definition\n */\n\nclass Config {\n  // Getters\n  static get Default() {\n    return {}\n  }\n\n  static get DefaultType() {\n    return {}\n  }\n\n  static get NAME() {\n    throw new Error('You have to implement the static method \"NAME\", for each component!')\n  }\n\n  _getConfig(config) {\n    config = this._mergeConfigObj(config)\n    config = this._configAfterMerge(config)\n    this._typeCheckConfig(config)\n    return config\n  }\n\n  _configAfterMerge(config) {\n    return config\n  }\n\n  _mergeConfigObj(config, element) {\n    const jsonConfig = isElement(element) ? Manipulator.getDataAttribute(element, 'config') : {} // try to parse\n\n    return {\n      ...this.constructor.Default,\n      ...(typeof jsonConfig === 'object' ? jsonConfig : {}),\n      ...(isElement(element) ? Manipulator.getDataAttributes(element) : {}),\n      ...(typeof config === 'object' ? config : {})\n    }\n  }\n\n  _typeCheckConfig(config, configTypes = this.constructor.DefaultType) {\n    for (const [property, expectedTypes] of Object.entries(configTypes)) {\n      const value = config[property]\n      const valueType = isElement(value) ? 'element' : toType(value)\n\n      if (!new RegExp(expectedTypes).test(valueType)) {\n        throw new TypeError(\n          `${this.constructor.NAME.toUpperCase()}: Option \"${property}\" provided type \"${valueType}\" but expected type \"${expectedTypes}\".`\n        )\n      }\n    }\n  }\n}\n\nexport default Config\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap base-component.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Data from './dom/data.js'\nimport EventHandler from './dom/event-handler.js'\nimport Config from './util/config.js'\nimport { executeAfterTransition, getElement } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst VERSION = '5.3.1'\n\n/**\n * Class definition\n */\n\nclass BaseComponent extends Config {\n  constructor(element, config) {\n    super()\n\n    element = getElement(element)\n    if (!element) {\n      return\n    }\n\n    this._element = element\n    this._config = this._getConfig(config)\n\n    Data.set(this._element, this.constructor.DATA_KEY, this)\n  }\n\n  // Public\n  dispose() {\n    Data.remove(this._element, this.constructor.DATA_KEY)\n    EventHandler.off(this._element, this.constructor.EVENT_KEY)\n\n    for (const propertyName of Object.getOwnPropertyNames(this)) {\n      this[propertyName] = null\n    }\n  }\n\n  _queueCallback(callback, element, isAnimated = true) {\n    executeAfterTransition(callback, element, isAnimated)\n  }\n\n  _getConfig(config) {\n    config = this._mergeConfigObj(config, this._element)\n    config = this._configAfterMerge(config)\n    this._typeCheckConfig(config)\n    return config\n  }\n\n  // Static\n  static getInstance(element) {\n    return Data.get(getElement(element), this.DATA_KEY)\n  }\n\n  static getOrCreateInstance(element, config = {}) {\n    return this.getInstance(element) || new this(element, typeof config === 'object' ? config : null)\n  }\n\n  static get VERSION() {\n    return VERSION\n  }\n\n  static get DATA_KEY() {\n    return `bs.${this.NAME}`\n  }\n\n  static get EVENT_KEY() {\n    return `.${this.DATA_KEY}`\n  }\n\n  static eventName(name) {\n    return `${name}${this.EVENT_KEY}`\n  }\n}\n\nexport default BaseComponent\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/selector-engine.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport { isDisabled, isVisible, parseSelector } from '../util/index.js'\n\nconst getSelector = element => {\n  let selector = element.getAttribute('data-bs-target')\n\n  if (!selector || selector === '#') {\n    let hrefAttribute = element.getAttribute('href')\n\n    // The only valid content that could double as a selector are IDs or classes,\n    // so everything starting with `#` or `.`. If a \"real\" URL is used as the selector,\n    // `document.querySelector` will rightfully complain it is invalid.\n    // See https://github.com/twbs/bootstrap/issues/32273\n    if (!hrefAttribute || (!hrefAttribute.includes('#') && !hrefAttribute.startsWith('.'))) {\n      return null\n    }\n\n    // Just in case some CMS puts out a full URL with the anchor appended\n    if (hrefAttribute.includes('#') && !hrefAttribute.startsWith('#')) {\n      hrefAttribute = `#${hrefAttribute.split('#')[1]}`\n    }\n\n    selector = hrefAttribute && hrefAttribute !== '#' ? hrefAttribute.trim() : null\n  }\n\n  return parseSelector(selector)\n}\n\nconst SelectorEngine = {\n  find(selector, element = document.documentElement) {\n    return [].concat(...Element.prototype.querySelectorAll.call(element, selector))\n  },\n\n  findOne(selector, element = document.documentElement) {\n    return Element.prototype.querySelector.call(element, selector)\n  },\n\n  children(element, selector) {\n    return [].concat(...element.children).filter(child => child.matches(selector))\n  },\n\n  parents(element, selector) {\n    const parents = []\n    let ancestor = element.parentNode.closest(selector)\n\n    while (ancestor) {\n      parents.push(ancestor)\n      ancestor = ancestor.parentNode.closest(selector)\n    }\n\n    return parents\n  },\n\n  prev(element, selector) {\n    let previous = element.previousElementSibling\n\n    while (previous) {\n      if (previous.matches(selector)) {\n        return [previous]\n      }\n\n      previous = previous.previousElementSibling\n    }\n\n    return []\n  },\n  // TODO: this is now unused; remove later along with prev()\n  next(element, selector) {\n    let next = element.nextElementSibling\n\n    while (next) {\n      if (next.matches(selector)) {\n        return [next]\n      }\n\n      next = next.nextElementSibling\n    }\n\n    return []\n  },\n\n  focusableChildren(element) {\n    const focusables = [\n      'a',\n      'button',\n      'input',\n      'textarea',\n      'select',\n      'details',\n      '[tabindex]',\n      '[contenteditable=\"true\"]'\n    ].map(selector => `${selector}:not([tabindex^=\"-\"])`).join(',')\n\n    return this.find(focusables, element).filter(el => !isDisabled(el) && isVisible(el))\n  },\n\n  getSelectorFromElement(element) {\n    const selector = getSelector(element)\n\n    if (selector) {\n      return SelectorEngine.findOne(selector) ? selector : null\n    }\n\n    return null\n  },\n\n  getElementFromSelector(element) {\n    const selector = getSelector(element)\n\n    return selector ? SelectorEngine.findOne(selector) : null\n  },\n\n  getMultipleElementsFromSelector(element) {\n    const selector = getSelector(element)\n\n    return selector ? SelectorEngine.find(selector) : []\n  }\n}\n\nexport default SelectorEngine\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/component-functions.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport { isDisabled } from './index.js'\n\nconst enableDismissTrigger = (component, method = 'hide') => {\n  const clickEvent = `click.dismiss${component.EVENT_KEY}`\n  const name = component.NAME\n\n  EventHandler.on(document, clickEvent, `[data-bs-dismiss=\"${name}\"]`, function (event) {\n    if (['A', 'AREA'].includes(this.tagName)) {\n      event.preventDefault()\n    }\n\n    if (isDisabled(this)) {\n      return\n    }\n\n    const target = SelectorEngine.getElementFromSelector(this) || this.closest(`.${name}`)\n    const instance = component.getOrCreateInstance(target)\n\n    // Method argument is left, for Alert and only, as it doesn't implement the 'hide' method\n    instance[method]()\n  })\n}\n\nexport {\n  enableDismissTrigger\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap alert.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'alert'\nconst DATA_KEY = 'bs.alert'\nconst EVENT_KEY = `.${DATA_KEY}`\n\nconst EVENT_CLOSE = `close${EVENT_KEY}`\nconst EVENT_CLOSED = `closed${EVENT_KEY}`\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\n\n/**\n * Class definition\n */\n\nclass Alert extends BaseComponent {\n  // Getters\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  close() {\n    const closeEvent = EventHandler.trigger(this._element, EVENT_CLOSE)\n\n    if (closeEvent.defaultPrevented) {\n      return\n    }\n\n    this._element.classList.remove(CLASS_NAME_SHOW)\n\n    const isAnimated = this._element.classList.contains(CLASS_NAME_FADE)\n    this._queueCallback(() => this._destroyElement(), this._element, isAnimated)\n  }\n\n  // Private\n  _destroyElement() {\n    this._element.remove()\n    EventHandler.trigger(this._element, EVENT_CLOSED)\n    this.dispose()\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Alert.getOrCreateInstance(this)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config](this)\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nenableDismissTrigger(Alert, 'close')\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Alert)\n\nexport default Alert\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap button.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'button'\nconst DATA_KEY = 'bs.button'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst CLASS_NAME_ACTIVE = 'active'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"button\"]'\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\n/**\n * Class definition\n */\n\nclass Button extends BaseComponent {\n  // Getters\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle() {\n    // Toggle class and sync the `aria-pressed` attribute with the return value of the `.toggle()` method\n    this._element.setAttribute('aria-pressed', this._element.classList.toggle(CLASS_NAME_ACTIVE))\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Button.getOrCreateInstance(this)\n\n      if (config === 'toggle') {\n        data[config]()\n      }\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, event => {\n  event.preventDefault()\n\n  const button = event.target.closest(SELECTOR_DATA_TOGGLE)\n  const data = Button.getOrCreateInstance(button)\n\n  data.toggle()\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Button)\n\nexport default Button\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/swipe.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport Config from './config.js'\nimport { execute } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'swipe'\nconst EVENT_KEY = '.bs.swipe'\nconst EVENT_TOUCHSTART = `touchstart${EVENT_KEY}`\nconst EVENT_TOUCHMOVE = `touchmove${EVENT_KEY}`\nconst EVENT_TOUCHEND = `touchend${EVENT_KEY}`\nconst EVENT_POINTERDOWN = `pointerdown${EVENT_KEY}`\nconst EVENT_POINTERUP = `pointerup${EVENT_KEY}`\nconst POINTER_TYPE_TOUCH = 'touch'\nconst POINTER_TYPE_PEN = 'pen'\nconst CLASS_NAME_POINTER_EVENT = 'pointer-event'\nconst SWIPE_THRESHOLD = 40\n\nconst Default = {\n  endCallback: null,\n  leftCallback: null,\n  rightCallback: null\n}\n\nconst DefaultType = {\n  endCallback: '(function|null)',\n  leftCallback: '(function|null)',\n  rightCallback: '(function|null)'\n}\n\n/**\n * Class definition\n */\n\nclass Swipe extends Config {\n  constructor(element, config) {\n    super()\n    this._element = element\n\n    if (!element || !Swipe.isSupported()) {\n      return\n    }\n\n    this._config = this._getConfig(config)\n    this._deltaX = 0\n    this._supportPointerEvents = Boolean(window.PointerEvent)\n    this._initEvents()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  dispose() {\n    EventHandler.off(this._element, EVENT_KEY)\n  }\n\n  // Private\n  _start(event) {\n    if (!this._supportPointerEvents) {\n      this._deltaX = event.touches[0].clientX\n\n      return\n    }\n\n    if (this._eventIsPointerPenTouch(event)) {\n      this._deltaX = event.clientX\n    }\n  }\n\n  _end(event) {\n    if (this._eventIsPointerPenTouch(event)) {\n      this._deltaX = event.clientX - this._deltaX\n    }\n\n    this._handleSwipe()\n    execute(this._config.endCallback)\n  }\n\n  _move(event) {\n    this._deltaX = event.touches && event.touches.length > 1 ?\n      0 :\n      event.touches[0].clientX - this._deltaX\n  }\n\n  _handleSwipe() {\n    const absDeltaX = Math.abs(this._deltaX)\n\n    if (absDeltaX <= SWIPE_THRESHOLD) {\n      return\n    }\n\n    const direction = absDeltaX / this._deltaX\n\n    this._deltaX = 0\n\n    if (!direction) {\n      return\n    }\n\n    execute(direction > 0 ? this._config.rightCallback : this._config.leftCallback)\n  }\n\n  _initEvents() {\n    if (this._supportPointerEvents) {\n      EventHandler.on(this._element, EVENT_POINTERDOWN, event => this._start(event))\n      EventHandler.on(this._element, EVENT_POINTERUP, event => this._end(event))\n\n      this._element.classList.add(CLASS_NAME_POINTER_EVENT)\n    } else {\n      EventHandler.on(this._element, EVENT_TOUCHSTART, event => this._start(event))\n      EventHandler.on(this._element, EVENT_TOUCHMOVE, event => this._move(event))\n      EventHandler.on(this._element, EVENT_TOUCHEND, event => this._end(event))\n    }\n  }\n\n  _eventIsPointerPenTouch(event) {\n    return this._supportPointerEvents && (event.pointerType === POINTER_TYPE_PEN || event.pointerType === POINTER_TYPE_TOUCH)\n  }\n\n  // Static\n  static isSupported() {\n    return 'ontouchstart' in document.documentElement || navigator.maxTouchPoints > 0\n  }\n}\n\nexport default Swipe\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap carousel.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n  defineJQueryPlugin,\n  getNextActiveElement,\n  isRTL,\n  isVisible,\n  reflow,\n  triggerTransitionEnd\n} from './util/index.js'\nimport Swipe from './util/swipe.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'carousel'\nconst DATA_KEY = 'bs.carousel'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst ARROW_LEFT_KEY = 'ArrowLeft'\nconst ARROW_RIGHT_KEY = 'ArrowRight'\nconst TOUCHEVENT_COMPAT_WAIT = 500 // Time for mouse compat events to fire after touch\n\nconst ORDER_NEXT = 'next'\nconst ORDER_PREV = 'prev'\nconst DIRECTION_LEFT = 'left'\nconst DIRECTION_RIGHT = 'right'\n\nconst EVENT_SLIDE = `slide${EVENT_KEY}`\nconst EVENT_SLID = `slid${EVENT_KEY}`\nconst EVENT_KEYDOWN = `keydown${EVENT_KEY}`\nconst EVENT_MOUSEENTER = `mouseenter${EVENT_KEY}`\nconst EVENT_MOUSELEAVE = `mouseleave${EVENT_KEY}`\nconst EVENT_DRAG_START = `dragstart${EVENT_KEY}`\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_CAROUSEL = 'carousel'\nconst CLASS_NAME_ACTIVE = 'active'\nconst CLASS_NAME_SLIDE = 'slide'\nconst CLASS_NAME_END = 'carousel-item-end'\nconst CLASS_NAME_START = 'carousel-item-start'\nconst CLASS_NAME_NEXT = 'carousel-item-next'\nconst CLASS_NAME_PREV = 'carousel-item-prev'\n\nconst SELECTOR_ACTIVE = '.active'\nconst SELECTOR_ITEM = '.carousel-item'\nconst SELECTOR_ACTIVE_ITEM = SELECTOR_ACTIVE + SELECTOR_ITEM\nconst SELECTOR_ITEM_IMG = '.carousel-item img'\nconst SELECTOR_INDICATORS = '.carousel-indicators'\nconst SELECTOR_DATA_SLIDE = '[data-bs-slide], [data-bs-slide-to]'\nconst SELECTOR_DATA_RIDE = '[data-bs-ride=\"carousel\"]'\n\nconst KEY_TO_DIRECTION = {\n  [ARROW_LEFT_KEY]: DIRECTION_RIGHT,\n  [ARROW_RIGHT_KEY]: DIRECTION_LEFT\n}\n\nconst Default = {\n  interval: 5000,\n  keyboard: true,\n  pause: 'hover',\n  ride: false,\n  touch: true,\n  wrap: true\n}\n\nconst DefaultType = {\n  interval: '(number|boolean)', // TODO:v6 remove boolean support\n  keyboard: 'boolean',\n  pause: '(string|boolean)',\n  ride: '(boolean|string)',\n  touch: 'boolean',\n  wrap: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Carousel extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._interval = null\n    this._activeElement = null\n    this._isSliding = false\n    this.touchTimeout = null\n    this._swipeHelper = null\n\n    this._indicatorsElement = SelectorEngine.findOne(SELECTOR_INDICATORS, this._element)\n    this._addEventListeners()\n\n    if (this._config.ride === CLASS_NAME_CAROUSEL) {\n      this.cycle()\n    }\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  next() {\n    this._slide(ORDER_NEXT)\n  }\n\n  nextWhenVisible() {\n    // FIXME TODO use `document.visibilityState`\n    // Don't call next when the page isn't visible\n    // or the carousel or its parent isn't visible\n    if (!document.hidden && isVisible(this._element)) {\n      this.next()\n    }\n  }\n\n  prev() {\n    this._slide(ORDER_PREV)\n  }\n\n  pause() {\n    if (this._isSliding) {\n      triggerTransitionEnd(this._element)\n    }\n\n    this._clearInterval()\n  }\n\n  cycle() {\n    this._clearInterval()\n    this._updateInterval()\n\n    this._interval = setInterval(() => this.nextWhenVisible(), this._config.interval)\n  }\n\n  _maybeEnableCycle() {\n    if (!this._config.ride) {\n      return\n    }\n\n    if (this._isSliding) {\n      EventHandler.one(this._element, EVENT_SLID, () => this.cycle())\n      return\n    }\n\n    this.cycle()\n  }\n\n  to(index) {\n    const items = this._getItems()\n    if (index > items.length - 1 || index < 0) {\n      return\n    }\n\n    if (this._isSliding) {\n      EventHandler.one(this._element, EVENT_SLID, () => this.to(index))\n      return\n    }\n\n    const activeIndex = this._getItemIndex(this._getActive())\n    if (activeIndex === index) {\n      return\n    }\n\n    const order = index > activeIndex ? ORDER_NEXT : ORDER_PREV\n\n    this._slide(order, items[index])\n  }\n\n  dispose() {\n    if (this._swipeHelper) {\n      this._swipeHelper.dispose()\n    }\n\n    super.dispose()\n  }\n\n  // Private\n  _configAfterMerge(config) {\n    config.defaultInterval = config.interval\n    return config\n  }\n\n  _addEventListeners() {\n    if (this._config.keyboard) {\n      EventHandler.on(this._element, EVENT_KEYDOWN, event => this._keydown(event))\n    }\n\n    if (this._config.pause === 'hover') {\n      EventHandler.on(this._element, EVENT_MOUSEENTER, () => this.pause())\n      EventHandler.on(this._element, EVENT_MOUSELEAVE, () => this._maybeEnableCycle())\n    }\n\n    if (this._config.touch && Swipe.isSupported()) {\n      this._addTouchEventListeners()\n    }\n  }\n\n  _addTouchEventListeners() {\n    for (const img of SelectorEngine.find(SELECTOR_ITEM_IMG, this._element)) {\n      EventHandler.on(img, EVENT_DRAG_START, event => event.preventDefault())\n    }\n\n    const endCallBack = () => {\n      if (this._config.pause !== 'hover') {\n        return\n      }\n\n      // If it's a touch-enabled device, mouseenter/leave are fired as\n      // part of the mouse compatibility events on first tap - the carousel\n      // would stop cycling until user tapped out of it;\n      // here, we listen for touchend, explicitly pause the carousel\n      // (as if it's the second time we tap on it, mouseenter compat event\n      // is NOT fired) and after a timeout (to allow for mouse compatibility\n      // events to fire) we explicitly restart cycling\n\n      this.pause()\n      if (this.touchTimeout) {\n        clearTimeout(this.touchTimeout)\n      }\n\n      this.touchTimeout = setTimeout(() => this._maybeEnableCycle(), TOUCHEVENT_COMPAT_WAIT + this._config.interval)\n    }\n\n    const swipeConfig = {\n      leftCallback: () => this._slide(this._directionToOrder(DIRECTION_LEFT)),\n      rightCallback: () => this._slide(this._directionToOrder(DIRECTION_RIGHT)),\n      endCallback: endCallBack\n    }\n\n    this._swipeHelper = new Swipe(this._element, swipeConfig)\n  }\n\n  _keydown(event) {\n    if (/input|textarea/i.test(event.target.tagName)) {\n      return\n    }\n\n    const direction = KEY_TO_DIRECTION[event.key]\n    if (direction) {\n      event.preventDefault()\n      this._slide(this._directionToOrder(direction))\n    }\n  }\n\n  _getItemIndex(element) {\n    return this._getItems().indexOf(element)\n  }\n\n  _setActiveIndicatorElement(index) {\n    if (!this._indicatorsElement) {\n      return\n    }\n\n    const activeIndicator = SelectorEngine.findOne(SELECTOR_ACTIVE, this._indicatorsElement)\n\n    activeIndicator.classList.remove(CLASS_NAME_ACTIVE)\n    activeIndicator.removeAttribute('aria-current')\n\n    const newActiveIndicator = SelectorEngine.findOne(`[data-bs-slide-to=\"${index}\"]`, this._indicatorsElement)\n\n    if (newActiveIndicator) {\n      newActiveIndicator.classList.add(CLASS_NAME_ACTIVE)\n      newActiveIndicator.setAttribute('aria-current', 'true')\n    }\n  }\n\n  _updateInterval() {\n    const element = this._activeElement || this._getActive()\n\n    if (!element) {\n      return\n    }\n\n    const elementInterval = Number.parseInt(element.getAttribute('data-bs-interval'), 10)\n\n    this._config.interval = elementInterval || this._config.defaultInterval\n  }\n\n  _slide(order, element = null) {\n    if (this._isSliding) {\n      return\n    }\n\n    const activeElement = this._getActive()\n    const isNext = order === ORDER_NEXT\n    const nextElement = element || getNextActiveElement(this._getItems(), activeElement, isNext, this._config.wrap)\n\n    if (nextElement === activeElement) {\n      return\n    }\n\n    const nextElementIndex = this._getItemIndex(nextElement)\n\n    const triggerEvent = eventName => {\n      return EventHandler.trigger(this._element, eventName, {\n        relatedTarget: nextElement,\n        direction: this._orderToDirection(order),\n        from: this._getItemIndex(activeElement),\n        to: nextElementIndex\n      })\n    }\n\n    const slideEvent = triggerEvent(EVENT_SLIDE)\n\n    if (slideEvent.defaultPrevented) {\n      return\n    }\n\n    if (!activeElement || !nextElement) {\n      // Some weirdness is happening, so we bail\n      // TODO: change tests that use empty divs to avoid this check\n      return\n    }\n\n    const isCycling = Boolean(this._interval)\n    this.pause()\n\n    this._isSliding = true\n\n    this._setActiveIndicatorElement(nextElementIndex)\n    this._activeElement = nextElement\n\n    const directionalClassName = isNext ? CLASS_NAME_START : CLASS_NAME_END\n    const orderClassName = isNext ? CLASS_NAME_NEXT : CLASS_NAME_PREV\n\n    nextElement.classList.add(orderClassName)\n\n    reflow(nextElement)\n\n    activeElement.classList.add(directionalClassName)\n    nextElement.classList.add(directionalClassName)\n\n    const completeCallBack = () => {\n      nextElement.classList.remove(directionalClassName, orderClassName)\n      nextElement.classList.add(CLASS_NAME_ACTIVE)\n\n      activeElement.classList.remove(CLASS_NAME_ACTIVE, orderClassName, directionalClassName)\n\n      this._isSliding = false\n\n      triggerEvent(EVENT_SLID)\n    }\n\n    this._queueCallback(completeCallBack, activeElement, this._isAnimated())\n\n    if (isCycling) {\n      this.cycle()\n    }\n  }\n\n  _isAnimated() {\n    return this._element.classList.contains(CLASS_NAME_SLIDE)\n  }\n\n  _getActive() {\n    return SelectorEngine.findOne(SELECTOR_ACTIVE_ITEM, this._element)\n  }\n\n  _getItems() {\n    return SelectorEngine.find(SELECTOR_ITEM, this._element)\n  }\n\n  _clearInterval() {\n    if (this._interval) {\n      clearInterval(this._interval)\n      this._interval = null\n    }\n  }\n\n  _directionToOrder(direction) {\n    if (isRTL()) {\n      return direction === DIRECTION_LEFT ? ORDER_PREV : ORDER_NEXT\n    }\n\n    return direction === DIRECTION_LEFT ? ORDER_NEXT : ORDER_PREV\n  }\n\n  _orderToDirection(order) {\n    if (isRTL()) {\n      return order === ORDER_PREV ? DIRECTION_LEFT : DIRECTION_RIGHT\n    }\n\n    return order === ORDER_PREV ? DIRECTION_RIGHT : DIRECTION_LEFT\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Carousel.getOrCreateInstance(this, config)\n\n      if (typeof config === 'number') {\n        data.to(config)\n        return\n      }\n\n      if (typeof config === 'string') {\n        if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n          throw new TypeError(`No method named \"${config}\"`)\n        }\n\n        data[config]()\n      }\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_SLIDE, function (event) {\n  const target = SelectorEngine.getElementFromSelector(this)\n\n  if (!target || !target.classList.contains(CLASS_NAME_CAROUSEL)) {\n    return\n  }\n\n  event.preventDefault()\n\n  const carousel = Carousel.getOrCreateInstance(target)\n  const slideIndex = this.getAttribute('data-bs-slide-to')\n\n  if (slideIndex) {\n    carousel.to(slideIndex)\n    carousel._maybeEnableCycle()\n    return\n  }\n\n  if (Manipulator.getDataAttribute(this, 'slide') === 'next') {\n    carousel.next()\n    carousel._maybeEnableCycle()\n    return\n  }\n\n  carousel.prev()\n  carousel._maybeEnableCycle()\n})\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n  const carousels = SelectorEngine.find(SELECTOR_DATA_RIDE)\n\n  for (const carousel of carousels) {\n    Carousel.getOrCreateInstance(carousel)\n  }\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Carousel)\n\nexport default Carousel\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap collapse.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n  defineJQueryPlugin,\n  getElement,\n  reflow\n} from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'collapse'\nconst DATA_KEY = 'bs.collapse'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_COLLAPSE = 'collapse'\nconst CLASS_NAME_COLLAPSING = 'collapsing'\nconst CLASS_NAME_COLLAPSED = 'collapsed'\nconst CLASS_NAME_DEEPER_CHILDREN = `:scope .${CLASS_NAME_COLLAPSE} .${CLASS_NAME_COLLAPSE}`\nconst CLASS_NAME_HORIZONTAL = 'collapse-horizontal'\n\nconst WIDTH = 'width'\nconst HEIGHT = 'height'\n\nconst SELECTOR_ACTIVES = '.collapse.show, .collapse.collapsing'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"collapse\"]'\n\nconst Default = {\n  parent: null,\n  toggle: true\n}\n\nconst DefaultType = {\n  parent: '(null|element)',\n  toggle: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Collapse extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._isTransitioning = false\n    this._triggerArray = []\n\n    const toggleList = SelectorEngine.find(SELECTOR_DATA_TOGGLE)\n\n    for (const elem of toggleList) {\n      const selector = SelectorEngine.getSelectorFromElement(elem)\n      const filterElement = SelectorEngine.find(selector)\n        .filter(foundElement => foundElement === this._element)\n\n      if (selector !== null && filterElement.length) {\n        this._triggerArray.push(elem)\n      }\n    }\n\n    this._initializeChildren()\n\n    if (!this._config.parent) {\n      this._addAriaAndCollapsedClass(this._triggerArray, this._isShown())\n    }\n\n    if (this._config.toggle) {\n      this.toggle()\n    }\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle() {\n    if (this._isShown()) {\n      this.hide()\n    } else {\n      this.show()\n    }\n  }\n\n  show() {\n    if (this._isTransitioning || this._isShown()) {\n      return\n    }\n\n    let activeChildren = []\n\n    // find active children\n    if (this._config.parent) {\n      activeChildren = this._getFirstLevelChildren(SELECTOR_ACTIVES)\n        .filter(element => element !== this._element)\n        .map(element => Collapse.getOrCreateInstance(element, { toggle: false }))\n    }\n\n    if (activeChildren.length && activeChildren[0]._isTransitioning) {\n      return\n    }\n\n    const startEvent = EventHandler.trigger(this._element, EVENT_SHOW)\n    if (startEvent.defaultPrevented) {\n      return\n    }\n\n    for (const activeInstance of activeChildren) {\n      activeInstance.hide()\n    }\n\n    const dimension = this._getDimension()\n\n    this._element.classList.remove(CLASS_NAME_COLLAPSE)\n    this._element.classList.add(CLASS_NAME_COLLAPSING)\n\n    this._element.style[dimension] = 0\n\n    this._addAriaAndCollapsedClass(this._triggerArray, true)\n    this._isTransitioning = true\n\n    const complete = () => {\n      this._isTransitioning = false\n\n      this._element.classList.remove(CLASS_NAME_COLLAPSING)\n      this._element.classList.add(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW)\n\n      this._element.style[dimension] = ''\n\n      EventHandler.trigger(this._element, EVENT_SHOWN)\n    }\n\n    const capitalizedDimension = dimension[0].toUpperCase() + dimension.slice(1)\n    const scrollSize = `scroll${capitalizedDimension}`\n\n    this._queueCallback(complete, this._element, true)\n    this._element.style[dimension] = `${this._element[scrollSize]}px`\n  }\n\n  hide() {\n    if (this._isTransitioning || !this._isShown()) {\n      return\n    }\n\n    const startEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n    if (startEvent.defaultPrevented) {\n      return\n    }\n\n    const dimension = this._getDimension()\n\n    this._element.style[dimension] = `${this._element.getBoundingClientRect()[dimension]}px`\n\n    reflow(this._element)\n\n    this._element.classList.add(CLASS_NAME_COLLAPSING)\n    this._element.classList.remove(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW)\n\n    for (const trigger of this._triggerArray) {\n      const element = SelectorEngine.getElementFromSelector(trigger)\n\n      if (element && !this._isShown(element)) {\n        this._addAriaAndCollapsedClass([trigger], false)\n      }\n    }\n\n    this._isTransitioning = true\n\n    const complete = () => {\n      this._isTransitioning = false\n      this._element.classList.remove(CLASS_NAME_COLLAPSING)\n      this._element.classList.add(CLASS_NAME_COLLAPSE)\n      EventHandler.trigger(this._element, EVENT_HIDDEN)\n    }\n\n    this._element.style[dimension] = ''\n\n    this._queueCallback(complete, this._element, true)\n  }\n\n  _isShown(element = this._element) {\n    return element.classList.contains(CLASS_NAME_SHOW)\n  }\n\n  // Private\n  _configAfterMerge(config) {\n    config.toggle = Boolean(config.toggle) // Coerce string values\n    config.parent = getElement(config.parent)\n    return config\n  }\n\n  _getDimension() {\n    return this._element.classList.contains(CLASS_NAME_HORIZONTAL) ? WIDTH : HEIGHT\n  }\n\n  _initializeChildren() {\n    if (!this._config.parent) {\n      return\n    }\n\n    const children = this._getFirstLevelChildren(SELECTOR_DATA_TOGGLE)\n\n    for (const element of children) {\n      const selected = SelectorEngine.getElementFromSelector(element)\n\n      if (selected) {\n        this._addAriaAndCollapsedClass([element], this._isShown(selected))\n      }\n    }\n  }\n\n  _getFirstLevelChildren(selector) {\n    const children = SelectorEngine.find(CLASS_NAME_DEEPER_CHILDREN, this._config.parent)\n    // remove children if greater depth\n    return SelectorEngine.find(selector, this._config.parent).filter(element => !children.includes(element))\n  }\n\n  _addAriaAndCollapsedClass(triggerArray, isOpen) {\n    if (!triggerArray.length) {\n      return\n    }\n\n    for (const element of triggerArray) {\n      element.classList.toggle(CLASS_NAME_COLLAPSED, !isOpen)\n      element.setAttribute('aria-expanded', isOpen)\n    }\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    const _config = {}\n    if (typeof config === 'string' && /show|hide/.test(config)) {\n      _config.toggle = false\n    }\n\n    return this.each(function () {\n      const data = Collapse.getOrCreateInstance(this, _config)\n\n      if (typeof config === 'string') {\n        if (typeof data[config] === 'undefined') {\n          throw new TypeError(`No method named \"${config}\"`)\n        }\n\n        data[config]()\n      }\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  // preventDefault only for  elements (which change the URL) not inside the collapsible element\n  if (event.target.tagName === 'A' || (event.delegateTarget && event.delegateTarget.tagName === 'A')) {\n    event.preventDefault()\n  }\n\n  for (const element of SelectorEngine.getMultipleElementsFromSelector(this)) {\n    Collapse.getOrCreateInstance(element, { toggle: false }).toggle()\n  }\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Collapse)\n\nexport default Collapse\n","export var top = 'top';\nexport var bottom = 'bottom';\nexport var right = 'right';\nexport var left = 'left';\nexport var auto = 'auto';\nexport var basePlacements = [top, bottom, right, left];\nexport var start = 'start';\nexport var end = 'end';\nexport var clippingParents = 'clippingParents';\nexport var viewport = 'viewport';\nexport var popper = 'popper';\nexport var reference = 'reference';\nexport var variationPlacements = /*#__PURE__*/basePlacements.reduce(function (acc, placement) {\n  return acc.concat([placement + \"-\" + start, placement + \"-\" + end]);\n}, []);\nexport var placements = /*#__PURE__*/[].concat(basePlacements, [auto]).reduce(function (acc, placement) {\n  return acc.concat([placement, placement + \"-\" + start, placement + \"-\" + end]);\n}, []); // modifiers that need to read the DOM\n\nexport var beforeRead = 'beforeRead';\nexport var read = 'read';\nexport var afterRead = 'afterRead'; // pure-logic modifiers\n\nexport var beforeMain = 'beforeMain';\nexport var main = 'main';\nexport var afterMain = 'afterMain'; // modifier with the purpose to write to the DOM (or write into a framework state)\n\nexport var beforeWrite = 'beforeWrite';\nexport var write = 'write';\nexport var afterWrite = 'afterWrite';\nexport var modifierPhases = [beforeRead, read, afterRead, beforeMain, main, afterMain, beforeWrite, write, afterWrite];","export default function getNodeName(element) {\n  return element ? (element.nodeName || '').toLowerCase() : null;\n}","export default function getWindow(node) {\n  if (node == null) {\n    return window;\n  }\n\n  if (node.toString() !== '[object Window]') {\n    var ownerDocument = node.ownerDocument;\n    return ownerDocument ? ownerDocument.defaultView || window : window;\n  }\n\n  return node;\n}","import getWindow from \"./getWindow.js\";\n\nfunction isElement(node) {\n  var OwnElement = getWindow(node).Element;\n  return node instanceof OwnElement || node instanceof Element;\n}\n\nfunction isHTMLElement(node) {\n  var OwnElement = getWindow(node).HTMLElement;\n  return node instanceof OwnElement || node instanceof HTMLElement;\n}\n\nfunction isShadowRoot(node) {\n  // IE 11 has no ShadowRoot\n  if (typeof ShadowRoot === 'undefined') {\n    return false;\n  }\n\n  var OwnElement = getWindow(node).ShadowRoot;\n  return node instanceof OwnElement || node instanceof ShadowRoot;\n}\n\nexport { isElement, isHTMLElement, isShadowRoot };","import getNodeName from \"../dom-utils/getNodeName.js\";\nimport { isHTMLElement } from \"../dom-utils/instanceOf.js\"; // This modifier takes the styles prepared by the `computeStyles` modifier\n// and applies them to the HTMLElements such as popper and arrow\n\nfunction applyStyles(_ref) {\n  var state = _ref.state;\n  Object.keys(state.elements).forEach(function (name) {\n    var style = state.styles[name] || {};\n    var attributes = state.attributes[name] || {};\n    var element = state.elements[name]; // arrow is optional + virtual elements\n\n    if (!isHTMLElement(element) || !getNodeName(element)) {\n      return;\n    } // Flow doesn't support to extend this property, but it's the most\n    // effective way to apply styles to an HTMLElement\n    // $FlowFixMe[cannot-write]\n\n\n    Object.assign(element.style, style);\n    Object.keys(attributes).forEach(function (name) {\n      var value = attributes[name];\n\n      if (value === false) {\n        element.removeAttribute(name);\n      } else {\n        element.setAttribute(name, value === true ? '' : value);\n      }\n    });\n  });\n}\n\nfunction effect(_ref2) {\n  var state = _ref2.state;\n  var initialStyles = {\n    popper: {\n      position: state.options.strategy,\n      left: '0',\n      top: '0',\n      margin: '0'\n    },\n    arrow: {\n      position: 'absolute'\n    },\n    reference: {}\n  };\n  Object.assign(state.elements.popper.style, initialStyles.popper);\n  state.styles = initialStyles;\n\n  if (state.elements.arrow) {\n    Object.assign(state.elements.arrow.style, initialStyles.arrow);\n  }\n\n  return function () {\n    Object.keys(state.elements).forEach(function (name) {\n      var element = state.elements[name];\n      var attributes = state.attributes[name] || {};\n      var styleProperties = Object.keys(state.styles.hasOwnProperty(name) ? state.styles[name] : initialStyles[name]); // Set all values to an empty string to unset them\n\n      var style = styleProperties.reduce(function (style, property) {\n        style[property] = '';\n        return style;\n      }, {}); // arrow is optional + virtual elements\n\n      if (!isHTMLElement(element) || !getNodeName(element)) {\n        return;\n      }\n\n      Object.assign(element.style, style);\n      Object.keys(attributes).forEach(function (attribute) {\n        element.removeAttribute(attribute);\n      });\n    });\n  };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'applyStyles',\n  enabled: true,\n  phase: 'write',\n  fn: applyStyles,\n  effect: effect,\n  requires: ['computeStyles']\n};","import { auto } from \"../enums.js\";\nexport default function getBasePlacement(placement) {\n  return placement.split('-')[0];\n}","export var max = Math.max;\nexport var min = Math.min;\nexport var round = Math.round;","export default function getUAString() {\n  var uaData = navigator.userAgentData;\n\n  if (uaData != null && uaData.brands && Array.isArray(uaData.brands)) {\n    return uaData.brands.map(function (item) {\n      return item.brand + \"/\" + item.version;\n    }).join(' ');\n  }\n\n  return navigator.userAgent;\n}","import getUAString from \"../utils/userAgent.js\";\nexport default function isLayoutViewport() {\n  return !/^((?!chrome|android).)*safari/i.test(getUAString());\n}","import { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport { round } from \"../utils/math.js\";\nimport getWindow from \"./getWindow.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getBoundingClientRect(element, includeScale, isFixedStrategy) {\n  if (includeScale === void 0) {\n    includeScale = false;\n  }\n\n  if (isFixedStrategy === void 0) {\n    isFixedStrategy = false;\n  }\n\n  var clientRect = element.getBoundingClientRect();\n  var scaleX = 1;\n  var scaleY = 1;\n\n  if (includeScale && isHTMLElement(element)) {\n    scaleX = element.offsetWidth > 0 ? round(clientRect.width) / element.offsetWidth || 1 : 1;\n    scaleY = element.offsetHeight > 0 ? round(clientRect.height) / element.offsetHeight || 1 : 1;\n  }\n\n  var _ref = isElement(element) ? getWindow(element) : window,\n      visualViewport = _ref.visualViewport;\n\n  var addVisualOffsets = !isLayoutViewport() && isFixedStrategy;\n  var x = (clientRect.left + (addVisualOffsets && visualViewport ? visualViewport.offsetLeft : 0)) / scaleX;\n  var y = (clientRect.top + (addVisualOffsets && visualViewport ? visualViewport.offsetTop : 0)) / scaleY;\n  var width = clientRect.width / scaleX;\n  var height = clientRect.height / scaleY;\n  return {\n    width: width,\n    height: height,\n    top: y,\n    right: x + width,\n    bottom: y + height,\n    left: x,\n    x: x,\n    y: y\n  };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\"; // Returns the layout rect of an element relative to its offsetParent. Layout\n// means it doesn't take into account transforms.\n\nexport default function getLayoutRect(element) {\n  var clientRect = getBoundingClientRect(element); // Use the clientRect sizes if it's not been transformed.\n  // Fixes https://github.com/popperjs/popper-core/issues/1223\n\n  var width = element.offsetWidth;\n  var height = element.offsetHeight;\n\n  if (Math.abs(clientRect.width - width) <= 1) {\n    width = clientRect.width;\n  }\n\n  if (Math.abs(clientRect.height - height) <= 1) {\n    height = clientRect.height;\n  }\n\n  return {\n    x: element.offsetLeft,\n    y: element.offsetTop,\n    width: width,\n    height: height\n  };\n}","import { isShadowRoot } from \"./instanceOf.js\";\nexport default function contains(parent, child) {\n  var rootNode = child.getRootNode && child.getRootNode(); // First, attempt with faster native method\n\n  if (parent.contains(child)) {\n    return true;\n  } // then fallback to custom implementation with Shadow DOM support\n  else if (rootNode && isShadowRoot(rootNode)) {\n      var next = child;\n\n      do {\n        if (next && parent.isSameNode(next)) {\n          return true;\n        } // $FlowFixMe[prop-missing]: need a better way to handle this...\n\n\n        next = next.parentNode || next.host;\n      } while (next);\n    } // Give up, the result is false\n\n\n  return false;\n}","import getWindow from \"./getWindow.js\";\nexport default function getComputedStyle(element) {\n  return getWindow(element).getComputedStyle(element);\n}","import getNodeName from \"./getNodeName.js\";\nexport default function isTableElement(element) {\n  return ['table', 'td', 'th'].indexOf(getNodeName(element)) >= 0;\n}","import { isElement } from \"./instanceOf.js\";\nexport default function getDocumentElement(element) {\n  // $FlowFixMe[incompatible-return]: assume body is always available\n  return ((isElement(element) ? element.ownerDocument : // $FlowFixMe[prop-missing]\n  element.document) || window.document).documentElement;\n}","import getNodeName from \"./getNodeName.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport { isShadowRoot } from \"./instanceOf.js\";\nexport default function getParentNode(element) {\n  if (getNodeName(element) === 'html') {\n    return element;\n  }\n\n  return (// this is a quicker (but less type safe) way to save quite some bytes from the bundle\n    // $FlowFixMe[incompatible-return]\n    // $FlowFixMe[prop-missing]\n    element.assignedSlot || // step into the shadow DOM of the parent of a slotted node\n    element.parentNode || ( // DOM Element detected\n    isShadowRoot(element) ? element.host : null) || // ShadowRoot detected\n    // $FlowFixMe[incompatible-call]: HTMLElement is a Node\n    getDocumentElement(element) // fallback\n\n  );\n}","import getWindow from \"./getWindow.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isHTMLElement, isShadowRoot } from \"./instanceOf.js\";\nimport isTableElement from \"./isTableElement.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getUAString from \"../utils/userAgent.js\";\n\nfunction getTrueOffsetParent(element) {\n  if (!isHTMLElement(element) || // https://github.com/popperjs/popper-core/issues/837\n  getComputedStyle(element).position === 'fixed') {\n    return null;\n  }\n\n  return element.offsetParent;\n} // `.offsetParent` reports `null` for fixed elements, while absolute elements\n// return the containing block\n\n\nfunction getContainingBlock(element) {\n  var isFirefox = /firefox/i.test(getUAString());\n  var isIE = /Trident/i.test(getUAString());\n\n  if (isIE && isHTMLElement(element)) {\n    // In IE 9, 10 and 11 fixed elements containing block is always established by the viewport\n    var elementCss = getComputedStyle(element);\n\n    if (elementCss.position === 'fixed') {\n      return null;\n    }\n  }\n\n  var currentNode = getParentNode(element);\n\n  if (isShadowRoot(currentNode)) {\n    currentNode = currentNode.host;\n  }\n\n  while (isHTMLElement(currentNode) && ['html', 'body'].indexOf(getNodeName(currentNode)) < 0) {\n    var css = getComputedStyle(currentNode); // This is non-exhaustive but covers the most common CSS properties that\n    // create a containing block.\n    // https://developer.mozilla.org/en-US/docs/Web/CSS/Containing_block#identifying_the_containing_block\n\n    if (css.transform !== 'none' || css.perspective !== 'none' || css.contain === 'paint' || ['transform', 'perspective'].indexOf(css.willChange) !== -1 || isFirefox && css.willChange === 'filter' || isFirefox && css.filter && css.filter !== 'none') {\n      return currentNode;\n    } else {\n      currentNode = currentNode.parentNode;\n    }\n  }\n\n  return null;\n} // Gets the closest ancestor positioned element. Handles some edge cases,\n// such as table ancestors and cross browser bugs.\n\n\nexport default function getOffsetParent(element) {\n  var window = getWindow(element);\n  var offsetParent = getTrueOffsetParent(element);\n\n  while (offsetParent && isTableElement(offsetParent) && getComputedStyle(offsetParent).position === 'static') {\n    offsetParent = getTrueOffsetParent(offsetParent);\n  }\n\n  if (offsetParent && (getNodeName(offsetParent) === 'html' || getNodeName(offsetParent) === 'body' && getComputedStyle(offsetParent).position === 'static')) {\n    return window;\n  }\n\n  return offsetParent || getContainingBlock(element) || window;\n}","export default function getMainAxisFromPlacement(placement) {\n  return ['top', 'bottom'].indexOf(placement) >= 0 ? 'x' : 'y';\n}","import { max as mathMax, min as mathMin } from \"./math.js\";\nexport function within(min, value, max) {\n  return mathMax(min, mathMin(value, max));\n}\nexport function withinMaxClamp(min, value, max) {\n  var v = within(min, value, max);\n  return v > max ? max : v;\n}","import getFreshSideObject from \"./getFreshSideObject.js\";\nexport default function mergePaddingObject(paddingObject) {\n  return Object.assign({}, getFreshSideObject(), paddingObject);\n}","export default function getFreshSideObject() {\n  return {\n    top: 0,\n    right: 0,\n    bottom: 0,\n    left: 0\n  };\n}","export default function expandToHashMap(value, keys) {\n  return keys.reduce(function (hashMap, key) {\n    hashMap[key] = value;\n    return hashMap;\n  }, {});\n}","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport contains from \"../dom-utils/contains.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport { within } from \"../utils/within.js\";\nimport mergePaddingObject from \"../utils/mergePaddingObject.js\";\nimport expandToHashMap from \"../utils/expandToHashMap.js\";\nimport { left, right, basePlacements, top, bottom } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar toPaddingObject = function toPaddingObject(padding, state) {\n  padding = typeof padding === 'function' ? padding(Object.assign({}, state.rects, {\n    placement: state.placement\n  })) : padding;\n  return mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n};\n\nfunction arrow(_ref) {\n  var _state$modifiersData$;\n\n  var state = _ref.state,\n      name = _ref.name,\n      options = _ref.options;\n  var arrowElement = state.elements.arrow;\n  var popperOffsets = state.modifiersData.popperOffsets;\n  var basePlacement = getBasePlacement(state.placement);\n  var axis = getMainAxisFromPlacement(basePlacement);\n  var isVertical = [left, right].indexOf(basePlacement) >= 0;\n  var len = isVertical ? 'height' : 'width';\n\n  if (!arrowElement || !popperOffsets) {\n    return;\n  }\n\n  var paddingObject = toPaddingObject(options.padding, state);\n  var arrowRect = getLayoutRect(arrowElement);\n  var minProp = axis === 'y' ? top : left;\n  var maxProp = axis === 'y' ? bottom : right;\n  var endDiff = state.rects.reference[len] + state.rects.reference[axis] - popperOffsets[axis] - state.rects.popper[len];\n  var startDiff = popperOffsets[axis] - state.rects.reference[axis];\n  var arrowOffsetParent = getOffsetParent(arrowElement);\n  var clientSize = arrowOffsetParent ? axis === 'y' ? arrowOffsetParent.clientHeight || 0 : arrowOffsetParent.clientWidth || 0 : 0;\n  var centerToReference = endDiff / 2 - startDiff / 2; // Make sure the arrow doesn't overflow the popper if the center point is\n  // outside of the popper bounds\n\n  var min = paddingObject[minProp];\n  var max = clientSize - arrowRect[len] - paddingObject[maxProp];\n  var center = clientSize / 2 - arrowRect[len] / 2 + centerToReference;\n  var offset = within(min, center, max); // Prevents breaking syntax highlighting...\n\n  var axisProp = axis;\n  state.modifiersData[name] = (_state$modifiersData$ = {}, _state$modifiersData$[axisProp] = offset, _state$modifiersData$.centerOffset = offset - center, _state$modifiersData$);\n}\n\nfunction effect(_ref2) {\n  var state = _ref2.state,\n      options = _ref2.options;\n  var _options$element = options.element,\n      arrowElement = _options$element === void 0 ? '[data-popper-arrow]' : _options$element;\n\n  if (arrowElement == null) {\n    return;\n  } // CSS selector\n\n\n  if (typeof arrowElement === 'string') {\n    arrowElement = state.elements.popper.querySelector(arrowElement);\n\n    if (!arrowElement) {\n      return;\n    }\n  }\n\n  if (!contains(state.elements.popper, arrowElement)) {\n    return;\n  }\n\n  state.elements.arrow = arrowElement;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'arrow',\n  enabled: true,\n  phase: 'main',\n  fn: arrow,\n  effect: effect,\n  requires: ['popperOffsets'],\n  requiresIfExists: ['preventOverflow']\n};","export default function getVariation(placement) {\n  return placement.split('-')[1];\n}","import { top, left, right, bottom, end } from \"../enums.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getWindow from \"../dom-utils/getWindow.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getComputedStyle from \"../dom-utils/getComputedStyle.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport { round } from \"../utils/math.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar unsetSides = {\n  top: 'auto',\n  right: 'auto',\n  bottom: 'auto',\n  left: 'auto'\n}; // Round the offsets to the nearest suitable subpixel based on the DPR.\n// Zooming can change the DPR, but it seems to report a value that will\n// cleanly divide the values into the appropriate subpixels.\n\nfunction roundOffsetsByDPR(_ref, win) {\n  var x = _ref.x,\n      y = _ref.y;\n  var dpr = win.devicePixelRatio || 1;\n  return {\n    x: round(x * dpr) / dpr || 0,\n    y: round(y * dpr) / dpr || 0\n  };\n}\n\nexport function mapToStyles(_ref2) {\n  var _Object$assign2;\n\n  var popper = _ref2.popper,\n      popperRect = _ref2.popperRect,\n      placement = _ref2.placement,\n      variation = _ref2.variation,\n      offsets = _ref2.offsets,\n      position = _ref2.position,\n      gpuAcceleration = _ref2.gpuAcceleration,\n      adaptive = _ref2.adaptive,\n      roundOffsets = _ref2.roundOffsets,\n      isFixed = _ref2.isFixed;\n  var _offsets$x = offsets.x,\n      x = _offsets$x === void 0 ? 0 : _offsets$x,\n      _offsets$y = offsets.y,\n      y = _offsets$y === void 0 ? 0 : _offsets$y;\n\n  var _ref3 = typeof roundOffsets === 'function' ? roundOffsets({\n    x: x,\n    y: y\n  }) : {\n    x: x,\n    y: y\n  };\n\n  x = _ref3.x;\n  y = _ref3.y;\n  var hasX = offsets.hasOwnProperty('x');\n  var hasY = offsets.hasOwnProperty('y');\n  var sideX = left;\n  var sideY = top;\n  var win = window;\n\n  if (adaptive) {\n    var offsetParent = getOffsetParent(popper);\n    var heightProp = 'clientHeight';\n    var widthProp = 'clientWidth';\n\n    if (offsetParent === getWindow(popper)) {\n      offsetParent = getDocumentElement(popper);\n\n      if (getComputedStyle(offsetParent).position !== 'static' && position === 'absolute') {\n        heightProp = 'scrollHeight';\n        widthProp = 'scrollWidth';\n      }\n    } // $FlowFixMe[incompatible-cast]: force type refinement, we compare offsetParent with window above, but Flow doesn't detect it\n\n\n    offsetParent = offsetParent;\n\n    if (placement === top || (placement === left || placement === right) && variation === end) {\n      sideY = bottom;\n      var offsetY = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.height : // $FlowFixMe[prop-missing]\n      offsetParent[heightProp];\n      y -= offsetY - popperRect.height;\n      y *= gpuAcceleration ? 1 : -1;\n    }\n\n    if (placement === left || (placement === top || placement === bottom) && variation === end) {\n      sideX = right;\n      var offsetX = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.width : // $FlowFixMe[prop-missing]\n      offsetParent[widthProp];\n      x -= offsetX - popperRect.width;\n      x *= gpuAcceleration ? 1 : -1;\n    }\n  }\n\n  var commonStyles = Object.assign({\n    position: position\n  }, adaptive && unsetSides);\n\n  var _ref4 = roundOffsets === true ? roundOffsetsByDPR({\n    x: x,\n    y: y\n  }, getWindow(popper)) : {\n    x: x,\n    y: y\n  };\n\n  x = _ref4.x;\n  y = _ref4.y;\n\n  if (gpuAcceleration) {\n    var _Object$assign;\n\n    return Object.assign({}, commonStyles, (_Object$assign = {}, _Object$assign[sideY] = hasY ? '0' : '', _Object$assign[sideX] = hasX ? '0' : '', _Object$assign.transform = (win.devicePixelRatio || 1) <= 1 ? \"translate(\" + x + \"px, \" + y + \"px)\" : \"translate3d(\" + x + \"px, \" + y + \"px, 0)\", _Object$assign));\n  }\n\n  return Object.assign({}, commonStyles, (_Object$assign2 = {}, _Object$assign2[sideY] = hasY ? y + \"px\" : '', _Object$assign2[sideX] = hasX ? x + \"px\" : '', _Object$assign2.transform = '', _Object$assign2));\n}\n\nfunction computeStyles(_ref5) {\n  var state = _ref5.state,\n      options = _ref5.options;\n  var _options$gpuAccelerat = options.gpuAcceleration,\n      gpuAcceleration = _options$gpuAccelerat === void 0 ? true : _options$gpuAccelerat,\n      _options$adaptive = options.adaptive,\n      adaptive = _options$adaptive === void 0 ? true : _options$adaptive,\n      _options$roundOffsets = options.roundOffsets,\n      roundOffsets = _options$roundOffsets === void 0 ? true : _options$roundOffsets;\n  var commonStyles = {\n    placement: getBasePlacement(state.placement),\n    variation: getVariation(state.placement),\n    popper: state.elements.popper,\n    popperRect: state.rects.popper,\n    gpuAcceleration: gpuAcceleration,\n    isFixed: state.options.strategy === 'fixed'\n  };\n\n  if (state.modifiersData.popperOffsets != null) {\n    state.styles.popper = Object.assign({}, state.styles.popper, mapToStyles(Object.assign({}, commonStyles, {\n      offsets: state.modifiersData.popperOffsets,\n      position: state.options.strategy,\n      adaptive: adaptive,\n      roundOffsets: roundOffsets\n    })));\n  }\n\n  if (state.modifiersData.arrow != null) {\n    state.styles.arrow = Object.assign({}, state.styles.arrow, mapToStyles(Object.assign({}, commonStyles, {\n      offsets: state.modifiersData.arrow,\n      position: 'absolute',\n      adaptive: false,\n      roundOffsets: roundOffsets\n    })));\n  }\n\n  state.attributes.popper = Object.assign({}, state.attributes.popper, {\n    'data-popper-placement': state.placement\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'computeStyles',\n  enabled: true,\n  phase: 'beforeWrite',\n  fn: computeStyles,\n  data: {}\n};","import getWindow from \"../dom-utils/getWindow.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar passive = {\n  passive: true\n};\n\nfunction effect(_ref) {\n  var state = _ref.state,\n      instance = _ref.instance,\n      options = _ref.options;\n  var _options$scroll = options.scroll,\n      scroll = _options$scroll === void 0 ? true : _options$scroll,\n      _options$resize = options.resize,\n      resize = _options$resize === void 0 ? true : _options$resize;\n  var window = getWindow(state.elements.popper);\n  var scrollParents = [].concat(state.scrollParents.reference, state.scrollParents.popper);\n\n  if (scroll) {\n    scrollParents.forEach(function (scrollParent) {\n      scrollParent.addEventListener('scroll', instance.update, passive);\n    });\n  }\n\n  if (resize) {\n    window.addEventListener('resize', instance.update, passive);\n  }\n\n  return function () {\n    if (scroll) {\n      scrollParents.forEach(function (scrollParent) {\n        scrollParent.removeEventListener('scroll', instance.update, passive);\n      });\n    }\n\n    if (resize) {\n      window.removeEventListener('resize', instance.update, passive);\n    }\n  };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'eventListeners',\n  enabled: true,\n  phase: 'write',\n  fn: function fn() {},\n  effect: effect,\n  data: {}\n};","var hash = {\n  left: 'right',\n  right: 'left',\n  bottom: 'top',\n  top: 'bottom'\n};\nexport default function getOppositePlacement(placement) {\n  return placement.replace(/left|right|bottom|top/g, function (matched) {\n    return hash[matched];\n  });\n}","var hash = {\n  start: 'end',\n  end: 'start'\n};\nexport default function getOppositeVariationPlacement(placement) {\n  return placement.replace(/start|end/g, function (matched) {\n    return hash[matched];\n  });\n}","import getWindow from \"./getWindow.js\";\nexport default function getWindowScroll(node) {\n  var win = getWindow(node);\n  var scrollLeft = win.pageXOffset;\n  var scrollTop = win.pageYOffset;\n  return {\n    scrollLeft: scrollLeft,\n    scrollTop: scrollTop\n  };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nexport default function getWindowScrollBarX(element) {\n  // If  has a CSS width greater than the viewport, then this will be\n  // incorrect for RTL.\n  // Popper 1 is broken in this case and never had a bug report so let's assume\n  // it's not an issue. I don't think anyone ever specifies width on \n  // anyway.\n  // Browsers where the left scrollbar doesn't cause an issue report `0` for\n  // this (e.g. Edge 2019, IE11, Safari)\n  return getBoundingClientRect(getDocumentElement(element)).left + getWindowScroll(element).scrollLeft;\n}","import getComputedStyle from \"./getComputedStyle.js\";\nexport default function isScrollParent(element) {\n  // Firefox wants us to check `-x` and `-y` variations as well\n  var _getComputedStyle = getComputedStyle(element),\n      overflow = _getComputedStyle.overflow,\n      overflowX = _getComputedStyle.overflowX,\n      overflowY = _getComputedStyle.overflowY;\n\n  return /auto|scroll|overlay|hidden/.test(overflow + overflowY + overflowX);\n}","import getParentNode from \"./getParentNode.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nexport default function getScrollParent(node) {\n  if (['html', 'body', '#document'].indexOf(getNodeName(node)) >= 0) {\n    // $FlowFixMe[incompatible-return]: assume body is always available\n    return node.ownerDocument.body;\n  }\n\n  if (isHTMLElement(node) && isScrollParent(node)) {\n    return node;\n  }\n\n  return getScrollParent(getParentNode(node));\n}","import getScrollParent from \"./getScrollParent.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getWindow from \"./getWindow.js\";\nimport isScrollParent from \"./isScrollParent.js\";\n/*\ngiven a DOM element, return the list of all scroll parents, up the list of ancesors\nuntil we get to the top window object. This list is what we attach scroll listeners\nto, because if any of these parent elements scroll, we'll need to re-calculate the\nreference element's position.\n*/\n\nexport default function listScrollParents(element, list) {\n  var _element$ownerDocumen;\n\n  if (list === void 0) {\n    list = [];\n  }\n\n  var scrollParent = getScrollParent(element);\n  var isBody = scrollParent === ((_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body);\n  var win = getWindow(scrollParent);\n  var target = isBody ? [win].concat(win.visualViewport || [], isScrollParent(scrollParent) ? scrollParent : []) : scrollParent;\n  var updatedList = list.concat(target);\n  return isBody ? updatedList : // $FlowFixMe[incompatible-call]: isBody tells us target will be an HTMLElement here\n  updatedList.concat(listScrollParents(getParentNode(target)));\n}","export default function rectToClientRect(rect) {\n  return Object.assign({}, rect, {\n    left: rect.x,\n    top: rect.y,\n    right: rect.x + rect.width,\n    bottom: rect.y + rect.height\n  });\n}","import { viewport } from \"../enums.js\";\nimport getViewportRect from \"./getViewportRect.js\";\nimport getDocumentRect from \"./getDocumentRect.js\";\nimport listScrollParents from \"./listScrollParents.js\";\nimport getOffsetParent from \"./getOffsetParent.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport contains from \"./contains.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport rectToClientRect from \"../utils/rectToClientRect.js\";\nimport { max, min } from \"../utils/math.js\";\n\nfunction getInnerBoundingClientRect(element, strategy) {\n  var rect = getBoundingClientRect(element, false, strategy === 'fixed');\n  rect.top = rect.top + element.clientTop;\n  rect.left = rect.left + element.clientLeft;\n  rect.bottom = rect.top + element.clientHeight;\n  rect.right = rect.left + element.clientWidth;\n  rect.width = element.clientWidth;\n  rect.height = element.clientHeight;\n  rect.x = rect.left;\n  rect.y = rect.top;\n  return rect;\n}\n\nfunction getClientRectFromMixedType(element, clippingParent, strategy) {\n  return clippingParent === viewport ? rectToClientRect(getViewportRect(element, strategy)) : isElement(clippingParent) ? getInnerBoundingClientRect(clippingParent, strategy) : rectToClientRect(getDocumentRect(getDocumentElement(element)));\n} // A \"clipping parent\" is an overflowable container with the characteristic of\n// clipping (or hiding) overflowing elements with a position different from\n// `initial`\n\n\nfunction getClippingParents(element) {\n  var clippingParents = listScrollParents(getParentNode(element));\n  var canEscapeClipping = ['absolute', 'fixed'].indexOf(getComputedStyle(element).position) >= 0;\n  var clipperElement = canEscapeClipping && isHTMLElement(element) ? getOffsetParent(element) : element;\n\n  if (!isElement(clipperElement)) {\n    return [];\n  } // $FlowFixMe[incompatible-return]: https://github.com/facebook/flow/issues/1414\n\n\n  return clippingParents.filter(function (clippingParent) {\n    return isElement(clippingParent) && contains(clippingParent, clipperElement) && getNodeName(clippingParent) !== 'body';\n  });\n} // Gets the maximum area that the element is visible in due to any number of\n// clipping parents\n\n\nexport default function getClippingRect(element, boundary, rootBoundary, strategy) {\n  var mainClippingParents = boundary === 'clippingParents' ? getClippingParents(element) : [].concat(boundary);\n  var clippingParents = [].concat(mainClippingParents, [rootBoundary]);\n  var firstClippingParent = clippingParents[0];\n  var clippingRect = clippingParents.reduce(function (accRect, clippingParent) {\n    var rect = getClientRectFromMixedType(element, clippingParent, strategy);\n    accRect.top = max(rect.top, accRect.top);\n    accRect.right = min(rect.right, accRect.right);\n    accRect.bottom = min(rect.bottom, accRect.bottom);\n    accRect.left = max(rect.left, accRect.left);\n    return accRect;\n  }, getClientRectFromMixedType(element, firstClippingParent, strategy));\n  clippingRect.width = clippingRect.right - clippingRect.left;\n  clippingRect.height = clippingRect.bottom - clippingRect.top;\n  clippingRect.x = clippingRect.left;\n  clippingRect.y = clippingRect.top;\n  return clippingRect;\n}","import getWindow from \"./getWindow.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getViewportRect(element, strategy) {\n  var win = getWindow(element);\n  var html = getDocumentElement(element);\n  var visualViewport = win.visualViewport;\n  var width = html.clientWidth;\n  var height = html.clientHeight;\n  var x = 0;\n  var y = 0;\n\n  if (visualViewport) {\n    width = visualViewport.width;\n    height = visualViewport.height;\n    var layoutViewport = isLayoutViewport();\n\n    if (layoutViewport || !layoutViewport && strategy === 'fixed') {\n      x = visualViewport.offsetLeft;\n      y = visualViewport.offsetTop;\n    }\n  }\n\n  return {\n    width: width,\n    height: height,\n    x: x + getWindowScrollBarX(element),\n    y: y\n  };\n}","import getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nimport { max } from \"../utils/math.js\"; // Gets the entire size of the scrollable document area, even extending outside\n// of the `` and `` rect bounds if horizontally scrollable\n\nexport default function getDocumentRect(element) {\n  var _element$ownerDocumen;\n\n  var html = getDocumentElement(element);\n  var winScroll = getWindowScroll(element);\n  var body = (_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body;\n  var width = max(html.scrollWidth, html.clientWidth, body ? body.scrollWidth : 0, body ? body.clientWidth : 0);\n  var height = max(html.scrollHeight, html.clientHeight, body ? body.scrollHeight : 0, body ? body.clientHeight : 0);\n  var x = -winScroll.scrollLeft + getWindowScrollBarX(element);\n  var y = -winScroll.scrollTop;\n\n  if (getComputedStyle(body || html).direction === 'rtl') {\n    x += max(html.clientWidth, body ? body.clientWidth : 0) - width;\n  }\n\n  return {\n    width: width,\n    height: height,\n    x: x,\n    y: y\n  };\n}","import getBasePlacement from \"./getBasePlacement.js\";\nimport getVariation from \"./getVariation.js\";\nimport getMainAxisFromPlacement from \"./getMainAxisFromPlacement.js\";\nimport { top, right, bottom, left, start, end } from \"../enums.js\";\nexport default function computeOffsets(_ref) {\n  var reference = _ref.reference,\n      element = _ref.element,\n      placement = _ref.placement;\n  var basePlacement = placement ? getBasePlacement(placement) : null;\n  var variation = placement ? getVariation(placement) : null;\n  var commonX = reference.x + reference.width / 2 - element.width / 2;\n  var commonY = reference.y + reference.height / 2 - element.height / 2;\n  var offsets;\n\n  switch (basePlacement) {\n    case top:\n      offsets = {\n        x: commonX,\n        y: reference.y - element.height\n      };\n      break;\n\n    case bottom:\n      offsets = {\n        x: commonX,\n        y: reference.y + reference.height\n      };\n      break;\n\n    case right:\n      offsets = {\n        x: reference.x + reference.width,\n        y: commonY\n      };\n      break;\n\n    case left:\n      offsets = {\n        x: reference.x - element.width,\n        y: commonY\n      };\n      break;\n\n    default:\n      offsets = {\n        x: reference.x,\n        y: reference.y\n      };\n  }\n\n  var mainAxis = basePlacement ? getMainAxisFromPlacement(basePlacement) : null;\n\n  if (mainAxis != null) {\n    var len = mainAxis === 'y' ? 'height' : 'width';\n\n    switch (variation) {\n      case start:\n        offsets[mainAxis] = offsets[mainAxis] - (reference[len] / 2 - element[len] / 2);\n        break;\n\n      case end:\n        offsets[mainAxis] = offsets[mainAxis] + (reference[len] / 2 - element[len] / 2);\n        break;\n\n      default:\n    }\n  }\n\n  return offsets;\n}","import getClippingRect from \"../dom-utils/getClippingRect.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getBoundingClientRect from \"../dom-utils/getBoundingClientRect.js\";\nimport computeOffsets from \"./computeOffsets.js\";\nimport rectToClientRect from \"./rectToClientRect.js\";\nimport { clippingParents, reference, popper, bottom, top, right, basePlacements, viewport } from \"../enums.js\";\nimport { isElement } from \"../dom-utils/instanceOf.js\";\nimport mergePaddingObject from \"./mergePaddingObject.js\";\nimport expandToHashMap from \"./expandToHashMap.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport default function detectOverflow(state, options) {\n  if (options === void 0) {\n    options = {};\n  }\n\n  var _options = options,\n      _options$placement = _options.placement,\n      placement = _options$placement === void 0 ? state.placement : _options$placement,\n      _options$strategy = _options.strategy,\n      strategy = _options$strategy === void 0 ? state.strategy : _options$strategy,\n      _options$boundary = _options.boundary,\n      boundary = _options$boundary === void 0 ? clippingParents : _options$boundary,\n      _options$rootBoundary = _options.rootBoundary,\n      rootBoundary = _options$rootBoundary === void 0 ? viewport : _options$rootBoundary,\n      _options$elementConte = _options.elementContext,\n      elementContext = _options$elementConte === void 0 ? popper : _options$elementConte,\n      _options$altBoundary = _options.altBoundary,\n      altBoundary = _options$altBoundary === void 0 ? false : _options$altBoundary,\n      _options$padding = _options.padding,\n      padding = _options$padding === void 0 ? 0 : _options$padding;\n  var paddingObject = mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n  var altContext = elementContext === popper ? reference : popper;\n  var popperRect = state.rects.popper;\n  var element = state.elements[altBoundary ? altContext : elementContext];\n  var clippingClientRect = getClippingRect(isElement(element) ? element : element.contextElement || getDocumentElement(state.elements.popper), boundary, rootBoundary, strategy);\n  var referenceClientRect = getBoundingClientRect(state.elements.reference);\n  var popperOffsets = computeOffsets({\n    reference: referenceClientRect,\n    element: popperRect,\n    strategy: 'absolute',\n    placement: placement\n  });\n  var popperClientRect = rectToClientRect(Object.assign({}, popperRect, popperOffsets));\n  var elementClientRect = elementContext === popper ? popperClientRect : referenceClientRect; // positive = overflowing the clipping rect\n  // 0 or negative = within the clipping rect\n\n  var overflowOffsets = {\n    top: clippingClientRect.top - elementClientRect.top + paddingObject.top,\n    bottom: elementClientRect.bottom - clippingClientRect.bottom + paddingObject.bottom,\n    left: clippingClientRect.left - elementClientRect.left + paddingObject.left,\n    right: elementClientRect.right - clippingClientRect.right + paddingObject.right\n  };\n  var offsetData = state.modifiersData.offset; // Offsets can be applied only to the popper element\n\n  if (elementContext === popper && offsetData) {\n    var offset = offsetData[placement];\n    Object.keys(overflowOffsets).forEach(function (key) {\n      var multiply = [right, bottom].indexOf(key) >= 0 ? 1 : -1;\n      var axis = [top, bottom].indexOf(key) >= 0 ? 'y' : 'x';\n      overflowOffsets[key] += offset[axis] * multiply;\n    });\n  }\n\n  return overflowOffsets;\n}","import getVariation from \"./getVariation.js\";\nimport { variationPlacements, basePlacements, placements as allPlacements } from \"../enums.js\";\nimport detectOverflow from \"./detectOverflow.js\";\nimport getBasePlacement from \"./getBasePlacement.js\";\nexport default function computeAutoPlacement(state, options) {\n  if (options === void 0) {\n    options = {};\n  }\n\n  var _options = options,\n      placement = _options.placement,\n      boundary = _options.boundary,\n      rootBoundary = _options.rootBoundary,\n      padding = _options.padding,\n      flipVariations = _options.flipVariations,\n      _options$allowedAutoP = _options.allowedAutoPlacements,\n      allowedAutoPlacements = _options$allowedAutoP === void 0 ? allPlacements : _options$allowedAutoP;\n  var variation = getVariation(placement);\n  var placements = variation ? flipVariations ? variationPlacements : variationPlacements.filter(function (placement) {\n    return getVariation(placement) === variation;\n  }) : basePlacements;\n  var allowedPlacements = placements.filter(function (placement) {\n    return allowedAutoPlacements.indexOf(placement) >= 0;\n  });\n\n  if (allowedPlacements.length === 0) {\n    allowedPlacements = placements;\n  } // $FlowFixMe[incompatible-type]: Flow seems to have problems with two array unions...\n\n\n  var overflows = allowedPlacements.reduce(function (acc, placement) {\n    acc[placement] = detectOverflow(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      padding: padding\n    })[getBasePlacement(placement)];\n    return acc;\n  }, {});\n  return Object.keys(overflows).sort(function (a, b) {\n    return overflows[a] - overflows[b];\n  });\n}","import getOppositePlacement from \"../utils/getOppositePlacement.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getOppositeVariationPlacement from \"../utils/getOppositeVariationPlacement.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport computeAutoPlacement from \"../utils/computeAutoPlacement.js\";\nimport { bottom, top, start, right, left, auto } from \"../enums.js\";\nimport getVariation from \"../utils/getVariation.js\"; // eslint-disable-next-line import/no-unused-modules\n\nfunction getExpandedFallbackPlacements(placement) {\n  if (getBasePlacement(placement) === auto) {\n    return [];\n  }\n\n  var oppositePlacement = getOppositePlacement(placement);\n  return [getOppositeVariationPlacement(placement), oppositePlacement, getOppositeVariationPlacement(oppositePlacement)];\n}\n\nfunction flip(_ref) {\n  var state = _ref.state,\n      options = _ref.options,\n      name = _ref.name;\n\n  if (state.modifiersData[name]._skip) {\n    return;\n  }\n\n  var _options$mainAxis = options.mainAxis,\n      checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n      _options$altAxis = options.altAxis,\n      checkAltAxis = _options$altAxis === void 0 ? true : _options$altAxis,\n      specifiedFallbackPlacements = options.fallbackPlacements,\n      padding = options.padding,\n      boundary = options.boundary,\n      rootBoundary = options.rootBoundary,\n      altBoundary = options.altBoundary,\n      _options$flipVariatio = options.flipVariations,\n      flipVariations = _options$flipVariatio === void 0 ? true : _options$flipVariatio,\n      allowedAutoPlacements = options.allowedAutoPlacements;\n  var preferredPlacement = state.options.placement;\n  var basePlacement = getBasePlacement(preferredPlacement);\n  var isBasePlacement = basePlacement === preferredPlacement;\n  var fallbackPlacements = specifiedFallbackPlacements || (isBasePlacement || !flipVariations ? [getOppositePlacement(preferredPlacement)] : getExpandedFallbackPlacements(preferredPlacement));\n  var placements = [preferredPlacement].concat(fallbackPlacements).reduce(function (acc, placement) {\n    return acc.concat(getBasePlacement(placement) === auto ? computeAutoPlacement(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      padding: padding,\n      flipVariations: flipVariations,\n      allowedAutoPlacements: allowedAutoPlacements\n    }) : placement);\n  }, []);\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var checksMap = new Map();\n  var makeFallbackChecks = true;\n  var firstFittingPlacement = placements[0];\n\n  for (var i = 0; i < placements.length; i++) {\n    var placement = placements[i];\n\n    var _basePlacement = getBasePlacement(placement);\n\n    var isStartVariation = getVariation(placement) === start;\n    var isVertical = [top, bottom].indexOf(_basePlacement) >= 0;\n    var len = isVertical ? 'width' : 'height';\n    var overflow = detectOverflow(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      altBoundary: altBoundary,\n      padding: padding\n    });\n    var mainVariationSide = isVertical ? isStartVariation ? right : left : isStartVariation ? bottom : top;\n\n    if (referenceRect[len] > popperRect[len]) {\n      mainVariationSide = getOppositePlacement(mainVariationSide);\n    }\n\n    var altVariationSide = getOppositePlacement(mainVariationSide);\n    var checks = [];\n\n    if (checkMainAxis) {\n      checks.push(overflow[_basePlacement] <= 0);\n    }\n\n    if (checkAltAxis) {\n      checks.push(overflow[mainVariationSide] <= 0, overflow[altVariationSide] <= 0);\n    }\n\n    if (checks.every(function (check) {\n      return check;\n    })) {\n      firstFittingPlacement = placement;\n      makeFallbackChecks = false;\n      break;\n    }\n\n    checksMap.set(placement, checks);\n  }\n\n  if (makeFallbackChecks) {\n    // `2` may be desired in some cases – research later\n    var numberOfChecks = flipVariations ? 3 : 1;\n\n    var _loop = function _loop(_i) {\n      var fittingPlacement = placements.find(function (placement) {\n        var checks = checksMap.get(placement);\n\n        if (checks) {\n          return checks.slice(0, _i).every(function (check) {\n            return check;\n          });\n        }\n      });\n\n      if (fittingPlacement) {\n        firstFittingPlacement = fittingPlacement;\n        return \"break\";\n      }\n    };\n\n    for (var _i = numberOfChecks; _i > 0; _i--) {\n      var _ret = _loop(_i);\n\n      if (_ret === \"break\") break;\n    }\n  }\n\n  if (state.placement !== firstFittingPlacement) {\n    state.modifiersData[name]._skip = true;\n    state.placement = firstFittingPlacement;\n    state.reset = true;\n  }\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'flip',\n  enabled: true,\n  phase: 'main',\n  fn: flip,\n  requiresIfExists: ['offset'],\n  data: {\n    _skip: false\n  }\n};","import { top, bottom, left, right } from \"../enums.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\n\nfunction getSideOffsets(overflow, rect, preventedOffsets) {\n  if (preventedOffsets === void 0) {\n    preventedOffsets = {\n      x: 0,\n      y: 0\n    };\n  }\n\n  return {\n    top: overflow.top - rect.height - preventedOffsets.y,\n    right: overflow.right - rect.width + preventedOffsets.x,\n    bottom: overflow.bottom - rect.height + preventedOffsets.y,\n    left: overflow.left - rect.width - preventedOffsets.x\n  };\n}\n\nfunction isAnySideFullyClipped(overflow) {\n  return [top, right, bottom, left].some(function (side) {\n    return overflow[side] >= 0;\n  });\n}\n\nfunction hide(_ref) {\n  var state = _ref.state,\n      name = _ref.name;\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var preventedOffsets = state.modifiersData.preventOverflow;\n  var referenceOverflow = detectOverflow(state, {\n    elementContext: 'reference'\n  });\n  var popperAltOverflow = detectOverflow(state, {\n    altBoundary: true\n  });\n  var referenceClippingOffsets = getSideOffsets(referenceOverflow, referenceRect);\n  var popperEscapeOffsets = getSideOffsets(popperAltOverflow, popperRect, preventedOffsets);\n  var isReferenceHidden = isAnySideFullyClipped(referenceClippingOffsets);\n  var hasPopperEscaped = isAnySideFullyClipped(popperEscapeOffsets);\n  state.modifiersData[name] = {\n    referenceClippingOffsets: referenceClippingOffsets,\n    popperEscapeOffsets: popperEscapeOffsets,\n    isReferenceHidden: isReferenceHidden,\n    hasPopperEscaped: hasPopperEscaped\n  };\n  state.attributes.popper = Object.assign({}, state.attributes.popper, {\n    'data-popper-reference-hidden': isReferenceHidden,\n    'data-popper-escaped': hasPopperEscaped\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'hide',\n  enabled: true,\n  phase: 'main',\n  requiresIfExists: ['preventOverflow'],\n  fn: hide\n};","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport { top, left, right, placements } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport function distanceAndSkiddingToXY(placement, rects, offset) {\n  var basePlacement = getBasePlacement(placement);\n  var invertDistance = [left, top].indexOf(basePlacement) >= 0 ? -1 : 1;\n\n  var _ref = typeof offset === 'function' ? offset(Object.assign({}, rects, {\n    placement: placement\n  })) : offset,\n      skidding = _ref[0],\n      distance = _ref[1];\n\n  skidding = skidding || 0;\n  distance = (distance || 0) * invertDistance;\n  return [left, right].indexOf(basePlacement) >= 0 ? {\n    x: distance,\n    y: skidding\n  } : {\n    x: skidding,\n    y: distance\n  };\n}\n\nfunction offset(_ref2) {\n  var state = _ref2.state,\n      options = _ref2.options,\n      name = _ref2.name;\n  var _options$offset = options.offset,\n      offset = _options$offset === void 0 ? [0, 0] : _options$offset;\n  var data = placements.reduce(function (acc, placement) {\n    acc[placement] = distanceAndSkiddingToXY(placement, state.rects, offset);\n    return acc;\n  }, {});\n  var _data$state$placement = data[state.placement],\n      x = _data$state$placement.x,\n      y = _data$state$placement.y;\n\n  if (state.modifiersData.popperOffsets != null) {\n    state.modifiersData.popperOffsets.x += x;\n    state.modifiersData.popperOffsets.y += y;\n  }\n\n  state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'offset',\n  enabled: true,\n  phase: 'main',\n  requires: ['popperOffsets'],\n  fn: offset\n};","import computeOffsets from \"../utils/computeOffsets.js\";\n\nfunction popperOffsets(_ref) {\n  var state = _ref.state,\n      name = _ref.name;\n  // Offsets are the actual position the popper needs to have to be\n  // properly positioned near its reference element\n  // This is the most basic placement, and will be adjusted by\n  // the modifiers in the next step\n  state.modifiersData[name] = computeOffsets({\n    reference: state.rects.reference,\n    element: state.rects.popper,\n    strategy: 'absolute',\n    placement: state.placement\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'popperOffsets',\n  enabled: true,\n  phase: 'read',\n  fn: popperOffsets,\n  data: {}\n};","import { top, left, right, bottom, start } from \"../enums.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport getAltAxis from \"../utils/getAltAxis.js\";\nimport { within, withinMaxClamp } from \"../utils/within.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport getFreshSideObject from \"../utils/getFreshSideObject.js\";\nimport { min as mathMin, max as mathMax } from \"../utils/math.js\";\n\nfunction preventOverflow(_ref) {\n  var state = _ref.state,\n      options = _ref.options,\n      name = _ref.name;\n  var _options$mainAxis = options.mainAxis,\n      checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n      _options$altAxis = options.altAxis,\n      checkAltAxis = _options$altAxis === void 0 ? false : _options$altAxis,\n      boundary = options.boundary,\n      rootBoundary = options.rootBoundary,\n      altBoundary = options.altBoundary,\n      padding = options.padding,\n      _options$tether = options.tether,\n      tether = _options$tether === void 0 ? true : _options$tether,\n      _options$tetherOffset = options.tetherOffset,\n      tetherOffset = _options$tetherOffset === void 0 ? 0 : _options$tetherOffset;\n  var overflow = detectOverflow(state, {\n    boundary: boundary,\n    rootBoundary: rootBoundary,\n    padding: padding,\n    altBoundary: altBoundary\n  });\n  var basePlacement = getBasePlacement(state.placement);\n  var variation = getVariation(state.placement);\n  var isBasePlacement = !variation;\n  var mainAxis = getMainAxisFromPlacement(basePlacement);\n  var altAxis = getAltAxis(mainAxis);\n  var popperOffsets = state.modifiersData.popperOffsets;\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var tetherOffsetValue = typeof tetherOffset === 'function' ? tetherOffset(Object.assign({}, state.rects, {\n    placement: state.placement\n  })) : tetherOffset;\n  var normalizedTetherOffsetValue = typeof tetherOffsetValue === 'number' ? {\n    mainAxis: tetherOffsetValue,\n    altAxis: tetherOffsetValue\n  } : Object.assign({\n    mainAxis: 0,\n    altAxis: 0\n  }, tetherOffsetValue);\n  var offsetModifierState = state.modifiersData.offset ? state.modifiersData.offset[state.placement] : null;\n  var data = {\n    x: 0,\n    y: 0\n  };\n\n  if (!popperOffsets) {\n    return;\n  }\n\n  if (checkMainAxis) {\n    var _offsetModifierState$;\n\n    var mainSide = mainAxis === 'y' ? top : left;\n    var altSide = mainAxis === 'y' ? bottom : right;\n    var len = mainAxis === 'y' ? 'height' : 'width';\n    var offset = popperOffsets[mainAxis];\n    var min = offset + overflow[mainSide];\n    var max = offset - overflow[altSide];\n    var additive = tether ? -popperRect[len] / 2 : 0;\n    var minLen = variation === start ? referenceRect[len] : popperRect[len];\n    var maxLen = variation === start ? -popperRect[len] : -referenceRect[len]; // We need to include the arrow in the calculation so the arrow doesn't go\n    // outside the reference bounds\n\n    var arrowElement = state.elements.arrow;\n    var arrowRect = tether && arrowElement ? getLayoutRect(arrowElement) : {\n      width: 0,\n      height: 0\n    };\n    var arrowPaddingObject = state.modifiersData['arrow#persistent'] ? state.modifiersData['arrow#persistent'].padding : getFreshSideObject();\n    var arrowPaddingMin = arrowPaddingObject[mainSide];\n    var arrowPaddingMax = arrowPaddingObject[altSide]; // If the reference length is smaller than the arrow length, we don't want\n    // to include its full size in the calculation. If the reference is small\n    // and near the edge of a boundary, the popper can overflow even if the\n    // reference is not overflowing as well (e.g. virtual elements with no\n    // width or height)\n\n    var arrowLen = within(0, referenceRect[len], arrowRect[len]);\n    var minOffset = isBasePlacement ? referenceRect[len] / 2 - additive - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis : minLen - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis;\n    var maxOffset = isBasePlacement ? -referenceRect[len] / 2 + additive + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis : maxLen + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis;\n    var arrowOffsetParent = state.elements.arrow && getOffsetParent(state.elements.arrow);\n    var clientOffset = arrowOffsetParent ? mainAxis === 'y' ? arrowOffsetParent.clientTop || 0 : arrowOffsetParent.clientLeft || 0 : 0;\n    var offsetModifierValue = (_offsetModifierState$ = offsetModifierState == null ? void 0 : offsetModifierState[mainAxis]) != null ? _offsetModifierState$ : 0;\n    var tetherMin = offset + minOffset - offsetModifierValue - clientOffset;\n    var tetherMax = offset + maxOffset - offsetModifierValue;\n    var preventedOffset = within(tether ? mathMin(min, tetherMin) : min, offset, tether ? mathMax(max, tetherMax) : max);\n    popperOffsets[mainAxis] = preventedOffset;\n    data[mainAxis] = preventedOffset - offset;\n  }\n\n  if (checkAltAxis) {\n    var _offsetModifierState$2;\n\n    var _mainSide = mainAxis === 'x' ? top : left;\n\n    var _altSide = mainAxis === 'x' ? bottom : right;\n\n    var _offset = popperOffsets[altAxis];\n\n    var _len = altAxis === 'y' ? 'height' : 'width';\n\n    var _min = _offset + overflow[_mainSide];\n\n    var _max = _offset - overflow[_altSide];\n\n    var isOriginSide = [top, left].indexOf(basePlacement) !== -1;\n\n    var _offsetModifierValue = (_offsetModifierState$2 = offsetModifierState == null ? void 0 : offsetModifierState[altAxis]) != null ? _offsetModifierState$2 : 0;\n\n    var _tetherMin = isOriginSide ? _min : _offset - referenceRect[_len] - popperRect[_len] - _offsetModifierValue + normalizedTetherOffsetValue.altAxis;\n\n    var _tetherMax = isOriginSide ? _offset + referenceRect[_len] + popperRect[_len] - _offsetModifierValue - normalizedTetherOffsetValue.altAxis : _max;\n\n    var _preventedOffset = tether && isOriginSide ? withinMaxClamp(_tetherMin, _offset, _tetherMax) : within(tether ? _tetherMin : _min, _offset, tether ? _tetherMax : _max);\n\n    popperOffsets[altAxis] = _preventedOffset;\n    data[altAxis] = _preventedOffset - _offset;\n  }\n\n  state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'preventOverflow',\n  enabled: true,\n  phase: 'main',\n  fn: preventOverflow,\n  requiresIfExists: ['offset']\n};","export default function getAltAxis(axis) {\n  return axis === 'x' ? 'y' : 'x';\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getNodeScroll from \"./getNodeScroll.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport { round } from \"../utils/math.js\";\n\nfunction isElementScaled(element) {\n  var rect = element.getBoundingClientRect();\n  var scaleX = round(rect.width) / element.offsetWidth || 1;\n  var scaleY = round(rect.height) / element.offsetHeight || 1;\n  return scaleX !== 1 || scaleY !== 1;\n} // Returns the composite rect of an element relative to its offsetParent.\n// Composite means it takes into account transforms as well as layout.\n\n\nexport default function getCompositeRect(elementOrVirtualElement, offsetParent, isFixed) {\n  if (isFixed === void 0) {\n    isFixed = false;\n  }\n\n  var isOffsetParentAnElement = isHTMLElement(offsetParent);\n  var offsetParentIsScaled = isHTMLElement(offsetParent) && isElementScaled(offsetParent);\n  var documentElement = getDocumentElement(offsetParent);\n  var rect = getBoundingClientRect(elementOrVirtualElement, offsetParentIsScaled, isFixed);\n  var scroll = {\n    scrollLeft: 0,\n    scrollTop: 0\n  };\n  var offsets = {\n    x: 0,\n    y: 0\n  };\n\n  if (isOffsetParentAnElement || !isOffsetParentAnElement && !isFixed) {\n    if (getNodeName(offsetParent) !== 'body' || // https://github.com/popperjs/popper-core/issues/1078\n    isScrollParent(documentElement)) {\n      scroll = getNodeScroll(offsetParent);\n    }\n\n    if (isHTMLElement(offsetParent)) {\n      offsets = getBoundingClientRect(offsetParent, true);\n      offsets.x += offsetParent.clientLeft;\n      offsets.y += offsetParent.clientTop;\n    } else if (documentElement) {\n      offsets.x = getWindowScrollBarX(documentElement);\n    }\n  }\n\n  return {\n    x: rect.left + scroll.scrollLeft - offsets.x,\n    y: rect.top + scroll.scrollTop - offsets.y,\n    width: rect.width,\n    height: rect.height\n  };\n}","import getWindowScroll from \"./getWindowScroll.js\";\nimport getWindow from \"./getWindow.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getHTMLElementScroll from \"./getHTMLElementScroll.js\";\nexport default function getNodeScroll(node) {\n  if (node === getWindow(node) || !isHTMLElement(node)) {\n    return getWindowScroll(node);\n  } else {\n    return getHTMLElementScroll(node);\n  }\n}","export default function getHTMLElementScroll(element) {\n  return {\n    scrollLeft: element.scrollLeft,\n    scrollTop: element.scrollTop\n  };\n}","import { modifierPhases } from \"../enums.js\"; // source: https://stackoverflow.com/questions/49875255\n\nfunction order(modifiers) {\n  var map = new Map();\n  var visited = new Set();\n  var result = [];\n  modifiers.forEach(function (modifier) {\n    map.set(modifier.name, modifier);\n  }); // On visiting object, check for its dependencies and visit them recursively\n\n  function sort(modifier) {\n    visited.add(modifier.name);\n    var requires = [].concat(modifier.requires || [], modifier.requiresIfExists || []);\n    requires.forEach(function (dep) {\n      if (!visited.has(dep)) {\n        var depModifier = map.get(dep);\n\n        if (depModifier) {\n          sort(depModifier);\n        }\n      }\n    });\n    result.push(modifier);\n  }\n\n  modifiers.forEach(function (modifier) {\n    if (!visited.has(modifier.name)) {\n      // check for visited object\n      sort(modifier);\n    }\n  });\n  return result;\n}\n\nexport default function orderModifiers(modifiers) {\n  // order based on dependencies\n  var orderedModifiers = order(modifiers); // order based on phase\n\n  return modifierPhases.reduce(function (acc, phase) {\n    return acc.concat(orderedModifiers.filter(function (modifier) {\n      return modifier.phase === phase;\n    }));\n  }, []);\n}","import getCompositeRect from \"./dom-utils/getCompositeRect.js\";\nimport getLayoutRect from \"./dom-utils/getLayoutRect.js\";\nimport listScrollParents from \"./dom-utils/listScrollParents.js\";\nimport getOffsetParent from \"./dom-utils/getOffsetParent.js\";\nimport orderModifiers from \"./utils/orderModifiers.js\";\nimport debounce from \"./utils/debounce.js\";\nimport mergeByName from \"./utils/mergeByName.js\";\nimport detectOverflow from \"./utils/detectOverflow.js\";\nimport { isElement } from \"./dom-utils/instanceOf.js\";\nvar DEFAULT_OPTIONS = {\n  placement: 'bottom',\n  modifiers: [],\n  strategy: 'absolute'\n};\n\nfunction areValidElements() {\n  for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n    args[_key] = arguments[_key];\n  }\n\n  return !args.some(function (element) {\n    return !(element && typeof element.getBoundingClientRect === 'function');\n  });\n}\n\nexport function popperGenerator(generatorOptions) {\n  if (generatorOptions === void 0) {\n    generatorOptions = {};\n  }\n\n  var _generatorOptions = generatorOptions,\n      _generatorOptions$def = _generatorOptions.defaultModifiers,\n      defaultModifiers = _generatorOptions$def === void 0 ? [] : _generatorOptions$def,\n      _generatorOptions$def2 = _generatorOptions.defaultOptions,\n      defaultOptions = _generatorOptions$def2 === void 0 ? DEFAULT_OPTIONS : _generatorOptions$def2;\n  return function createPopper(reference, popper, options) {\n    if (options === void 0) {\n      options = defaultOptions;\n    }\n\n    var state = {\n      placement: 'bottom',\n      orderedModifiers: [],\n      options: Object.assign({}, DEFAULT_OPTIONS, defaultOptions),\n      modifiersData: {},\n      elements: {\n        reference: reference,\n        popper: popper\n      },\n      attributes: {},\n      styles: {}\n    };\n    var effectCleanupFns = [];\n    var isDestroyed = false;\n    var instance = {\n      state: state,\n      setOptions: function setOptions(setOptionsAction) {\n        var options = typeof setOptionsAction === 'function' ? setOptionsAction(state.options) : setOptionsAction;\n        cleanupModifierEffects();\n        state.options = Object.assign({}, defaultOptions, state.options, options);\n        state.scrollParents = {\n          reference: isElement(reference) ? listScrollParents(reference) : reference.contextElement ? listScrollParents(reference.contextElement) : [],\n          popper: listScrollParents(popper)\n        }; // Orders the modifiers based on their dependencies and `phase`\n        // properties\n\n        var orderedModifiers = orderModifiers(mergeByName([].concat(defaultModifiers, state.options.modifiers))); // Strip out disabled modifiers\n\n        state.orderedModifiers = orderedModifiers.filter(function (m) {\n          return m.enabled;\n        });\n        runModifierEffects();\n        return instance.update();\n      },\n      // Sync update – it will always be executed, even if not necessary. This\n      // is useful for low frequency updates where sync behavior simplifies the\n      // logic.\n      // For high frequency updates (e.g. `resize` and `scroll` events), always\n      // prefer the async Popper#update method\n      forceUpdate: function forceUpdate() {\n        if (isDestroyed) {\n          return;\n        }\n\n        var _state$elements = state.elements,\n            reference = _state$elements.reference,\n            popper = _state$elements.popper; // Don't proceed if `reference` or `popper` are not valid elements\n        // anymore\n\n        if (!areValidElements(reference, popper)) {\n          return;\n        } // Store the reference and popper rects to be read by modifiers\n\n\n        state.rects = {\n          reference: getCompositeRect(reference, getOffsetParent(popper), state.options.strategy === 'fixed'),\n          popper: getLayoutRect(popper)\n        }; // Modifiers have the ability to reset the current update cycle. The\n        // most common use case for this is the `flip` modifier changing the\n        // placement, which then needs to re-run all the modifiers, because the\n        // logic was previously ran for the previous placement and is therefore\n        // stale/incorrect\n\n        state.reset = false;\n        state.placement = state.options.placement; // On each update cycle, the `modifiersData` property for each modifier\n        // is filled with the initial data specified by the modifier. This means\n        // it doesn't persist and is fresh on each update.\n        // To ensure persistent data, use `${name}#persistent`\n\n        state.orderedModifiers.forEach(function (modifier) {\n          return state.modifiersData[modifier.name] = Object.assign({}, modifier.data);\n        });\n\n        for (var index = 0; index < state.orderedModifiers.length; index++) {\n          if (state.reset === true) {\n            state.reset = false;\n            index = -1;\n            continue;\n          }\n\n          var _state$orderedModifie = state.orderedModifiers[index],\n              fn = _state$orderedModifie.fn,\n              _state$orderedModifie2 = _state$orderedModifie.options,\n              _options = _state$orderedModifie2 === void 0 ? {} : _state$orderedModifie2,\n              name = _state$orderedModifie.name;\n\n          if (typeof fn === 'function') {\n            state = fn({\n              state: state,\n              options: _options,\n              name: name,\n              instance: instance\n            }) || state;\n          }\n        }\n      },\n      // Async and optimistically optimized update – it will not be executed if\n      // not necessary (debounced to run at most once-per-tick)\n      update: debounce(function () {\n        return new Promise(function (resolve) {\n          instance.forceUpdate();\n          resolve(state);\n        });\n      }),\n      destroy: function destroy() {\n        cleanupModifierEffects();\n        isDestroyed = true;\n      }\n    };\n\n    if (!areValidElements(reference, popper)) {\n      return instance;\n    }\n\n    instance.setOptions(options).then(function (state) {\n      if (!isDestroyed && options.onFirstUpdate) {\n        options.onFirstUpdate(state);\n      }\n    }); // Modifiers have the ability to execute arbitrary code before the first\n    // update cycle runs. They will be executed in the same order as the update\n    // cycle. This is useful when a modifier adds some persistent data that\n    // other modifiers need to use, but the modifier is run after the dependent\n    // one.\n\n    function runModifierEffects() {\n      state.orderedModifiers.forEach(function (_ref) {\n        var name = _ref.name,\n            _ref$options = _ref.options,\n            options = _ref$options === void 0 ? {} : _ref$options,\n            effect = _ref.effect;\n\n        if (typeof effect === 'function') {\n          var cleanupFn = effect({\n            state: state,\n            name: name,\n            instance: instance,\n            options: options\n          });\n\n          var noopFn = function noopFn() {};\n\n          effectCleanupFns.push(cleanupFn || noopFn);\n        }\n      });\n    }\n\n    function cleanupModifierEffects() {\n      effectCleanupFns.forEach(function (fn) {\n        return fn();\n      });\n      effectCleanupFns = [];\n    }\n\n    return instance;\n  };\n}\nexport var createPopper = /*#__PURE__*/popperGenerator(); // eslint-disable-next-line import/no-unused-modules\n\nexport { detectOverflow };","export default function debounce(fn) {\n  var pending;\n  return function () {\n    if (!pending) {\n      pending = new Promise(function (resolve) {\n        Promise.resolve().then(function () {\n          pending = undefined;\n          resolve(fn());\n        });\n      });\n    }\n\n    return pending;\n  };\n}","export default function mergeByName(modifiers) {\n  var merged = modifiers.reduce(function (merged, current) {\n    var existing = merged[current.name];\n    merged[current.name] = existing ? Object.assign({}, existing, current, {\n      options: Object.assign({}, existing.options, current.options),\n      data: Object.assign({}, existing.data, current.data)\n    }) : current;\n    return merged;\n  }, {}); // IE11 does not support Object.values\n\n  return Object.keys(merged).map(function (key) {\n    return merged[key];\n  });\n}","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles];\nvar createPopper = /*#__PURE__*/popperGenerator({\n  defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow };","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nimport offset from \"./modifiers/offset.js\";\nimport flip from \"./modifiers/flip.js\";\nimport preventOverflow from \"./modifiers/preventOverflow.js\";\nimport arrow from \"./modifiers/arrow.js\";\nimport hide from \"./modifiers/hide.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles, offset, flip, preventOverflow, arrow, hide];\nvar createPopper = /*#__PURE__*/popperGenerator({\n  defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow }; // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper as createPopperLite } from \"./popper-lite.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport * from \"./modifiers/index.js\";","/**\n * --------------------------------------------------------------------------\n * Bootstrap dropdown.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport * as Popper from '@popperjs/core'\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport {\n  defineJQueryPlugin,\n  execute,\n  getElement,\n  getNextActiveElement,\n  isDisabled,\n  isElement,\n  isRTL,\n  isVisible,\n  noop\n} from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'dropdown'\nconst DATA_KEY = 'bs.dropdown'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst ESCAPE_KEY = 'Escape'\nconst TAB_KEY = 'Tab'\nconst ARROW_UP_KEY = 'ArrowUp'\nconst ARROW_DOWN_KEY = 'ArrowDown'\nconst RIGHT_MOUSE_BUTTON = 2 // MouseEvent.button value for the secondary button, usually the right button\n\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYDOWN_DATA_API = `keydown${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYUP_DATA_API = `keyup${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_DROPUP = 'dropup'\nconst CLASS_NAME_DROPEND = 'dropend'\nconst CLASS_NAME_DROPSTART = 'dropstart'\nconst CLASS_NAME_DROPUP_CENTER = 'dropup-center'\nconst CLASS_NAME_DROPDOWN_CENTER = 'dropdown-center'\n\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"dropdown\"]:not(.disabled):not(:disabled)'\nconst SELECTOR_DATA_TOGGLE_SHOWN = `${SELECTOR_DATA_TOGGLE}.${CLASS_NAME_SHOW}`\nconst SELECTOR_MENU = '.dropdown-menu'\nconst SELECTOR_NAVBAR = '.navbar'\nconst SELECTOR_NAVBAR_NAV = '.navbar-nav'\nconst SELECTOR_VISIBLE_ITEMS = '.dropdown-menu .dropdown-item:not(.disabled):not(:disabled)'\n\nconst PLACEMENT_TOP = isRTL() ? 'top-end' : 'top-start'\nconst PLACEMENT_TOPEND = isRTL() ? 'top-start' : 'top-end'\nconst PLACEMENT_BOTTOM = isRTL() ? 'bottom-end' : 'bottom-start'\nconst PLACEMENT_BOTTOMEND = isRTL() ? 'bottom-start' : 'bottom-end'\nconst PLACEMENT_RIGHT = isRTL() ? 'left-start' : 'right-start'\nconst PLACEMENT_LEFT = isRTL() ? 'right-start' : 'left-start'\nconst PLACEMENT_TOPCENTER = 'top'\nconst PLACEMENT_BOTTOMCENTER = 'bottom'\n\nconst Default = {\n  autoClose: true,\n  boundary: 'clippingParents',\n  display: 'dynamic',\n  offset: [0, 2],\n  popperConfig: null,\n  reference: 'toggle'\n}\n\nconst DefaultType = {\n  autoClose: '(boolean|string)',\n  boundary: '(string|element)',\n  display: 'string',\n  offset: '(array|string|function)',\n  popperConfig: '(null|object|function)',\n  reference: '(string|element|object)'\n}\n\n/**\n * Class definition\n */\n\nclass Dropdown extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._popper = null\n    this._parent = this._element.parentNode // dropdown wrapper\n    // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n    this._menu = SelectorEngine.next(this._element, SELECTOR_MENU)[0] ||\n      SelectorEngine.prev(this._element, SELECTOR_MENU)[0] ||\n      SelectorEngine.findOne(SELECTOR_MENU, this._parent)\n    this._inNavbar = this._detectNavbar()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle() {\n    return this._isShown() ? this.hide() : this.show()\n  }\n\n  show() {\n    if (isDisabled(this._element) || this._isShown()) {\n      return\n    }\n\n    const relatedTarget = {\n      relatedTarget: this._element\n    }\n\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, relatedTarget)\n\n    if (showEvent.defaultPrevented) {\n      return\n    }\n\n    this._createPopper()\n\n    // If this is a touch-enabled device we add extra\n    // empty mouseover listeners to the body's immediate children;\n    // only needed because of broken event delegation on iOS\n    // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n    if ('ontouchstart' in document.documentElement && !this._parent.closest(SELECTOR_NAVBAR_NAV)) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.on(element, 'mouseover', noop)\n      }\n    }\n\n    this._element.focus()\n    this._element.setAttribute('aria-expanded', true)\n\n    this._menu.classList.add(CLASS_NAME_SHOW)\n    this._element.classList.add(CLASS_NAME_SHOW)\n    EventHandler.trigger(this._element, EVENT_SHOWN, relatedTarget)\n  }\n\n  hide() {\n    if (isDisabled(this._element) || !this._isShown()) {\n      return\n    }\n\n    const relatedTarget = {\n      relatedTarget: this._element\n    }\n\n    this._completeHide(relatedTarget)\n  }\n\n  dispose() {\n    if (this._popper) {\n      this._popper.destroy()\n    }\n\n    super.dispose()\n  }\n\n  update() {\n    this._inNavbar = this._detectNavbar()\n    if (this._popper) {\n      this._popper.update()\n    }\n  }\n\n  // Private\n  _completeHide(relatedTarget) {\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE, relatedTarget)\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    // If this is a touch-enabled device we remove the extra\n    // empty mouseover listeners we added for iOS support\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.off(element, 'mouseover', noop)\n      }\n    }\n\n    if (this._popper) {\n      this._popper.destroy()\n    }\n\n    this._menu.classList.remove(CLASS_NAME_SHOW)\n    this._element.classList.remove(CLASS_NAME_SHOW)\n    this._element.setAttribute('aria-expanded', 'false')\n    Manipulator.removeDataAttribute(this._menu, 'popper')\n    EventHandler.trigger(this._element, EVENT_HIDDEN, relatedTarget)\n  }\n\n  _getConfig(config) {\n    config = super._getConfig(config)\n\n    if (typeof config.reference === 'object' && !isElement(config.reference) &&\n      typeof config.reference.getBoundingClientRect !== 'function'\n    ) {\n      // Popper virtual elements require a getBoundingClientRect method\n      throw new TypeError(`${NAME.toUpperCase()}: Option \"reference\" provided type \"object\" without a required \"getBoundingClientRect\" method.`)\n    }\n\n    return config\n  }\n\n  _createPopper() {\n    if (typeof Popper === 'undefined') {\n      throw new TypeError('Bootstrap\\'s dropdowns require Popper (https://popper.js.org)')\n    }\n\n    let referenceElement = this._element\n\n    if (this._config.reference === 'parent') {\n      referenceElement = this._parent\n    } else if (isElement(this._config.reference)) {\n      referenceElement = getElement(this._config.reference)\n    } else if (typeof this._config.reference === 'object') {\n      referenceElement = this._config.reference\n    }\n\n    const popperConfig = this._getPopperConfig()\n    this._popper = Popper.createPopper(referenceElement, this._menu, popperConfig)\n  }\n\n  _isShown() {\n    return this._menu.classList.contains(CLASS_NAME_SHOW)\n  }\n\n  _getPlacement() {\n    const parentDropdown = this._parent\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPEND)) {\n      return PLACEMENT_RIGHT\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPSTART)) {\n      return PLACEMENT_LEFT\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPUP_CENTER)) {\n      return PLACEMENT_TOPCENTER\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPDOWN_CENTER)) {\n      return PLACEMENT_BOTTOMCENTER\n    }\n\n    // We need to trim the value because custom properties can also include spaces\n    const isEnd = getComputedStyle(this._menu).getPropertyValue('--bs-position').trim() === 'end'\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPUP)) {\n      return isEnd ? PLACEMENT_TOPEND : PLACEMENT_TOP\n    }\n\n    return isEnd ? PLACEMENT_BOTTOMEND : PLACEMENT_BOTTOM\n  }\n\n  _detectNavbar() {\n    return this._element.closest(SELECTOR_NAVBAR) !== null\n  }\n\n  _getOffset() {\n    const { offset } = this._config\n\n    if (typeof offset === 'string') {\n      return offset.split(',').map(value => Number.parseInt(value, 10))\n    }\n\n    if (typeof offset === 'function') {\n      return popperData => offset(popperData, this._element)\n    }\n\n    return offset\n  }\n\n  _getPopperConfig() {\n    const defaultBsPopperConfig = {\n      placement: this._getPlacement(),\n      modifiers: [{\n        name: 'preventOverflow',\n        options: {\n          boundary: this._config.boundary\n        }\n      },\n      {\n        name: 'offset',\n        options: {\n          offset: this._getOffset()\n        }\n      }]\n    }\n\n    // Disable Popper if we have a static display or Dropdown is in Navbar\n    if (this._inNavbar || this._config.display === 'static') {\n      Manipulator.setDataAttribute(this._menu, 'popper', 'static') // TODO: v6 remove\n      defaultBsPopperConfig.modifiers = [{\n        name: 'applyStyles',\n        enabled: false\n      }]\n    }\n\n    return {\n      ...defaultBsPopperConfig,\n      ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n    }\n  }\n\n  _selectMenuItem({ key, target }) {\n    const items = SelectorEngine.find(SELECTOR_VISIBLE_ITEMS, this._menu).filter(element => isVisible(element))\n\n    if (!items.length) {\n      return\n    }\n\n    // if target isn't included in items (e.g. when expanding the dropdown)\n    // allow cycling to get the last item in case key equals ARROW_UP_KEY\n    getNextActiveElement(items, target, key === ARROW_DOWN_KEY, !items.includes(target)).focus()\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Dropdown.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config]()\n    })\n  }\n\n  static clearMenus(event) {\n    if (event.button === RIGHT_MOUSE_BUTTON || (event.type === 'keyup' && event.key !== TAB_KEY)) {\n      return\n    }\n\n    const openToggles = SelectorEngine.find(SELECTOR_DATA_TOGGLE_SHOWN)\n\n    for (const toggle of openToggles) {\n      const context = Dropdown.getInstance(toggle)\n      if (!context || context._config.autoClose === false) {\n        continue\n      }\n\n      const composedPath = event.composedPath()\n      const isMenuTarget = composedPath.includes(context._menu)\n      if (\n        composedPath.includes(context._element) ||\n        (context._config.autoClose === 'inside' && !isMenuTarget) ||\n        (context._config.autoClose === 'outside' && isMenuTarget)\n      ) {\n        continue\n      }\n\n      // Tab navigation through the dropdown menu or events from contained inputs shouldn't close the menu\n      if (context._menu.contains(event.target) && ((event.type === 'keyup' && event.key === TAB_KEY) || /input|select|option|textarea|form/i.test(event.target.tagName))) {\n        continue\n      }\n\n      const relatedTarget = { relatedTarget: context._element }\n\n      if (event.type === 'click') {\n        relatedTarget.clickEvent = event\n      }\n\n      context._completeHide(relatedTarget)\n    }\n  }\n\n  static dataApiKeydownHandler(event) {\n    // If not an UP | DOWN | ESCAPE key => not a dropdown command\n    // If input/textarea && if key is other than ESCAPE => not a dropdown command\n\n    const isInput = /input|textarea/i.test(event.target.tagName)\n    const isEscapeEvent = event.key === ESCAPE_KEY\n    const isUpOrDownEvent = [ARROW_UP_KEY, ARROW_DOWN_KEY].includes(event.key)\n\n    if (!isUpOrDownEvent && !isEscapeEvent) {\n      return\n    }\n\n    if (isInput && !isEscapeEvent) {\n      return\n    }\n\n    event.preventDefault()\n\n    // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n    const getToggleButton = this.matches(SELECTOR_DATA_TOGGLE) ?\n      this :\n      (SelectorEngine.prev(this, SELECTOR_DATA_TOGGLE)[0] ||\n        SelectorEngine.next(this, SELECTOR_DATA_TOGGLE)[0] ||\n        SelectorEngine.findOne(SELECTOR_DATA_TOGGLE, event.delegateTarget.parentNode))\n\n    const instance = Dropdown.getOrCreateInstance(getToggleButton)\n\n    if (isUpOrDownEvent) {\n      event.stopPropagation()\n      instance.show()\n      instance._selectMenuItem(event)\n      return\n    }\n\n    if (instance._isShown()) { // else is escape and we check if it is shown\n      event.stopPropagation()\n      instance.hide()\n      getToggleButton.focus()\n    }\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_DATA_TOGGLE, Dropdown.dataApiKeydownHandler)\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_MENU, Dropdown.dataApiKeydownHandler)\nEventHandler.on(document, EVENT_CLICK_DATA_API, Dropdown.clearMenus)\nEventHandler.on(document, EVENT_KEYUP_DATA_API, Dropdown.clearMenus)\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  event.preventDefault()\n  Dropdown.getOrCreateInstance(this).toggle()\n})\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Dropdown)\n\nexport default Dropdown\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/backdrop.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport Config from './config.js'\nimport { execute, executeAfterTransition, getElement, reflow } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'backdrop'\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\nconst EVENT_MOUSEDOWN = `mousedown.bs.${NAME}`\n\nconst Default = {\n  className: 'modal-backdrop',\n  clickCallback: null,\n  isAnimated: false,\n  isVisible: true, // if false, we use the backdrop helper without adding any element to the dom\n  rootElement: 'body' // give the choice to place backdrop under different elements\n}\n\nconst DefaultType = {\n  className: 'string',\n  clickCallback: '(function|null)',\n  isAnimated: 'boolean',\n  isVisible: 'boolean',\n  rootElement: '(element|string)'\n}\n\n/**\n * Class definition\n */\n\nclass Backdrop extends Config {\n  constructor(config) {\n    super()\n    this._config = this._getConfig(config)\n    this._isAppended = false\n    this._element = null\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  show(callback) {\n    if (!this._config.isVisible) {\n      execute(callback)\n      return\n    }\n\n    this._append()\n\n    const element = this._getElement()\n    if (this._config.isAnimated) {\n      reflow(element)\n    }\n\n    element.classList.add(CLASS_NAME_SHOW)\n\n    this._emulateAnimation(() => {\n      execute(callback)\n    })\n  }\n\n  hide(callback) {\n    if (!this._config.isVisible) {\n      execute(callback)\n      return\n    }\n\n    this._getElement().classList.remove(CLASS_NAME_SHOW)\n\n    this._emulateAnimation(() => {\n      this.dispose()\n      execute(callback)\n    })\n  }\n\n  dispose() {\n    if (!this._isAppended) {\n      return\n    }\n\n    EventHandler.off(this._element, EVENT_MOUSEDOWN)\n\n    this._element.remove()\n    this._isAppended = false\n  }\n\n  // Private\n  _getElement() {\n    if (!this._element) {\n      const backdrop = document.createElement('div')\n      backdrop.className = this._config.className\n      if (this._config.isAnimated) {\n        backdrop.classList.add(CLASS_NAME_FADE)\n      }\n\n      this._element = backdrop\n    }\n\n    return this._element\n  }\n\n  _configAfterMerge(config) {\n    // use getElement() with the default \"body\" to get a fresh Element on each instantiation\n    config.rootElement = getElement(config.rootElement)\n    return config\n  }\n\n  _append() {\n    if (this._isAppended) {\n      return\n    }\n\n    const element = this._getElement()\n    this._config.rootElement.append(element)\n\n    EventHandler.on(element, EVENT_MOUSEDOWN, () => {\n      execute(this._config.clickCallback)\n    })\n\n    this._isAppended = true\n  }\n\n  _emulateAnimation(callback) {\n    executeAfterTransition(callback, this._getElement(), this._config.isAnimated)\n  }\n}\n\nexport default Backdrop\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/focustrap.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport EventHandler from '../dom/event-handler.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport Config from './config.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'focustrap'\nconst DATA_KEY = 'bs.focustrap'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst EVENT_FOCUSIN = `focusin${EVENT_KEY}`\nconst EVENT_KEYDOWN_TAB = `keydown.tab${EVENT_KEY}`\n\nconst TAB_KEY = 'Tab'\nconst TAB_NAV_FORWARD = 'forward'\nconst TAB_NAV_BACKWARD = 'backward'\n\nconst Default = {\n  autofocus: true,\n  trapElement: null // The element to trap focus inside of\n}\n\nconst DefaultType = {\n  autofocus: 'boolean',\n  trapElement: 'element'\n}\n\n/**\n * Class definition\n */\n\nclass FocusTrap extends Config {\n  constructor(config) {\n    super()\n    this._config = this._getConfig(config)\n    this._isActive = false\n    this._lastTabNavDirection = null\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  activate() {\n    if (this._isActive) {\n      return\n    }\n\n    if (this._config.autofocus) {\n      this._config.trapElement.focus()\n    }\n\n    EventHandler.off(document, EVENT_KEY) // guard against infinite focus loop\n    EventHandler.on(document, EVENT_FOCUSIN, event => this._handleFocusin(event))\n    EventHandler.on(document, EVENT_KEYDOWN_TAB, event => this._handleKeydown(event))\n\n    this._isActive = true\n  }\n\n  deactivate() {\n    if (!this._isActive) {\n      return\n    }\n\n    this._isActive = false\n    EventHandler.off(document, EVENT_KEY)\n  }\n\n  // Private\n  _handleFocusin(event) {\n    const { trapElement } = this._config\n\n    if (event.target === document || event.target === trapElement || trapElement.contains(event.target)) {\n      return\n    }\n\n    const elements = SelectorEngine.focusableChildren(trapElement)\n\n    if (elements.length === 0) {\n      trapElement.focus()\n    } else if (this._lastTabNavDirection === TAB_NAV_BACKWARD) {\n      elements[elements.length - 1].focus()\n    } else {\n      elements[0].focus()\n    }\n  }\n\n  _handleKeydown(event) {\n    if (event.key !== TAB_KEY) {\n      return\n    }\n\n    this._lastTabNavDirection = event.shiftKey ? TAB_NAV_BACKWARD : TAB_NAV_FORWARD\n  }\n}\n\nexport default FocusTrap\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/scrollBar.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Manipulator from '../dom/manipulator.js'\nimport SelectorEngine from '../dom/selector-engine.js'\nimport { isElement } from './index.js'\n\n/**\n * Constants\n */\n\nconst SELECTOR_FIXED_CONTENT = '.fixed-top, .fixed-bottom, .is-fixed, .sticky-top'\nconst SELECTOR_STICKY_CONTENT = '.sticky-top'\nconst PROPERTY_PADDING = 'padding-right'\nconst PROPERTY_MARGIN = 'margin-right'\n\n/**\n * Class definition\n */\n\nclass ScrollBarHelper {\n  constructor() {\n    this._element = document.body\n  }\n\n  // Public\n  getWidth() {\n    // https://developer.mozilla.org/en-US/docs/Web/API/Window/innerWidth#usage_notes\n    const documentWidth = document.documentElement.clientWidth\n    return Math.abs(window.innerWidth - documentWidth)\n  }\n\n  hide() {\n    const width = this.getWidth()\n    this._disableOverFlow()\n    // give padding to element to balance the hidden scrollbar width\n    this._setElementAttributes(this._element, PROPERTY_PADDING, calculatedValue => calculatedValue + width)\n    // trick: We adjust positive paddingRight and negative marginRight to sticky-top elements to keep showing fullwidth\n    this._setElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING, calculatedValue => calculatedValue + width)\n    this._setElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN, calculatedValue => calculatedValue - width)\n  }\n\n  reset() {\n    this._resetElementAttributes(this._element, 'overflow')\n    this._resetElementAttributes(this._element, PROPERTY_PADDING)\n    this._resetElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING)\n    this._resetElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN)\n  }\n\n  isOverflowing() {\n    return this.getWidth() > 0\n  }\n\n  // Private\n  _disableOverFlow() {\n    this._saveInitialAttribute(this._element, 'overflow')\n    this._element.style.overflow = 'hidden'\n  }\n\n  _setElementAttributes(selector, styleProperty, callback) {\n    const scrollbarWidth = this.getWidth()\n    const manipulationCallBack = element => {\n      if (element !== this._element && window.innerWidth > element.clientWidth + scrollbarWidth) {\n        return\n      }\n\n      this._saveInitialAttribute(element, styleProperty)\n      const calculatedValue = window.getComputedStyle(element).getPropertyValue(styleProperty)\n      element.style.setProperty(styleProperty, `${callback(Number.parseFloat(calculatedValue))}px`)\n    }\n\n    this._applyManipulationCallback(selector, manipulationCallBack)\n  }\n\n  _saveInitialAttribute(element, styleProperty) {\n    const actualValue = element.style.getPropertyValue(styleProperty)\n    if (actualValue) {\n      Manipulator.setDataAttribute(element, styleProperty, actualValue)\n    }\n  }\n\n  _resetElementAttributes(selector, styleProperty) {\n    const manipulationCallBack = element => {\n      const value = Manipulator.getDataAttribute(element, styleProperty)\n      // We only want to remove the property if the value is `null`; the value can also be zero\n      if (value === null) {\n        element.style.removeProperty(styleProperty)\n        return\n      }\n\n      Manipulator.removeDataAttribute(element, styleProperty)\n      element.style.setProperty(styleProperty, value)\n    }\n\n    this._applyManipulationCallback(selector, manipulationCallBack)\n  }\n\n  _applyManipulationCallback(selector, callBack) {\n    if (isElement(selector)) {\n      callBack(selector)\n      return\n    }\n\n    for (const sel of SelectorEngine.find(selector, this._element)) {\n      callBack(sel)\n    }\n  }\n}\n\nexport default ScrollBarHelper\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap modal.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport Backdrop from './util/backdrop.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport FocusTrap from './util/focustrap.js'\nimport { defineJQueryPlugin, isRTL, isVisible, reflow } from './util/index.js'\nimport ScrollBarHelper from './util/scrollbar.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'modal'\nconst DATA_KEY = 'bs.modal'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\nconst ESCAPE_KEY = 'Escape'\n\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_RESIZE = `resize${EVENT_KEY}`\nconst EVENT_CLICK_DISMISS = `click.dismiss${EVENT_KEY}`\nconst EVENT_MOUSEDOWN_DISMISS = `mousedown.dismiss${EVENT_KEY}`\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_OPEN = 'modal-open'\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_STATIC = 'modal-static'\n\nconst OPEN_SELECTOR = '.modal.show'\nconst SELECTOR_DIALOG = '.modal-dialog'\nconst SELECTOR_MODAL_BODY = '.modal-body'\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"modal\"]'\n\nconst Default = {\n  backdrop: true,\n  focus: true,\n  keyboard: true\n}\n\nconst DefaultType = {\n  backdrop: '(boolean|string)',\n  focus: 'boolean',\n  keyboard: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Modal extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._dialog = SelectorEngine.findOne(SELECTOR_DIALOG, this._element)\n    this._backdrop = this._initializeBackDrop()\n    this._focustrap = this._initializeFocusTrap()\n    this._isShown = false\n    this._isTransitioning = false\n    this._scrollBar = new ScrollBarHelper()\n\n    this._addEventListeners()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle(relatedTarget) {\n    return this._isShown ? this.hide() : this.show(relatedTarget)\n  }\n\n  show(relatedTarget) {\n    if (this._isShown || this._isTransitioning) {\n      return\n    }\n\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, {\n      relatedTarget\n    })\n\n    if (showEvent.defaultPrevented) {\n      return\n    }\n\n    this._isShown = true\n    this._isTransitioning = true\n\n    this._scrollBar.hide()\n\n    document.body.classList.add(CLASS_NAME_OPEN)\n\n    this._adjustDialog()\n\n    this._backdrop.show(() => this._showElement(relatedTarget))\n  }\n\n  hide() {\n    if (!this._isShown || this._isTransitioning) {\n      return\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    this._isShown = false\n    this._isTransitioning = true\n    this._focustrap.deactivate()\n\n    this._element.classList.remove(CLASS_NAME_SHOW)\n\n    this._queueCallback(() => this._hideModal(), this._element, this._isAnimated())\n  }\n\n  dispose() {\n    EventHandler.off(window, EVENT_KEY)\n    EventHandler.off(this._dialog, EVENT_KEY)\n\n    this._backdrop.dispose()\n    this._focustrap.deactivate()\n\n    super.dispose()\n  }\n\n  handleUpdate() {\n    this._adjustDialog()\n  }\n\n  // Private\n  _initializeBackDrop() {\n    return new Backdrop({\n      isVisible: Boolean(this._config.backdrop), // 'static' option will be translated to true, and booleans will keep their value,\n      isAnimated: this._isAnimated()\n    })\n  }\n\n  _initializeFocusTrap() {\n    return new FocusTrap({\n      trapElement: this._element\n    })\n  }\n\n  _showElement(relatedTarget) {\n    // try to append dynamic modal\n    if (!document.body.contains(this._element)) {\n      document.body.append(this._element)\n    }\n\n    this._element.style.display = 'block'\n    this._element.removeAttribute('aria-hidden')\n    this._element.setAttribute('aria-modal', true)\n    this._element.setAttribute('role', 'dialog')\n    this._element.scrollTop = 0\n\n    const modalBody = SelectorEngine.findOne(SELECTOR_MODAL_BODY, this._dialog)\n    if (modalBody) {\n      modalBody.scrollTop = 0\n    }\n\n    reflow(this._element)\n\n    this._element.classList.add(CLASS_NAME_SHOW)\n\n    const transitionComplete = () => {\n      if (this._config.focus) {\n        this._focustrap.activate()\n      }\n\n      this._isTransitioning = false\n      EventHandler.trigger(this._element, EVENT_SHOWN, {\n        relatedTarget\n      })\n    }\n\n    this._queueCallback(transitionComplete, this._dialog, this._isAnimated())\n  }\n\n  _addEventListeners() {\n    EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n      if (event.key !== ESCAPE_KEY) {\n        return\n      }\n\n      if (this._config.keyboard) {\n        this.hide()\n        return\n      }\n\n      this._triggerBackdropTransition()\n    })\n\n    EventHandler.on(window, EVENT_RESIZE, () => {\n      if (this._isShown && !this._isTransitioning) {\n        this._adjustDialog()\n      }\n    })\n\n    EventHandler.on(this._element, EVENT_MOUSEDOWN_DISMISS, event => {\n      // a bad trick to segregate clicks that may start inside dialog but end outside, and avoid listen to scrollbar clicks\n      EventHandler.one(this._element, EVENT_CLICK_DISMISS, event2 => {\n        if (this._element !== event.target || this._element !== event2.target) {\n          return\n        }\n\n        if (this._config.backdrop === 'static') {\n          this._triggerBackdropTransition()\n          return\n        }\n\n        if (this._config.backdrop) {\n          this.hide()\n        }\n      })\n    })\n  }\n\n  _hideModal() {\n    this._element.style.display = 'none'\n    this._element.setAttribute('aria-hidden', true)\n    this._element.removeAttribute('aria-modal')\n    this._element.removeAttribute('role')\n    this._isTransitioning = false\n\n    this._backdrop.hide(() => {\n      document.body.classList.remove(CLASS_NAME_OPEN)\n      this._resetAdjustments()\n      this._scrollBar.reset()\n      EventHandler.trigger(this._element, EVENT_HIDDEN)\n    })\n  }\n\n  _isAnimated() {\n    return this._element.classList.contains(CLASS_NAME_FADE)\n  }\n\n  _triggerBackdropTransition() {\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight\n    const initialOverflowY = this._element.style.overflowY\n    // return if the following background transition hasn't yet completed\n    if (initialOverflowY === 'hidden' || this._element.classList.contains(CLASS_NAME_STATIC)) {\n      return\n    }\n\n    if (!isModalOverflowing) {\n      this._element.style.overflowY = 'hidden'\n    }\n\n    this._element.classList.add(CLASS_NAME_STATIC)\n    this._queueCallback(() => {\n      this._element.classList.remove(CLASS_NAME_STATIC)\n      this._queueCallback(() => {\n        this._element.style.overflowY = initialOverflowY\n      }, this._dialog)\n    }, this._dialog)\n\n    this._element.focus()\n  }\n\n  /**\n   * The following methods are used to handle overflowing modals\n   */\n\n  _adjustDialog() {\n    const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight\n    const scrollbarWidth = this._scrollBar.getWidth()\n    const isBodyOverflowing = scrollbarWidth > 0\n\n    if (isBodyOverflowing && !isModalOverflowing) {\n      const property = isRTL() ? 'paddingLeft' : 'paddingRight'\n      this._element.style[property] = `${scrollbarWidth}px`\n    }\n\n    if (!isBodyOverflowing && isModalOverflowing) {\n      const property = isRTL() ? 'paddingRight' : 'paddingLeft'\n      this._element.style[property] = `${scrollbarWidth}px`\n    }\n  }\n\n  _resetAdjustments() {\n    this._element.style.paddingLeft = ''\n    this._element.style.paddingRight = ''\n  }\n\n  // Static\n  static jQueryInterface(config, relatedTarget) {\n    return this.each(function () {\n      const data = Modal.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config](relatedTarget)\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  const target = SelectorEngine.getElementFromSelector(this)\n\n  if (['A', 'AREA'].includes(this.tagName)) {\n    event.preventDefault()\n  }\n\n  EventHandler.one(target, EVENT_SHOW, showEvent => {\n    if (showEvent.defaultPrevented) {\n      // only register focus restorer if modal will actually get shown\n      return\n    }\n\n    EventHandler.one(target, EVENT_HIDDEN, () => {\n      if (isVisible(this)) {\n        this.focus()\n      }\n    })\n  })\n\n  // avoid conflict when clicking modal toggler while another one is open\n  const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR)\n  if (alreadyOpen) {\n    Modal.getInstance(alreadyOpen).hide()\n  }\n\n  const data = Modal.getOrCreateInstance(target)\n\n  data.toggle(this)\n})\n\nenableDismissTrigger(Modal)\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Modal)\n\nexport default Modal\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap offcanvas.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport Backdrop from './util/backdrop.js'\nimport { enableDismissTrigger } from './util/component-functions.js'\nimport FocusTrap from './util/focustrap.js'\nimport {\n  defineJQueryPlugin,\n  isDisabled,\n  isVisible\n} from './util/index.js'\nimport ScrollBarHelper from './util/scrollbar.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'offcanvas'\nconst DATA_KEY = 'bs.offcanvas'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\nconst ESCAPE_KEY = 'Escape'\n\nconst CLASS_NAME_SHOW = 'show'\nconst CLASS_NAME_SHOWING = 'showing'\nconst CLASS_NAME_HIDING = 'hiding'\nconst CLASS_NAME_BACKDROP = 'offcanvas-backdrop'\nconst OPEN_SELECTOR = '.offcanvas.show'\n\nconst EVENT_SHOW = `show${EVENT_KEY}`\nconst EVENT_SHOWN = `shown${EVENT_KEY}`\nconst EVENT_HIDE = `hide${EVENT_KEY}`\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY}`\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`\nconst EVENT_RESIZE = `resize${EVENT_KEY}`\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY}${DATA_API_KEY}`\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY}`\n\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"offcanvas\"]'\n\nconst Default = {\n  backdrop: true,\n  keyboard: true,\n  scroll: false\n}\n\nconst DefaultType = {\n  backdrop: '(boolean|string)',\n  keyboard: 'boolean',\n  scroll: 'boolean'\n}\n\n/**\n * Class definition\n */\n\nclass Offcanvas extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    this._isShown = false\n    this._backdrop = this._initializeBackDrop()\n    this._focustrap = this._initializeFocusTrap()\n    this._addEventListeners()\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  toggle(relatedTarget) {\n    return this._isShown ? this.hide() : this.show(relatedTarget)\n  }\n\n  show(relatedTarget) {\n    if (this._isShown) {\n      return\n    }\n\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW, { relatedTarget })\n\n    if (showEvent.defaultPrevented) {\n      return\n    }\n\n    this._isShown = true\n    this._backdrop.show()\n\n    if (!this._config.scroll) {\n      new ScrollBarHelper().hide()\n    }\n\n    this._element.setAttribute('aria-modal', true)\n    this._element.setAttribute('role', 'dialog')\n    this._element.classList.add(CLASS_NAME_SHOWING)\n\n    const completeCallBack = () => {\n      if (!this._config.scroll || this._config.backdrop) {\n        this._focustrap.activate()\n      }\n\n      this._element.classList.add(CLASS_NAME_SHOW)\n      this._element.classList.remove(CLASS_NAME_SHOWING)\n      EventHandler.trigger(this._element, EVENT_SHOWN, { relatedTarget })\n    }\n\n    this._queueCallback(completeCallBack, this._element, true)\n  }\n\n  hide() {\n    if (!this._isShown) {\n      return\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE)\n\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    this._focustrap.deactivate()\n    this._element.blur()\n    this._isShown = false\n    this._element.classList.add(CLASS_NAME_HIDING)\n    this._backdrop.hide()\n\n    const completeCallback = () => {\n      this._element.classList.remove(CLASS_NAME_SHOW, CLASS_NAME_HIDING)\n      this._element.removeAttribute('aria-modal')\n      this._element.removeAttribute('role')\n\n      if (!this._config.scroll) {\n        new ScrollBarHelper().reset()\n      }\n\n      EventHandler.trigger(this._element, EVENT_HIDDEN)\n    }\n\n    this._queueCallback(completeCallback, this._element, true)\n  }\n\n  dispose() {\n    this._backdrop.dispose()\n    this._focustrap.deactivate()\n    super.dispose()\n  }\n\n  // Private\n  _initializeBackDrop() {\n    const clickCallback = () => {\n      if (this._config.backdrop === 'static') {\n        EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n        return\n      }\n\n      this.hide()\n    }\n\n    // 'static' option will be translated to true, and booleans will keep their value\n    const isVisible = Boolean(this._config.backdrop)\n\n    return new Backdrop({\n      className: CLASS_NAME_BACKDROP,\n      isVisible,\n      isAnimated: true,\n      rootElement: this._element.parentNode,\n      clickCallback: isVisible ? clickCallback : null\n    })\n  }\n\n  _initializeFocusTrap() {\n    return new FocusTrap({\n      trapElement: this._element\n    })\n  }\n\n  _addEventListeners() {\n    EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n      if (event.key !== ESCAPE_KEY) {\n        return\n      }\n\n      if (this._config.keyboard) {\n        this.hide()\n        return\n      }\n\n      EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED)\n    })\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Offcanvas.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config](this)\n    })\n  }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  const target = SelectorEngine.getElementFromSelector(this)\n\n  if (['A', 'AREA'].includes(this.tagName)) {\n    event.preventDefault()\n  }\n\n  if (isDisabled(this)) {\n    return\n  }\n\n  EventHandler.one(target, EVENT_HIDDEN, () => {\n    // focus on trigger when it is closed\n    if (isVisible(this)) {\n      this.focus()\n    }\n  })\n\n  // avoid conflict when clicking a toggler of an offcanvas, while another is open\n  const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR)\n  if (alreadyOpen && alreadyOpen !== target) {\n    Offcanvas.getInstance(alreadyOpen).hide()\n  }\n\n  const data = Offcanvas.getOrCreateInstance(target)\n  data.toggle(this)\n})\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n  for (const selector of SelectorEngine.find(OPEN_SELECTOR)) {\n    Offcanvas.getOrCreateInstance(selector).show()\n  }\n})\n\nEventHandler.on(window, EVENT_RESIZE, () => {\n  for (const element of SelectorEngine.find('[aria-modal][class*=show][class*=offcanvas-]')) {\n    if (getComputedStyle(element).position !== 'fixed') {\n      Offcanvas.getOrCreateInstance(element).hide()\n    }\n  }\n})\n\nenableDismissTrigger(Offcanvas)\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Offcanvas)\n\nexport default Offcanvas\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/sanitizer.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n// js-docs-start allow-list\nconst ARIA_ATTRIBUTE_PATTERN = /^aria-[\\w-]*$/i\n\nexport const DefaultAllowlist = {\n  // Global attributes allowed on any supplied element below.\n  '*': ['class', 'dir', 'id', 'lang', 'role', ARIA_ATTRIBUTE_PATTERN],\n  a: ['target', 'href', 'title', 'rel'],\n  area: [],\n  b: [],\n  br: [],\n  col: [],\n  code: [],\n  div: [],\n  em: [],\n  hr: [],\n  h1: [],\n  h2: [],\n  h3: [],\n  h4: [],\n  h5: [],\n  h6: [],\n  i: [],\n  img: ['src', 'srcset', 'alt', 'title', 'width', 'height'],\n  li: [],\n  ol: [],\n  p: [],\n  pre: [],\n  s: [],\n  small: [],\n  span: [],\n  sub: [],\n  sup: [],\n  strong: [],\n  u: [],\n  ul: []\n}\n// js-docs-end allow-list\n\nconst uriAttributes = new Set([\n  'background',\n  'cite',\n  'href',\n  'itemtype',\n  'longdesc',\n  'poster',\n  'src',\n  'xlink:href'\n])\n\n/**\n * A pattern that recognizes URLs that are safe wrt. XSS in URL navigation\n * contexts.\n *\n * Shout-out to Angular https://github.com/angular/angular/blob/15.2.8/packages/core/src/sanitization/url_sanitizer.ts#L38\n */\n// eslint-disable-next-line unicorn/better-regex\nconst SAFE_URL_PATTERN = /^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i\n\nconst allowedAttribute = (attribute, allowedAttributeList) => {\n  const attributeName = attribute.nodeName.toLowerCase()\n\n  if (allowedAttributeList.includes(attributeName)) {\n    if (uriAttributes.has(attributeName)) {\n      return Boolean(SAFE_URL_PATTERN.test(attribute.nodeValue))\n    }\n\n    return true\n  }\n\n  // Check if a regular expression validates the attribute.\n  return allowedAttributeList.filter(attributeRegex => attributeRegex instanceof RegExp)\n    .some(regex => regex.test(attributeName))\n}\n\nexport function sanitizeHtml(unsafeHtml, allowList, sanitizeFunction) {\n  if (!unsafeHtml.length) {\n    return unsafeHtml\n  }\n\n  if (sanitizeFunction && typeof sanitizeFunction === 'function') {\n    return sanitizeFunction(unsafeHtml)\n  }\n\n  const domParser = new window.DOMParser()\n  const createdDocument = domParser.parseFromString(unsafeHtml, 'text/html')\n  const elements = [].concat(...createdDocument.body.querySelectorAll('*'))\n\n  for (const element of elements) {\n    const elementName = element.nodeName.toLowerCase()\n\n    if (!Object.keys(allowList).includes(elementName)) {\n      element.remove()\n      continue\n    }\n\n    const attributeList = [].concat(...element.attributes)\n    const allowedAttributes = [].concat(allowList['*'] || [], allowList[elementName] || [])\n\n    for (const attribute of attributeList) {\n      if (!allowedAttribute(attribute, allowedAttributes)) {\n        element.removeAttribute(attribute.nodeName)\n      }\n    }\n  }\n\n  return createdDocument.body.innerHTML\n}\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap util/template-factory.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport SelectorEngine from '../dom/selector-engine.js'\nimport Config from './config.js'\nimport { DefaultAllowlist, sanitizeHtml } from './sanitizer.js'\nimport { execute, getElement, isElement } from './index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'TemplateFactory'\n\nconst Default = {\n  allowList: DefaultAllowlist,\n  content: {}, // { selector : text ,  selector2 : text2 , }\n  extraClass: '',\n  html: false,\n  sanitize: true,\n  sanitizeFn: null,\n  template: '
    '\n}\n\nconst DefaultType = {\n  allowList: 'object',\n  content: 'object',\n  extraClass: '(string|function)',\n  html: 'boolean',\n  sanitize: 'boolean',\n  sanitizeFn: '(null|function)',\n  template: 'string'\n}\n\nconst DefaultContentType = {\n  entry: '(string|element|function|null)',\n  selector: '(string|element)'\n}\n\n/**\n * Class definition\n */\n\nclass TemplateFactory extends Config {\n  constructor(config) {\n    super()\n    this._config = this._getConfig(config)\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  getContent() {\n    return Object.values(this._config.content)\n      .map(config => this._resolvePossibleFunction(config))\n      .filter(Boolean)\n  }\n\n  hasContent() {\n    return this.getContent().length > 0\n  }\n\n  changeContent(content) {\n    this._checkContent(content)\n    this._config.content = { ...this._config.content, ...content }\n    return this\n  }\n\n  toHtml() {\n    const templateWrapper = document.createElement('div')\n    templateWrapper.innerHTML = this._maybeSanitize(this._config.template)\n\n    for (const [selector, text] of Object.entries(this._config.content)) {\n      this._setContent(templateWrapper, text, selector)\n    }\n\n    const template = templateWrapper.children[0]\n    const extraClass = this._resolvePossibleFunction(this._config.extraClass)\n\n    if (extraClass) {\n      template.classList.add(...extraClass.split(' '))\n    }\n\n    return template\n  }\n\n  // Private\n  _typeCheckConfig(config) {\n    super._typeCheckConfig(config)\n    this._checkContent(config.content)\n  }\n\n  _checkContent(arg) {\n    for (const [selector, content] of Object.entries(arg)) {\n      super._typeCheckConfig({ selector, entry: content }, DefaultContentType)\n    }\n  }\n\n  _setContent(template, content, selector) {\n    const templateElement = SelectorEngine.findOne(selector, template)\n\n    if (!templateElement) {\n      return\n    }\n\n    content = this._resolvePossibleFunction(content)\n\n    if (!content) {\n      templateElement.remove()\n      return\n    }\n\n    if (isElement(content)) {\n      this._putElementInTemplate(getElement(content), templateElement)\n      return\n    }\n\n    if (this._config.html) {\n      templateElement.innerHTML = this._maybeSanitize(content)\n      return\n    }\n\n    templateElement.textContent = content\n  }\n\n  _maybeSanitize(arg) {\n    return this._config.sanitize ? sanitizeHtml(arg, this._config.allowList, this._config.sanitizeFn) : arg\n  }\n\n  _resolvePossibleFunction(arg) {\n    return execute(arg, [this])\n  }\n\n  _putElementInTemplate(element, templateElement) {\n    if (this._config.html) {\n      templateElement.innerHTML = ''\n      templateElement.append(element)\n      return\n    }\n\n    templateElement.textContent = element.textContent\n  }\n}\n\nexport default TemplateFactory\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap tooltip.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport * as Popper from '@popperjs/core'\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport Manipulator from './dom/manipulator.js'\nimport { defineJQueryPlugin, execute, findShadowRoot, getElement, getUID, isRTL, noop } from './util/index.js'\nimport { DefaultAllowlist } from './util/sanitizer.js'\nimport TemplateFactory from './util/template-factory.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'tooltip'\nconst DISALLOWED_ATTRIBUTES = new Set(['sanitize', 'allowList', 'sanitizeFn'])\n\nconst CLASS_NAME_FADE = 'fade'\nconst CLASS_NAME_MODAL = 'modal'\nconst CLASS_NAME_SHOW = 'show'\n\nconst SELECTOR_TOOLTIP_INNER = '.tooltip-inner'\nconst SELECTOR_MODAL = `.${CLASS_NAME_MODAL}`\n\nconst EVENT_MODAL_HIDE = 'hide.bs.modal'\n\nconst TRIGGER_HOVER = 'hover'\nconst TRIGGER_FOCUS = 'focus'\nconst TRIGGER_CLICK = 'click'\nconst TRIGGER_MANUAL = 'manual'\n\nconst EVENT_HIDE = 'hide'\nconst EVENT_HIDDEN = 'hidden'\nconst EVENT_SHOW = 'show'\nconst EVENT_SHOWN = 'shown'\nconst EVENT_INSERTED = 'inserted'\nconst EVENT_CLICK = 'click'\nconst EVENT_FOCUSIN = 'focusin'\nconst EVENT_FOCUSOUT = 'focusout'\nconst EVENT_MOUSEENTER = 'mouseenter'\nconst EVENT_MOUSELEAVE = 'mouseleave'\n\nconst AttachmentMap = {\n  AUTO: 'auto',\n  TOP: 'top',\n  RIGHT: isRTL() ? 'left' : 'right',\n  BOTTOM: 'bottom',\n  LEFT: isRTL() ? 'right' : 'left'\n}\n\nconst Default = {\n  allowList: DefaultAllowlist,\n  animation: true,\n  boundary: 'clippingParents',\n  container: false,\n  customClass: '',\n  delay: 0,\n  fallbackPlacements: ['top', 'right', 'bottom', 'left'],\n  html: false,\n  offset: [0, 6],\n  placement: 'top',\n  popperConfig: null,\n  sanitize: true,\n  sanitizeFn: null,\n  selector: false,\n  template: '
    ' +\n            '
    ' +\n            '
    ' +\n            '
    ',\n  title: '',\n  trigger: 'hover focus'\n}\n\nconst DefaultType = {\n  allowList: 'object',\n  animation: 'boolean',\n  boundary: '(string|element)',\n  container: '(string|element|boolean)',\n  customClass: '(string|function)',\n  delay: '(number|object)',\n  fallbackPlacements: 'array',\n  html: 'boolean',\n  offset: '(array|string|function)',\n  placement: '(string|function)',\n  popperConfig: '(null|object|function)',\n  sanitize: 'boolean',\n  sanitizeFn: '(null|function)',\n  selector: '(string|boolean)',\n  template: 'string',\n  title: '(string|element|function)',\n  trigger: 'string'\n}\n\n/**\n * Class definition\n */\n\nclass Tooltip extends BaseComponent {\n  constructor(element, config) {\n    if (typeof Popper === 'undefined') {\n      throw new TypeError('Bootstrap\\'s tooltips require Popper (https://popper.js.org)')\n    }\n\n    super(element, config)\n\n    // Private\n    this._isEnabled = true\n    this._timeout = 0\n    this._isHovered = null\n    this._activeTrigger = {}\n    this._popper = null\n    this._templateFactory = null\n    this._newContent = null\n\n    // Protected\n    this.tip = null\n\n    this._setListeners()\n\n    if (!this._config.selector) {\n      this._fixTitle()\n    }\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  enable() {\n    this._isEnabled = true\n  }\n\n  disable() {\n    this._isEnabled = false\n  }\n\n  toggleEnabled() {\n    this._isEnabled = !this._isEnabled\n  }\n\n  toggle() {\n    if (!this._isEnabled) {\n      return\n    }\n\n    this._activeTrigger.click = !this._activeTrigger.click\n    if (this._isShown()) {\n      this._leave()\n      return\n    }\n\n    this._enter()\n  }\n\n  dispose() {\n    clearTimeout(this._timeout)\n\n    EventHandler.off(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler)\n\n    if (this._element.getAttribute('data-bs-original-title')) {\n      this._element.setAttribute('title', this._element.getAttribute('data-bs-original-title'))\n    }\n\n    this._disposePopper()\n    super.dispose()\n  }\n\n  show() {\n    if (this._element.style.display === 'none') {\n      throw new Error('Please use show on visible elements')\n    }\n\n    if (!(this._isWithContent() && this._isEnabled)) {\n      return\n    }\n\n    const showEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOW))\n    const shadowRoot = findShadowRoot(this._element)\n    const isInTheDom = (shadowRoot || this._element.ownerDocument.documentElement).contains(this._element)\n\n    if (showEvent.defaultPrevented || !isInTheDom) {\n      return\n    }\n\n    // TODO: v6 remove this or make it optional\n    this._disposePopper()\n\n    const tip = this._getTipElement()\n\n    this._element.setAttribute('aria-describedby', tip.getAttribute('id'))\n\n    const { container } = this._config\n\n    if (!this._element.ownerDocument.documentElement.contains(this.tip)) {\n      container.append(tip)\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_INSERTED))\n    }\n\n    this._popper = this._createPopper(tip)\n\n    tip.classList.add(CLASS_NAME_SHOW)\n\n    // If this is a touch-enabled device we add extra\n    // empty mouseover listeners to the body's immediate children;\n    // only needed because of broken event delegation on iOS\n    // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.on(element, 'mouseover', noop)\n      }\n    }\n\n    const complete = () => {\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOWN))\n\n      if (this._isHovered === false) {\n        this._leave()\n      }\n\n      this._isHovered = false\n    }\n\n    this._queueCallback(complete, this.tip, this._isAnimated())\n  }\n\n  hide() {\n    if (!this._isShown()) {\n      return\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDE))\n    if (hideEvent.defaultPrevented) {\n      return\n    }\n\n    const tip = this._getTipElement()\n    tip.classList.remove(CLASS_NAME_SHOW)\n\n    // If this is a touch-enabled device we remove the extra\n    // empty mouseover listeners we added for iOS support\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.off(element, 'mouseover', noop)\n      }\n    }\n\n    this._activeTrigger[TRIGGER_CLICK] = false\n    this._activeTrigger[TRIGGER_FOCUS] = false\n    this._activeTrigger[TRIGGER_HOVER] = false\n    this._isHovered = null // it is a trick to support manual triggering\n\n    const complete = () => {\n      if (this._isWithActiveTrigger()) {\n        return\n      }\n\n      if (!this._isHovered) {\n        this._disposePopper()\n      }\n\n      this._element.removeAttribute('aria-describedby')\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDDEN))\n    }\n\n    this._queueCallback(complete, this.tip, this._isAnimated())\n  }\n\n  update() {\n    if (this._popper) {\n      this._popper.update()\n    }\n  }\n\n  // Protected\n  _isWithContent() {\n    return Boolean(this._getTitle())\n  }\n\n  _getTipElement() {\n    if (!this.tip) {\n      this.tip = this._createTipElement(this._newContent || this._getContentForTemplate())\n    }\n\n    return this.tip\n  }\n\n  _createTipElement(content) {\n    const tip = this._getTemplateFactory(content).toHtml()\n\n    // TODO: remove this check in v6\n    if (!tip) {\n      return null\n    }\n\n    tip.classList.remove(CLASS_NAME_FADE, CLASS_NAME_SHOW)\n    // TODO: v6 the following can be achieved with CSS only\n    tip.classList.add(`bs-${this.constructor.NAME}-auto`)\n\n    const tipId = getUID(this.constructor.NAME).toString()\n\n    tip.setAttribute('id', tipId)\n\n    if (this._isAnimated()) {\n      tip.classList.add(CLASS_NAME_FADE)\n    }\n\n    return tip\n  }\n\n  setContent(content) {\n    this._newContent = content\n    if (this._isShown()) {\n      this._disposePopper()\n      this.show()\n    }\n  }\n\n  _getTemplateFactory(content) {\n    if (this._templateFactory) {\n      this._templateFactory.changeContent(content)\n    } else {\n      this._templateFactory = new TemplateFactory({\n        ...this._config,\n        // the `content` var has to be after `this._config`\n        // to override config.content in case of popover\n        content,\n        extraClass: this._resolvePossibleFunction(this._config.customClass)\n      })\n    }\n\n    return this._templateFactory\n  }\n\n  _getContentForTemplate() {\n    return {\n      [SELECTOR_TOOLTIP_INNER]: this._getTitle()\n    }\n  }\n\n  _getTitle() {\n    return this._resolvePossibleFunction(this._config.title) || this._element.getAttribute('data-bs-original-title')\n  }\n\n  // Private\n  _initializeOnDelegatedTarget(event) {\n    return this.constructor.getOrCreateInstance(event.delegateTarget, this._getDelegateConfig())\n  }\n\n  _isAnimated() {\n    return this._config.animation || (this.tip && this.tip.classList.contains(CLASS_NAME_FADE))\n  }\n\n  _isShown() {\n    return this.tip && this.tip.classList.contains(CLASS_NAME_SHOW)\n  }\n\n  _createPopper(tip) {\n    const placement = execute(this._config.placement, [this, tip, this._element])\n    const attachment = AttachmentMap[placement.toUpperCase()]\n    return Popper.createPopper(this._element, tip, this._getPopperConfig(attachment))\n  }\n\n  _getOffset() {\n    const { offset } = this._config\n\n    if (typeof offset === 'string') {\n      return offset.split(',').map(value => Number.parseInt(value, 10))\n    }\n\n    if (typeof offset === 'function') {\n      return popperData => offset(popperData, this._element)\n    }\n\n    return offset\n  }\n\n  _resolvePossibleFunction(arg) {\n    return execute(arg, [this._element])\n  }\n\n  _getPopperConfig(attachment) {\n    const defaultBsPopperConfig = {\n      placement: attachment,\n      modifiers: [\n        {\n          name: 'flip',\n          options: {\n            fallbackPlacements: this._config.fallbackPlacements\n          }\n        },\n        {\n          name: 'offset',\n          options: {\n            offset: this._getOffset()\n          }\n        },\n        {\n          name: 'preventOverflow',\n          options: {\n            boundary: this._config.boundary\n          }\n        },\n        {\n          name: 'arrow',\n          options: {\n            element: `.${this.constructor.NAME}-arrow`\n          }\n        },\n        {\n          name: 'preSetPlacement',\n          enabled: true,\n          phase: 'beforeMain',\n          fn: data => {\n            // Pre-set Popper's placement attribute in order to read the arrow sizes properly.\n            // Otherwise, Popper mixes up the width and height dimensions since the initial arrow style is for top placement\n            this._getTipElement().setAttribute('data-popper-placement', data.state.placement)\n          }\n        }\n      ]\n    }\n\n    return {\n      ...defaultBsPopperConfig,\n      ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n    }\n  }\n\n  _setListeners() {\n    const triggers = this._config.trigger.split(' ')\n\n    for (const trigger of triggers) {\n      if (trigger === 'click') {\n        EventHandler.on(this._element, this.constructor.eventName(EVENT_CLICK), this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event)\n          context.toggle()\n        })\n      } else if (trigger !== TRIGGER_MANUAL) {\n        const eventIn = trigger === TRIGGER_HOVER ?\n          this.constructor.eventName(EVENT_MOUSEENTER) :\n          this.constructor.eventName(EVENT_FOCUSIN)\n        const eventOut = trigger === TRIGGER_HOVER ?\n          this.constructor.eventName(EVENT_MOUSELEAVE) :\n          this.constructor.eventName(EVENT_FOCUSOUT)\n\n        EventHandler.on(this._element, eventIn, this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event)\n          context._activeTrigger[event.type === 'focusin' ? TRIGGER_FOCUS : TRIGGER_HOVER] = true\n          context._enter()\n        })\n        EventHandler.on(this._element, eventOut, this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event)\n          context._activeTrigger[event.type === 'focusout' ? TRIGGER_FOCUS : TRIGGER_HOVER] =\n            context._element.contains(event.relatedTarget)\n\n          context._leave()\n        })\n      }\n    }\n\n    this._hideModalHandler = () => {\n      if (this._element) {\n        this.hide()\n      }\n    }\n\n    EventHandler.on(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler)\n  }\n\n  _fixTitle() {\n    const title = this._element.getAttribute('title')\n\n    if (!title) {\n      return\n    }\n\n    if (!this._element.getAttribute('aria-label') && !this._element.textContent.trim()) {\n      this._element.setAttribute('aria-label', title)\n    }\n\n    this._element.setAttribute('data-bs-original-title', title) // DO NOT USE IT. Is only for backwards compatibility\n    this._element.removeAttribute('title')\n  }\n\n  _enter() {\n    if (this._isShown() || this._isHovered) {\n      this._isHovered = true\n      return\n    }\n\n    this._isHovered = true\n\n    this._setTimeout(() => {\n      if (this._isHovered) {\n        this.show()\n      }\n    }, this._config.delay.show)\n  }\n\n  _leave() {\n    if (this._isWithActiveTrigger()) {\n      return\n    }\n\n    this._isHovered = false\n\n    this._setTimeout(() => {\n      if (!this._isHovered) {\n        this.hide()\n      }\n    }, this._config.delay.hide)\n  }\n\n  _setTimeout(handler, timeout) {\n    clearTimeout(this._timeout)\n    this._timeout = setTimeout(handler, timeout)\n  }\n\n  _isWithActiveTrigger() {\n    return Object.values(this._activeTrigger).includes(true)\n  }\n\n  _getConfig(config) {\n    const dataAttributes = Manipulator.getDataAttributes(this._element)\n\n    for (const dataAttribute of Object.keys(dataAttributes)) {\n      if (DISALLOWED_ATTRIBUTES.has(dataAttribute)) {\n        delete dataAttributes[dataAttribute]\n      }\n    }\n\n    config = {\n      ...dataAttributes,\n      ...(typeof config === 'object' && config ? config : {})\n    }\n    config = this._mergeConfigObj(config)\n    config = this._configAfterMerge(config)\n    this._typeCheckConfig(config)\n    return config\n  }\n\n  _configAfterMerge(config) {\n    config.container = config.container === false ? document.body : getElement(config.container)\n\n    if (typeof config.delay === 'number') {\n      config.delay = {\n        show: config.delay,\n        hide: config.delay\n      }\n    }\n\n    if (typeof config.title === 'number') {\n      config.title = config.title.toString()\n    }\n\n    if (typeof config.content === 'number') {\n      config.content = config.content.toString()\n    }\n\n    return config\n  }\n\n  _getDelegateConfig() {\n    const config = {}\n\n    for (const [key, value] of Object.entries(this._config)) {\n      if (this.constructor.Default[key] !== value) {\n        config[key] = value\n      }\n    }\n\n    config.selector = false\n    config.trigger = 'manual'\n\n    // In the future can be replaced with:\n    // const keysWithDifferentValues = Object.entries(this._config).filter(entry => this.constructor.Default[entry[0]] !== this._config[entry[0]])\n    // `Object.fromEntries(keysWithDifferentValues)`\n    return config\n  }\n\n  _disposePopper() {\n    if (this._popper) {\n      this._popper.destroy()\n      this._popper = null\n    }\n\n    if (this.tip) {\n      this.tip.remove()\n      this.tip = null\n    }\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Tooltip.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config]()\n    })\n  }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Tooltip)\n\nexport default Tooltip\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap popover.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport Tooltip from './tooltip.js'\nimport { defineJQueryPlugin } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'popover'\n\nconst SELECTOR_TITLE = '.popover-header'\nconst SELECTOR_CONTENT = '.popover-body'\n\nconst Default = {\n  ...Tooltip.Default,\n  content: '',\n  offset: [0, 8],\n  placement: 'right',\n  template: '
    ' +\n    '
    ' +\n    '
    ' +\n    '
    ' +\n    '
    ',\n  trigger: 'click'\n}\n\nconst DefaultType = {\n  ...Tooltip.DefaultType,\n  content: '(null|string|element|function)'\n}\n\n/**\n * Class definition\n */\n\nclass Popover extends Tooltip {\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Overrides\n  _isWithContent() {\n    return this._getTitle() || this._getContent()\n  }\n\n  // Private\n  _getContentForTemplate() {\n    return {\n      [SELECTOR_TITLE]: this._getTitle(),\n      [SELECTOR_CONTENT]: this._getContent()\n    }\n  }\n\n  _getContent() {\n    return this._resolvePossibleFunction(this._config.content)\n  }\n\n  // Static\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Popover.getOrCreateInstance(this, config)\n\n      if (typeof config !== 'string') {\n        return\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`)\n      }\n\n      data[config]()\n    })\n  }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Popover)\n\nexport default Popover\n","/**\n * --------------------------------------------------------------------------\n * Bootstrap scrollspy.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nimport BaseComponent from './base-component.js'\nimport EventHandler from './dom/event-handler.js'\nimport SelectorEngine from './dom/selector-engine.js'\nimport { defineJQueryPlugin, getElement, isDisabled, isVisible } from './util/index.js'\n\n/**\n * Constants\n */\n\nconst NAME = 'scrollspy'\nconst DATA_KEY = 'bs.scrollspy'\nconst EVENT_KEY = `.${DATA_KEY}`\nconst DATA_API_KEY = '.data-api'\n\nconst EVENT_ACTIVATE = `activate${EVENT_KEY}`\nconst EVENT_CLICK = `click${EVENT_KEY}`\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY}${DATA_API_KEY}`\n\nconst CLASS_NAME_DROPDOWN_ITEM = 'dropdown-item'\nconst CLASS_NAME_ACTIVE = 'active'\n\nconst SELECTOR_DATA_SPY = '[data-bs-spy=\"scroll\"]'\nconst SELECTOR_TARGET_LINKS = '[href]'\nconst SELECTOR_NAV_LIST_GROUP = '.nav, .list-group'\nconst SELECTOR_NAV_LINKS = '.nav-link'\nconst SELECTOR_NAV_ITEMS = '.nav-item'\nconst SELECTOR_LIST_ITEMS = '.list-group-item'\nconst SELECTOR_LINK_ITEMS = `${SELECTOR_NAV_LINKS}, ${SELECTOR_NAV_ITEMS} > ${SELECTOR_NAV_LINKS}, ${SELECTOR_LIST_ITEMS}`\nconst SELECTOR_DROPDOWN = '.dropdown'\nconst SELECTOR_DROPDOWN_TOGGLE = '.dropdown-toggle'\n\nconst Default = {\n  offset: null, // TODO: v6 @deprecated, keep it for backwards compatibility reasons\n  rootMargin: '0px 0px -25%',\n  smoothScroll: false,\n  target: null,\n  threshold: [0.1, 0.5, 1]\n}\n\nconst DefaultType = {\n  offset: '(number|null)', // TODO v6 @deprecated, keep it for backwards compatibility reasons\n  rootMargin: 'string',\n  smoothScroll: 'boolean',\n  target: 'element',\n  threshold: 'array'\n}\n\n/**\n * Class definition\n */\n\nclass ScrollSpy extends BaseComponent {\n  constructor(element, config) {\n    super(element, config)\n\n    // this._element is the observablesContainer and config.target the menu links wrapper\n    this._targetLinks = new Map()\n    this._observableSections = new Map()\n    this._rootElement = getComputedStyle(this._element).overflowY === 'visible' ? null : this._element\n    this._activeTarget = null\n    this._observer = null\n    this._previousScrollData = {\n      visibleEntryTop: 0,\n      parentScrollTop: 0\n    }\n    this.refresh() // initialize\n  }\n\n  // Getters\n  static get Default() {\n    return Default\n  }\n\n  static get DefaultType() {\n    return DefaultType\n  }\n\n  static get NAME() {\n    return NAME\n  }\n\n  // Public\n  refresh() {\n    this._initializeTargetsAndObservables()\n    this._maybeEnableSmoothScroll()\n\n    if (this._observer) {\n      this._observer.disconnect()\n    } else {\n      this._observer = this._getNewObserver()\n    }\n\n    for (const section of this._observableSections.values()) {\n      this._observer.observe(section)\n    }\n  }\n\n  dispose() {\n    this._observer.disconnect()\n    super.dispose()\n  }\n\n  // Private\n  _configAfterMerge(config) {\n    // TODO: on v6 target should be given explicitly & remove the {target: 'ss-target'} case\n    config.target = getElement(config.target) || document.body\n\n    // TODO: v6 Only for backwards compatibility reasons. Use rootMargin only\n    config.rootMargin = config.offset ? `${config.offset}px 0px -30%` : config.rootMargin\n\n    if (typeof config.threshold === 'string') {\n      config.threshold = config.threshold.split(',').map(value => Number.parseFloat(value))\n    }\n\n    return config\n  }\n\n  _maybeEnableSmoothScroll() {\n    if (!this._config.smoothScroll) {\n      return\n    }\n\n    // unregister any previous listeners\n    EventHandler.off(this._config.target, EVENT_CLICK)\n\n    EventHandler.on(this._config.target, EVENT_CLICK, SELECTOR_TARGET_LINKS, event => {\n      const observableSection = this._observableSections.get(event.target.hash)\n      if (observableSection) {\n        event.preventDefault()\n        const root = this._rootElement || window\n        const height = observableSection.offsetTop - this._element.offsetTop\n        if (root.scrollTo) {\n          root.scrollTo({ top: height, behavior: 'smooth' })\n          return\n        }\n\n        // Chrome 60 doesn't support `scrollTo`\n        root.scrollTop = height\n      }\n    })\n  }\n\n  _getNewObserver() {\n    const options = {\n      root: this._rootElement,\n      threshold: this._config.threshold,\n      rootMargin: this._config.rootMargin\n    }\n\n    return new IntersectionObserver(entries => this._observerCallback(entries), options)\n  }\n\n  // The logic of selection\n  _observerCallback(entries) {\n    const targetElement = entry => this._targetLinks.get(`#${entry.target.id}`)\n    const activate = entry => {\n      this._previousScrollData.visibleEntryTop = entry.target.offsetTop\n      this._process(targetElement(entry))\n    }\n\n    const parentScrollTop = (this._rootElement || document.documentElement).scrollTop\n    const userScrollsDown = parentScrollTop >= this._previousScrollData.parentScrollTop\n    this._previousScrollData.parentScrollTop = parentScrollTop\n\n    for (const entry of entries) {\n      if (!entry.isIntersecting) {\n        this._activeTarget = null\n        this._clearActiveClass(targetElement(entry))\n\n        continue\n      }\n\n      const entryIsLowerThanPrevious = entry.target.offsetTop >= this._previousScrollData.visibleEntryTop\n      // if we are scrolling down, pick the bigger offsetTop\n      if (userScrollsDown && entryIsLowerThanPrevious) {\n        activate(entry)\n        // if parent isn't scrolled, let's keep the first visible item, breaking the iteration\n        if (!parentScrollTop) {\n          return\n        }\n\n        continue\n      }\n\n      // if we are scrolling up, pick the smallest offsetTop\n      if (!userScrollsDown && !entryIsLowerThanPrevious) {\n        activate(entry)\n      }\n    }\n  }\n\n  _initializeTargetsAndObservables() {\n    this._targetLinks = new Map()\n    this._observableSections = new Map()\n\n    const targetLinks = SelectorEngine.find(SELECTOR_TARGET_LINKS, this._config.target)\n\n    for (const anchor of targetLinks) {\n      // ensure that the anchor has an id and is not disabled\n      if (!anchor.hash || isDisabled(anchor)) {\n        continue\n      }\n\n      const observableSection = SelectorEngine.findOne(decodeURI(anchor.hash), this._element)\n\n      // ensure that the observableSection exists & is visible\n      if (isVisible(observableSection)) {\n        this._targetLinks.set(decodeURI(anchor.hash), anchor)\n        this._observableSections.set(anchor.hash, observableSection)\n      }\n    }\n  }\n\n  _process(target) {\n    if (this._activeTarget === target) {\n      return\n    }\n\n    this._clearActiveClass(this._config.target)\n    this._activeTarget = target\n    target.classList.add(CLASS_NAME_ACTIVE)\n    this._activateParents(target)\n\n    EventHandler.trigger(this._element, EVENT_ACTIVATE, { relatedTarget: target })\n  }\n\n  _activateParents(target) {\n    // Activate dropdown parents\n    if (target.classList.contains(CLASS_NAME_DROPDOWN_ITEM)) {\n      SelectorEngine.findOne(SELECTOR_DROPDOWN_TOGGLE, target.closest(SELECTOR_DROPDOWN))\n        .classList.add(CLASS_NAME_ACTIVE)\n      return\n    }\n\n    for (const listGroup of SelectorEngine.parents(target, SELECTOR_NAV_LIST_GROUP)) {\n      // Set triggered links parents as active\n      // With both 
       and 
    ')},createChildNavList:function(e){var t=this.createNavList();return e.append(t),t},generateNavEl:function(e,t){var n=a('    ');n.attr("href","#"+e),n.text(t);var r=a("
  • ");return r.append(n),r},generateNavItem:function(e){var t=this.generateAnchor(e),n=a(e),r=n.data("toc-text")||n.text();return this.generateNavEl(t,r)},getTopLevel:function(e){for(var t=1;t<=6;t++){if(1
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/docs/deps/font-awesome-6.5.2/css/all.css b/docs/deps/font-awesome-6.5.2/css/all.css
new file mode 100644
index 0000000..151dd57
--- /dev/null
+++ b/docs/deps/font-awesome-6.5.2/css/all.css
@@ -0,0 +1,8028 @@
+/*!
+ * Font Awesome Free 6.5.2 by @fontawesome - https://fontawesome.com
+ * License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License)
+ * Copyright 2024 Fonticons, Inc.
+ */
+.fa {
+  font-family: var(--fa-style-family, "Font Awesome 6 Free");
+  font-weight: var(--fa-style, 900); }
+
+.fa,
+.fa-classic,
+.fa-sharp,
+.fas,
+.fa-solid,
+.far,
+.fa-regular,
+.fab,
+.fa-brands {
+  -moz-osx-font-smoothing: grayscale;
+  -webkit-font-smoothing: antialiased;
+  display: var(--fa-display, inline-block);
+  font-style: normal;
+  font-variant: normal;
+  line-height: 1;
+  text-rendering: auto; }
+
+.fas,
+.fa-classic,
+.fa-solid,
+.far,
+.fa-regular {
+  font-family: 'Font Awesome 6 Free'; }
+
+.fab,
+.fa-brands {
+  font-family: 'Font Awesome 6 Brands'; }
+
+.fa-1x {
+  font-size: 1em; }
+
+.fa-2x {
+  font-size: 2em; }
+
+.fa-3x {
+  font-size: 3em; }
+
+.fa-4x {
+  font-size: 4em; }
+
+.fa-5x {
+  font-size: 5em; }
+
+.fa-6x {
+  font-size: 6em; }
+
+.fa-7x {
+  font-size: 7em; }
+
+.fa-8x {
+  font-size: 8em; }
+
+.fa-9x {
+  font-size: 9em; }
+
+.fa-10x {
+  font-size: 10em; }
+
+.fa-2xs {
+  font-size: 0.625em;
+  line-height: 0.1em;
+  vertical-align: 0.225em; }
+
+.fa-xs {
+  font-size: 0.75em;
+  line-height: 0.08333em;
+  vertical-align: 0.125em; }
+
+.fa-sm {
+  font-size: 0.875em;
+  line-height: 0.07143em;
+  vertical-align: 0.05357em; }
+
+.fa-lg {
+  font-size: 1.25em;
+  line-height: 0.05em;
+  vertical-align: -0.075em; }
+
+.fa-xl {
+  font-size: 1.5em;
+  line-height: 0.04167em;
+  vertical-align: -0.125em; }
+
+.fa-2xl {
+  font-size: 2em;
+  line-height: 0.03125em;
+  vertical-align: -0.1875em; }
+
+.fa-fw {
+  text-align: center;
+  width: 1.25em; }
+
+.fa-ul {
+  list-style-type: none;
+  margin-left: var(--fa-li-margin, 2.5em);
+  padding-left: 0; }
+  .fa-ul > li {
+    position: relative; }
+
+.fa-li {
+  left: calc(var(--fa-li-width, 2em) * -1);
+  position: absolute;
+  text-align: center;
+  width: var(--fa-li-width, 2em);
+  line-height: inherit; }
+
+.fa-border {
+  border-color: var(--fa-border-color, #eee);
+  border-radius: var(--fa-border-radius, 0.1em);
+  border-style: var(--fa-border-style, solid);
+  border-width: var(--fa-border-width, 0.08em);
+  padding: var(--fa-border-padding, 0.2em 0.25em 0.15em); }
+
+.fa-pull-left {
+  float: left;
+  margin-right: var(--fa-pull-margin, 0.3em); }
+
+.fa-pull-right {
+  float: right;
+  margin-left: var(--fa-pull-margin, 0.3em); }
+
+.fa-beat {
+  -webkit-animation-name: fa-beat;
+          animation-name: fa-beat;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, ease-in-out);
+          animation-timing-function: var(--fa-animation-timing, ease-in-out); }
+
+.fa-bounce {
+  -webkit-animation-name: fa-bounce;
+          animation-name: fa-bounce;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.28, 0.84, 0.42, 1));
+          animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.28, 0.84, 0.42, 1)); }
+
+.fa-fade {
+  -webkit-animation-name: fa-fade;
+          animation-name: fa-fade;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1));
+          animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1)); }
+
+.fa-beat-fade {
+  -webkit-animation-name: fa-beat-fade;
+          animation-name: fa-beat-fade;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1));
+          animation-timing-function: var(--fa-animation-timing, cubic-bezier(0.4, 0, 0.6, 1)); }
+
+.fa-flip {
+  -webkit-animation-name: fa-flip;
+          animation-name: fa-flip;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, ease-in-out);
+          animation-timing-function: var(--fa-animation-timing, ease-in-out); }
+
+.fa-shake {
+  -webkit-animation-name: fa-shake;
+          animation-name: fa-shake;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, linear);
+          animation-timing-function: var(--fa-animation-timing, linear); }
+
+.fa-spin {
+  -webkit-animation-name: fa-spin;
+          animation-name: fa-spin;
+  -webkit-animation-delay: var(--fa-animation-delay, 0s);
+          animation-delay: var(--fa-animation-delay, 0s);
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 2s);
+          animation-duration: var(--fa-animation-duration, 2s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, linear);
+          animation-timing-function: var(--fa-animation-timing, linear); }
+
+.fa-spin-reverse {
+  --fa-animation-direction: reverse; }
+
+.fa-pulse,
+.fa-spin-pulse {
+  -webkit-animation-name: fa-spin;
+          animation-name: fa-spin;
+  -webkit-animation-direction: var(--fa-animation-direction, normal);
+          animation-direction: var(--fa-animation-direction, normal);
+  -webkit-animation-duration: var(--fa-animation-duration, 1s);
+          animation-duration: var(--fa-animation-duration, 1s);
+  -webkit-animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+          animation-iteration-count: var(--fa-animation-iteration-count, infinite);
+  -webkit-animation-timing-function: var(--fa-animation-timing, steps(8));
+          animation-timing-function: var(--fa-animation-timing, steps(8)); }
+
+@media (prefers-reduced-motion: reduce) {
+  .fa-beat,
+  .fa-bounce,
+  .fa-fade,
+  .fa-beat-fade,
+  .fa-flip,
+  .fa-pulse,
+  .fa-shake,
+  .fa-spin,
+  .fa-spin-pulse {
+    -webkit-animation-delay: -1ms;
+            animation-delay: -1ms;
+    -webkit-animation-duration: 1ms;
+            animation-duration: 1ms;
+    -webkit-animation-iteration-count: 1;
+            animation-iteration-count: 1;
+    -webkit-transition-delay: 0s;
+            transition-delay: 0s;
+    -webkit-transition-duration: 0s;
+            transition-duration: 0s; } }
+
+@-webkit-keyframes fa-beat {
+  0%, 90% {
+    -webkit-transform: scale(1);
+            transform: scale(1); }
+  45% {
+    -webkit-transform: scale(var(--fa-beat-scale, 1.25));
+            transform: scale(var(--fa-beat-scale, 1.25)); } }
+
+@keyframes fa-beat {
+  0%, 90% {
+    -webkit-transform: scale(1);
+            transform: scale(1); }
+  45% {
+    -webkit-transform: scale(var(--fa-beat-scale, 1.25));
+            transform: scale(var(--fa-beat-scale, 1.25)); } }
+
+@-webkit-keyframes fa-bounce {
+  0% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); }
+  10% {
+    -webkit-transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0);
+            transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0); }
+  30% {
+    -webkit-transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em));
+            transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em)); }
+  50% {
+    -webkit-transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0);
+            transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0); }
+  57% {
+    -webkit-transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em));
+            transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em)); }
+  64% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); }
+  100% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); } }
+
+@keyframes fa-bounce {
+  0% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); }
+  10% {
+    -webkit-transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0);
+            transform: scale(var(--fa-bounce-start-scale-x, 1.1), var(--fa-bounce-start-scale-y, 0.9)) translateY(0); }
+  30% {
+    -webkit-transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em));
+            transform: scale(var(--fa-bounce-jump-scale-x, 0.9), var(--fa-bounce-jump-scale-y, 1.1)) translateY(var(--fa-bounce-height, -0.5em)); }
+  50% {
+    -webkit-transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0);
+            transform: scale(var(--fa-bounce-land-scale-x, 1.05), var(--fa-bounce-land-scale-y, 0.95)) translateY(0); }
+  57% {
+    -webkit-transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em));
+            transform: scale(1, 1) translateY(var(--fa-bounce-rebound, -0.125em)); }
+  64% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); }
+  100% {
+    -webkit-transform: scale(1, 1) translateY(0);
+            transform: scale(1, 1) translateY(0); } }
+
+@-webkit-keyframes fa-fade {
+  50% {
+    opacity: var(--fa-fade-opacity, 0.4); } }
+
+@keyframes fa-fade {
+  50% {
+    opacity: var(--fa-fade-opacity, 0.4); } }
+
+@-webkit-keyframes fa-beat-fade {
+  0%, 100% {
+    opacity: var(--fa-beat-fade-opacity, 0.4);
+    -webkit-transform: scale(1);
+            transform: scale(1); }
+  50% {
+    opacity: 1;
+    -webkit-transform: scale(var(--fa-beat-fade-scale, 1.125));
+            transform: scale(var(--fa-beat-fade-scale, 1.125)); } }
+
+@keyframes fa-beat-fade {
+  0%, 100% {
+    opacity: var(--fa-beat-fade-opacity, 0.4);
+    -webkit-transform: scale(1);
+            transform: scale(1); }
+  50% {
+    opacity: 1;
+    -webkit-transform: scale(var(--fa-beat-fade-scale, 1.125));
+            transform: scale(var(--fa-beat-fade-scale, 1.125)); } }
+
+@-webkit-keyframes fa-flip {
+  50% {
+    -webkit-transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg));
+            transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg)); } }
+
+@keyframes fa-flip {
+  50% {
+    -webkit-transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg));
+            transform: rotate3d(var(--fa-flip-x, 0), var(--fa-flip-y, 1), var(--fa-flip-z, 0), var(--fa-flip-angle, -180deg)); } }
+
+@-webkit-keyframes fa-shake {
+  0% {
+    -webkit-transform: rotate(-15deg);
+            transform: rotate(-15deg); }
+  4% {
+    -webkit-transform: rotate(15deg);
+            transform: rotate(15deg); }
+  8%, 24% {
+    -webkit-transform: rotate(-18deg);
+            transform: rotate(-18deg); }
+  12%, 28% {
+    -webkit-transform: rotate(18deg);
+            transform: rotate(18deg); }
+  16% {
+    -webkit-transform: rotate(-22deg);
+            transform: rotate(-22deg); }
+  20% {
+    -webkit-transform: rotate(22deg);
+            transform: rotate(22deg); }
+  32% {
+    -webkit-transform: rotate(-12deg);
+            transform: rotate(-12deg); }
+  36% {
+    -webkit-transform: rotate(12deg);
+            transform: rotate(12deg); }
+  40%, 100% {
+    -webkit-transform: rotate(0deg);
+            transform: rotate(0deg); } }
+
+@keyframes fa-shake {
+  0% {
+    -webkit-transform: rotate(-15deg);
+            transform: rotate(-15deg); }
+  4% {
+    -webkit-transform: rotate(15deg);
+            transform: rotate(15deg); }
+  8%, 24% {
+    -webkit-transform: rotate(-18deg);
+            transform: rotate(-18deg); }
+  12%, 28% {
+    -webkit-transform: rotate(18deg);
+            transform: rotate(18deg); }
+  16% {
+    -webkit-transform: rotate(-22deg);
+            transform: rotate(-22deg); }
+  20% {
+    -webkit-transform: rotate(22deg);
+            transform: rotate(22deg); }
+  32% {
+    -webkit-transform: rotate(-12deg);
+            transform: rotate(-12deg); }
+  36% {
+    -webkit-transform: rotate(12deg);
+            transform: rotate(12deg); }
+  40%, 100% {
+    -webkit-transform: rotate(0deg);
+            transform: rotate(0deg); } }
+
+@-webkit-keyframes fa-spin {
+  0% {
+    -webkit-transform: rotate(0deg);
+            transform: rotate(0deg); }
+  100% {
+    -webkit-transform: rotate(360deg);
+            transform: rotate(360deg); } }
+
+@keyframes fa-spin {
+  0% {
+    -webkit-transform: rotate(0deg);
+            transform: rotate(0deg); }
+  100% {
+    -webkit-transform: rotate(360deg);
+            transform: rotate(360deg); } }
+
+.fa-rotate-90 {
+  -webkit-transform: rotate(90deg);
+          transform: rotate(90deg); }
+
+.fa-rotate-180 {
+  -webkit-transform: rotate(180deg);
+          transform: rotate(180deg); }
+
+.fa-rotate-270 {
+  -webkit-transform: rotate(270deg);
+          transform: rotate(270deg); }
+
+.fa-flip-horizontal {
+  -webkit-transform: scale(-1, 1);
+          transform: scale(-1, 1); }
+
+.fa-flip-vertical {
+  -webkit-transform: scale(1, -1);
+          transform: scale(1, -1); }
+
+.fa-flip-both,
+.fa-flip-horizontal.fa-flip-vertical {
+  -webkit-transform: scale(-1, -1);
+          transform: scale(-1, -1); }
+
+.fa-rotate-by {
+  -webkit-transform: rotate(var(--fa-rotate-angle, 0));
+          transform: rotate(var(--fa-rotate-angle, 0)); }
+
+.fa-stack {
+  display: inline-block;
+  height: 2em;
+  line-height: 2em;
+  position: relative;
+  vertical-align: middle;
+  width: 2.5em; }
+
+.fa-stack-1x,
+.fa-stack-2x {
+  left: 0;
+  position: absolute;
+  text-align: center;
+  width: 100%;
+  z-index: var(--fa-stack-z-index, auto); }
+
+.fa-stack-1x {
+  line-height: inherit; }
+
+.fa-stack-2x {
+  font-size: 2em; }
+
+.fa-inverse {
+  color: var(--fa-inverse, #fff); }
+
+/* Font Awesome uses the Unicode Private Use Area (PUA) to ensure screen
+readers do not read off random characters that represent icons */
+
+.fa-0::before {
+  content: "\30"; }
+
+.fa-1::before {
+  content: "\31"; }
+
+.fa-2::before {
+  content: "\32"; }
+
+.fa-3::before {
+  content: "\33"; }
+
+.fa-4::before {
+  content: "\34"; }
+
+.fa-5::before {
+  content: "\35"; }
+
+.fa-6::before {
+  content: "\36"; }
+
+.fa-7::before {
+  content: "\37"; }
+
+.fa-8::before {
+  content: "\38"; }
+
+.fa-9::before {
+  content: "\39"; }
+
+.fa-fill-drip::before {
+  content: "\f576"; }
+
+.fa-arrows-to-circle::before {
+  content: "\e4bd"; }
+
+.fa-circle-chevron-right::before {
+  content: "\f138"; }
+
+.fa-chevron-circle-right::before {
+  content: "\f138"; }
+
+.fa-at::before {
+  content: "\40"; }
+
+.fa-trash-can::before {
+  content: "\f2ed"; }
+
+.fa-trash-alt::before {
+  content: "\f2ed"; }
+
+.fa-text-height::before {
+  content: "\f034"; }
+
+.fa-user-xmark::before {
+  content: "\f235"; }
+
+.fa-user-times::before {
+  content: "\f235"; }
+
+.fa-stethoscope::before {
+  content: "\f0f1"; }
+
+.fa-message::before {
+  content: "\f27a"; }
+
+.fa-comment-alt::before {
+  content: "\f27a"; }
+
+.fa-info::before {
+  content: "\f129"; }
+
+.fa-down-left-and-up-right-to-center::before {
+  content: "\f422"; }
+
+.fa-compress-alt::before {
+  content: "\f422"; }
+
+.fa-explosion::before {
+  content: "\e4e9"; }
+
+.fa-file-lines::before {
+  content: "\f15c"; }
+
+.fa-file-alt::before {
+  content: "\f15c"; }
+
+.fa-file-text::before {
+  content: "\f15c"; }
+
+.fa-wave-square::before {
+  content: "\f83e"; }
+
+.fa-ring::before {
+  content: "\f70b"; }
+
+.fa-building-un::before {
+  content: "\e4d9"; }
+
+.fa-dice-three::before {
+  content: "\f527"; }
+
+.fa-calendar-days::before {
+  content: "\f073"; }
+
+.fa-calendar-alt::before {
+  content: "\f073"; }
+
+.fa-anchor-circle-check::before {
+  content: "\e4aa"; }
+
+.fa-building-circle-arrow-right::before {
+  content: "\e4d1"; }
+
+.fa-volleyball::before {
+  content: "\f45f"; }
+
+.fa-volleyball-ball::before {
+  content: "\f45f"; }
+
+.fa-arrows-up-to-line::before {
+  content: "\e4c2"; }
+
+.fa-sort-down::before {
+  content: "\f0dd"; }
+
+.fa-sort-desc::before {
+  content: "\f0dd"; }
+
+.fa-circle-minus::before {
+  content: "\f056"; }
+
+.fa-minus-circle::before {
+  content: "\f056"; }
+
+.fa-door-open::before {
+  content: "\f52b"; }
+
+.fa-right-from-bracket::before {
+  content: "\f2f5"; }
+
+.fa-sign-out-alt::before {
+  content: "\f2f5"; }
+
+.fa-atom::before {
+  content: "\f5d2"; }
+
+.fa-soap::before {
+  content: "\e06e"; }
+
+.fa-icons::before {
+  content: "\f86d"; }
+
+.fa-heart-music-camera-bolt::before {
+  content: "\f86d"; }
+
+.fa-microphone-lines-slash::before {
+  content: "\f539"; }
+
+.fa-microphone-alt-slash::before {
+  content: "\f539"; }
+
+.fa-bridge-circle-check::before {
+  content: "\e4c9"; }
+
+.fa-pump-medical::before {
+  content: "\e06a"; }
+
+.fa-fingerprint::before {
+  content: "\f577"; }
+
+.fa-hand-point-right::before {
+  content: "\f0a4"; }
+
+.fa-magnifying-glass-location::before {
+  content: "\f689"; }
+
+.fa-search-location::before {
+  content: "\f689"; }
+
+.fa-forward-step::before {
+  content: "\f051"; }
+
+.fa-step-forward::before {
+  content: "\f051"; }
+
+.fa-face-smile-beam::before {
+  content: "\f5b8"; }
+
+.fa-smile-beam::before {
+  content: "\f5b8"; }
+
+.fa-flag-checkered::before {
+  content: "\f11e"; }
+
+.fa-football::before {
+  content: "\f44e"; }
+
+.fa-football-ball::before {
+  content: "\f44e"; }
+
+.fa-school-circle-exclamation::before {
+  content: "\e56c"; }
+
+.fa-crop::before {
+  content: "\f125"; }
+
+.fa-angles-down::before {
+  content: "\f103"; }
+
+.fa-angle-double-down::before {
+  content: "\f103"; }
+
+.fa-users-rectangle::before {
+  content: "\e594"; }
+
+.fa-people-roof::before {
+  content: "\e537"; }
+
+.fa-people-line::before {
+  content: "\e534"; }
+
+.fa-beer-mug-empty::before {
+  content: "\f0fc"; }
+
+.fa-beer::before {
+  content: "\f0fc"; }
+
+.fa-diagram-predecessor::before {
+  content: "\e477"; }
+
+.fa-arrow-up-long::before {
+  content: "\f176"; }
+
+.fa-long-arrow-up::before {
+  content: "\f176"; }
+
+.fa-fire-flame-simple::before {
+  content: "\f46a"; }
+
+.fa-burn::before {
+  content: "\f46a"; }
+
+.fa-person::before {
+  content: "\f183"; }
+
+.fa-male::before {
+  content: "\f183"; }
+
+.fa-laptop::before {
+  content: "\f109"; }
+
+.fa-file-csv::before {
+  content: "\f6dd"; }
+
+.fa-menorah::before {
+  content: "\f676"; }
+
+.fa-truck-plane::before {
+  content: "\e58f"; }
+
+.fa-record-vinyl::before {
+  content: "\f8d9"; }
+
+.fa-face-grin-stars::before {
+  content: "\f587"; }
+
+.fa-grin-stars::before {
+  content: "\f587"; }
+
+.fa-bong::before {
+  content: "\f55c"; }
+
+.fa-spaghetti-monster-flying::before {
+  content: "\f67b"; }
+
+.fa-pastafarianism::before {
+  content: "\f67b"; }
+
+.fa-arrow-down-up-across-line::before {
+  content: "\e4af"; }
+
+.fa-spoon::before {
+  content: "\f2e5"; }
+
+.fa-utensil-spoon::before {
+  content: "\f2e5"; }
+
+.fa-jar-wheat::before {
+  content: "\e517"; }
+
+.fa-envelopes-bulk::before {
+  content: "\f674"; }
+
+.fa-mail-bulk::before {
+  content: "\f674"; }
+
+.fa-file-circle-exclamation::before {
+  content: "\e4eb"; }
+
+.fa-circle-h::before {
+  content: "\f47e"; }
+
+.fa-hospital-symbol::before {
+  content: "\f47e"; }
+
+.fa-pager::before {
+  content: "\f815"; }
+
+.fa-address-book::before {
+  content: "\f2b9"; }
+
+.fa-contact-book::before {
+  content: "\f2b9"; }
+
+.fa-strikethrough::before {
+  content: "\f0cc"; }
+
+.fa-k::before {
+  content: "\4b"; }
+
+.fa-landmark-flag::before {
+  content: "\e51c"; }
+
+.fa-pencil::before {
+  content: "\f303"; }
+
+.fa-pencil-alt::before {
+  content: "\f303"; }
+
+.fa-backward::before {
+  content: "\f04a"; }
+
+.fa-caret-right::before {
+  content: "\f0da"; }
+
+.fa-comments::before {
+  content: "\f086"; }
+
+.fa-paste::before {
+  content: "\f0ea"; }
+
+.fa-file-clipboard::before {
+  content: "\f0ea"; }
+
+.fa-code-pull-request::before {
+  content: "\e13c"; }
+
+.fa-clipboard-list::before {
+  content: "\f46d"; }
+
+.fa-truck-ramp-box::before {
+  content: "\f4de"; }
+
+.fa-truck-loading::before {
+  content: "\f4de"; }
+
+.fa-user-check::before {
+  content: "\f4fc"; }
+
+.fa-vial-virus::before {
+  content: "\e597"; }
+
+.fa-sheet-plastic::before {
+  content: "\e571"; }
+
+.fa-blog::before {
+  content: "\f781"; }
+
+.fa-user-ninja::before {
+  content: "\f504"; }
+
+.fa-person-arrow-up-from-line::before {
+  content: "\e539"; }
+
+.fa-scroll-torah::before {
+  content: "\f6a0"; }
+
+.fa-torah::before {
+  content: "\f6a0"; }
+
+.fa-broom-ball::before {
+  content: "\f458"; }
+
+.fa-quidditch::before {
+  content: "\f458"; }
+
+.fa-quidditch-broom-ball::before {
+  content: "\f458"; }
+
+.fa-toggle-off::before {
+  content: "\f204"; }
+
+.fa-box-archive::before {
+  content: "\f187"; }
+
+.fa-archive::before {
+  content: "\f187"; }
+
+.fa-person-drowning::before {
+  content: "\e545"; }
+
+.fa-arrow-down-9-1::before {
+  content: "\f886"; }
+
+.fa-sort-numeric-desc::before {
+  content: "\f886"; }
+
+.fa-sort-numeric-down-alt::before {
+  content: "\f886"; }
+
+.fa-face-grin-tongue-squint::before {
+  content: "\f58a"; }
+
+.fa-grin-tongue-squint::before {
+  content: "\f58a"; }
+
+.fa-spray-can::before {
+  content: "\f5bd"; }
+
+.fa-truck-monster::before {
+  content: "\f63b"; }
+
+.fa-w::before {
+  content: "\57"; }
+
+.fa-earth-africa::before {
+  content: "\f57c"; }
+
+.fa-globe-africa::before {
+  content: "\f57c"; }
+
+.fa-rainbow::before {
+  content: "\f75b"; }
+
+.fa-circle-notch::before {
+  content: "\f1ce"; }
+
+.fa-tablet-screen-button::before {
+  content: "\f3fa"; }
+
+.fa-tablet-alt::before {
+  content: "\f3fa"; }
+
+.fa-paw::before {
+  content: "\f1b0"; }
+
+.fa-cloud::before {
+  content: "\f0c2"; }
+
+.fa-trowel-bricks::before {
+  content: "\e58a"; }
+
+.fa-face-flushed::before {
+  content: "\f579"; }
+
+.fa-flushed::before {
+  content: "\f579"; }
+
+.fa-hospital-user::before {
+  content: "\f80d"; }
+
+.fa-tent-arrow-left-right::before {
+  content: "\e57f"; }
+
+.fa-gavel::before {
+  content: "\f0e3"; }
+
+.fa-legal::before {
+  content: "\f0e3"; }
+
+.fa-binoculars::before {
+  content: "\f1e5"; }
+
+.fa-microphone-slash::before {
+  content: "\f131"; }
+
+.fa-box-tissue::before {
+  content: "\e05b"; }
+
+.fa-motorcycle::before {
+  content: "\f21c"; }
+
+.fa-bell-concierge::before {
+  content: "\f562"; }
+
+.fa-concierge-bell::before {
+  content: "\f562"; }
+
+.fa-pen-ruler::before {
+  content: "\f5ae"; }
+
+.fa-pencil-ruler::before {
+  content: "\f5ae"; }
+
+.fa-people-arrows::before {
+  content: "\e068"; }
+
+.fa-people-arrows-left-right::before {
+  content: "\e068"; }
+
+.fa-mars-and-venus-burst::before {
+  content: "\e523"; }
+
+.fa-square-caret-right::before {
+  content: "\f152"; }
+
+.fa-caret-square-right::before {
+  content: "\f152"; }
+
+.fa-scissors::before {
+  content: "\f0c4"; }
+
+.fa-cut::before {
+  content: "\f0c4"; }
+
+.fa-sun-plant-wilt::before {
+  content: "\e57a"; }
+
+.fa-toilets-portable::before {
+  content: "\e584"; }
+
+.fa-hockey-puck::before {
+  content: "\f453"; }
+
+.fa-table::before {
+  content: "\f0ce"; }
+
+.fa-magnifying-glass-arrow-right::before {
+  content: "\e521"; }
+
+.fa-tachograph-digital::before {
+  content: "\f566"; }
+
+.fa-digital-tachograph::before {
+  content: "\f566"; }
+
+.fa-users-slash::before {
+  content: "\e073"; }
+
+.fa-clover::before {
+  content: "\e139"; }
+
+.fa-reply::before {
+  content: "\f3e5"; }
+
+.fa-mail-reply::before {
+  content: "\f3e5"; }
+
+.fa-star-and-crescent::before {
+  content: "\f699"; }
+
+.fa-house-fire::before {
+  content: "\e50c"; }
+
+.fa-square-minus::before {
+  content: "\f146"; }
+
+.fa-minus-square::before {
+  content: "\f146"; }
+
+.fa-helicopter::before {
+  content: "\f533"; }
+
+.fa-compass::before {
+  content: "\f14e"; }
+
+.fa-square-caret-down::before {
+  content: "\f150"; }
+
+.fa-caret-square-down::before {
+  content: "\f150"; }
+
+.fa-file-circle-question::before {
+  content: "\e4ef"; }
+
+.fa-laptop-code::before {
+  content: "\f5fc"; }
+
+.fa-swatchbook::before {
+  content: "\f5c3"; }
+
+.fa-prescription-bottle::before {
+  content: "\f485"; }
+
+.fa-bars::before {
+  content: "\f0c9"; }
+
+.fa-navicon::before {
+  content: "\f0c9"; }
+
+.fa-people-group::before {
+  content: "\e533"; }
+
+.fa-hourglass-end::before {
+  content: "\f253"; }
+
+.fa-hourglass-3::before {
+  content: "\f253"; }
+
+.fa-heart-crack::before {
+  content: "\f7a9"; }
+
+.fa-heart-broken::before {
+  content: "\f7a9"; }
+
+.fa-square-up-right::before {
+  content: "\f360"; }
+
+.fa-external-link-square-alt::before {
+  content: "\f360"; }
+
+.fa-face-kiss-beam::before {
+  content: "\f597"; }
+
+.fa-kiss-beam::before {
+  content: "\f597"; }
+
+.fa-film::before {
+  content: "\f008"; }
+
+.fa-ruler-horizontal::before {
+  content: "\f547"; }
+
+.fa-people-robbery::before {
+  content: "\e536"; }
+
+.fa-lightbulb::before {
+  content: "\f0eb"; }
+
+.fa-caret-left::before {
+  content: "\f0d9"; }
+
+.fa-circle-exclamation::before {
+  content: "\f06a"; }
+
+.fa-exclamation-circle::before {
+  content: "\f06a"; }
+
+.fa-school-circle-xmark::before {
+  content: "\e56d"; }
+
+.fa-arrow-right-from-bracket::before {
+  content: "\f08b"; }
+
+.fa-sign-out::before {
+  content: "\f08b"; }
+
+.fa-circle-chevron-down::before {
+  content: "\f13a"; }
+
+.fa-chevron-circle-down::before {
+  content: "\f13a"; }
+
+.fa-unlock-keyhole::before {
+  content: "\f13e"; }
+
+.fa-unlock-alt::before {
+  content: "\f13e"; }
+
+.fa-cloud-showers-heavy::before {
+  content: "\f740"; }
+
+.fa-headphones-simple::before {
+  content: "\f58f"; }
+
+.fa-headphones-alt::before {
+  content: "\f58f"; }
+
+.fa-sitemap::before {
+  content: "\f0e8"; }
+
+.fa-circle-dollar-to-slot::before {
+  content: "\f4b9"; }
+
+.fa-donate::before {
+  content: "\f4b9"; }
+
+.fa-memory::before {
+  content: "\f538"; }
+
+.fa-road-spikes::before {
+  content: "\e568"; }
+
+.fa-fire-burner::before {
+  content: "\e4f1"; }
+
+.fa-flag::before {
+  content: "\f024"; }
+
+.fa-hanukiah::before {
+  content: "\f6e6"; }
+
+.fa-feather::before {
+  content: "\f52d"; }
+
+.fa-volume-low::before {
+  content: "\f027"; }
+
+.fa-volume-down::before {
+  content: "\f027"; }
+
+.fa-comment-slash::before {
+  content: "\f4b3"; }
+
+.fa-cloud-sun-rain::before {
+  content: "\f743"; }
+
+.fa-compress::before {
+  content: "\f066"; }
+
+.fa-wheat-awn::before {
+  content: "\e2cd"; }
+
+.fa-wheat-alt::before {
+  content: "\e2cd"; }
+
+.fa-ankh::before {
+  content: "\f644"; }
+
+.fa-hands-holding-child::before {
+  content: "\e4fa"; }
+
+.fa-asterisk::before {
+  content: "\2a"; }
+
+.fa-square-check::before {
+  content: "\f14a"; }
+
+.fa-check-square::before {
+  content: "\f14a"; }
+
+.fa-peseta-sign::before {
+  content: "\e221"; }
+
+.fa-heading::before {
+  content: "\f1dc"; }
+
+.fa-header::before {
+  content: "\f1dc"; }
+
+.fa-ghost::before {
+  content: "\f6e2"; }
+
+.fa-list::before {
+  content: "\f03a"; }
+
+.fa-list-squares::before {
+  content: "\f03a"; }
+
+.fa-square-phone-flip::before {
+  content: "\f87b"; }
+
+.fa-phone-square-alt::before {
+  content: "\f87b"; }
+
+.fa-cart-plus::before {
+  content: "\f217"; }
+
+.fa-gamepad::before {
+  content: "\f11b"; }
+
+.fa-circle-dot::before {
+  content: "\f192"; }
+
+.fa-dot-circle::before {
+  content: "\f192"; }
+
+.fa-face-dizzy::before {
+  content: "\f567"; }
+
+.fa-dizzy::before {
+  content: "\f567"; }
+
+.fa-egg::before {
+  content: "\f7fb"; }
+
+.fa-house-medical-circle-xmark::before {
+  content: "\e513"; }
+
+.fa-campground::before {
+  content: "\f6bb"; }
+
+.fa-folder-plus::before {
+  content: "\f65e"; }
+
+.fa-futbol::before {
+  content: "\f1e3"; }
+
+.fa-futbol-ball::before {
+  content: "\f1e3"; }
+
+.fa-soccer-ball::before {
+  content: "\f1e3"; }
+
+.fa-paintbrush::before {
+  content: "\f1fc"; }
+
+.fa-paint-brush::before {
+  content: "\f1fc"; }
+
+.fa-lock::before {
+  content: "\f023"; }
+
+.fa-gas-pump::before {
+  content: "\f52f"; }
+
+.fa-hot-tub-person::before {
+  content: "\f593"; }
+
+.fa-hot-tub::before {
+  content: "\f593"; }
+
+.fa-map-location::before {
+  content: "\f59f"; }
+
+.fa-map-marked::before {
+  content: "\f59f"; }
+
+.fa-house-flood-water::before {
+  content: "\e50e"; }
+
+.fa-tree::before {
+  content: "\f1bb"; }
+
+.fa-bridge-lock::before {
+  content: "\e4cc"; }
+
+.fa-sack-dollar::before {
+  content: "\f81d"; }
+
+.fa-pen-to-square::before {
+  content: "\f044"; }
+
+.fa-edit::before {
+  content: "\f044"; }
+
+.fa-car-side::before {
+  content: "\f5e4"; }
+
+.fa-share-nodes::before {
+  content: "\f1e0"; }
+
+.fa-share-alt::before {
+  content: "\f1e0"; }
+
+.fa-heart-circle-minus::before {
+  content: "\e4ff"; }
+
+.fa-hourglass-half::before {
+  content: "\f252"; }
+
+.fa-hourglass-2::before {
+  content: "\f252"; }
+
+.fa-microscope::before {
+  content: "\f610"; }
+
+.fa-sink::before {
+  content: "\e06d"; }
+
+.fa-bag-shopping::before {
+  content: "\f290"; }
+
+.fa-shopping-bag::before {
+  content: "\f290"; }
+
+.fa-arrow-down-z-a::before {
+  content: "\f881"; }
+
+.fa-sort-alpha-desc::before {
+  content: "\f881"; }
+
+.fa-sort-alpha-down-alt::before {
+  content: "\f881"; }
+
+.fa-mitten::before {
+  content: "\f7b5"; }
+
+.fa-person-rays::before {
+  content: "\e54d"; }
+
+.fa-users::before {
+  content: "\f0c0"; }
+
+.fa-eye-slash::before {
+  content: "\f070"; }
+
+.fa-flask-vial::before {
+  content: "\e4f3"; }
+
+.fa-hand::before {
+  content: "\f256"; }
+
+.fa-hand-paper::before {
+  content: "\f256"; }
+
+.fa-om::before {
+  content: "\f679"; }
+
+.fa-worm::before {
+  content: "\e599"; }
+
+.fa-house-circle-xmark::before {
+  content: "\e50b"; }
+
+.fa-plug::before {
+  content: "\f1e6"; }
+
+.fa-chevron-up::before {
+  content: "\f077"; }
+
+.fa-hand-spock::before {
+  content: "\f259"; }
+
+.fa-stopwatch::before {
+  content: "\f2f2"; }
+
+.fa-face-kiss::before {
+  content: "\f596"; }
+
+.fa-kiss::before {
+  content: "\f596"; }
+
+.fa-bridge-circle-xmark::before {
+  content: "\e4cb"; }
+
+.fa-face-grin-tongue::before {
+  content: "\f589"; }
+
+.fa-grin-tongue::before {
+  content: "\f589"; }
+
+.fa-chess-bishop::before {
+  content: "\f43a"; }
+
+.fa-face-grin-wink::before {
+  content: "\f58c"; }
+
+.fa-grin-wink::before {
+  content: "\f58c"; }
+
+.fa-ear-deaf::before {
+  content: "\f2a4"; }
+
+.fa-deaf::before {
+  content: "\f2a4"; }
+
+.fa-deafness::before {
+  content: "\f2a4"; }
+
+.fa-hard-of-hearing::before {
+  content: "\f2a4"; }
+
+.fa-road-circle-check::before {
+  content: "\e564"; }
+
+.fa-dice-five::before {
+  content: "\f523"; }
+
+.fa-square-rss::before {
+  content: "\f143"; }
+
+.fa-rss-square::before {
+  content: "\f143"; }
+
+.fa-land-mine-on::before {
+  content: "\e51b"; }
+
+.fa-i-cursor::before {
+  content: "\f246"; }
+
+.fa-stamp::before {
+  content: "\f5bf"; }
+
+.fa-stairs::before {
+  content: "\e289"; }
+
+.fa-i::before {
+  content: "\49"; }
+
+.fa-hryvnia-sign::before {
+  content: "\f6f2"; }
+
+.fa-hryvnia::before {
+  content: "\f6f2"; }
+
+.fa-pills::before {
+  content: "\f484"; }
+
+.fa-face-grin-wide::before {
+  content: "\f581"; }
+
+.fa-grin-alt::before {
+  content: "\f581"; }
+
+.fa-tooth::before {
+  content: "\f5c9"; }
+
+.fa-v::before {
+  content: "\56"; }
+
+.fa-bangladeshi-taka-sign::before {
+  content: "\e2e6"; }
+
+.fa-bicycle::before {
+  content: "\f206"; }
+
+.fa-staff-snake::before {
+  content: "\e579"; }
+
+.fa-rod-asclepius::before {
+  content: "\e579"; }
+
+.fa-rod-snake::before {
+  content: "\e579"; }
+
+.fa-staff-aesculapius::before {
+  content: "\e579"; }
+
+.fa-head-side-cough-slash::before {
+  content: "\e062"; }
+
+.fa-truck-medical::before {
+  content: "\f0f9"; }
+
+.fa-ambulance::before {
+  content: "\f0f9"; }
+
+.fa-wheat-awn-circle-exclamation::before {
+  content: "\e598"; }
+
+.fa-snowman::before {
+  content: "\f7d0"; }
+
+.fa-mortar-pestle::before {
+  content: "\f5a7"; }
+
+.fa-road-barrier::before {
+  content: "\e562"; }
+
+.fa-school::before {
+  content: "\f549"; }
+
+.fa-igloo::before {
+  content: "\f7ae"; }
+
+.fa-joint::before {
+  content: "\f595"; }
+
+.fa-angle-right::before {
+  content: "\f105"; }
+
+.fa-horse::before {
+  content: "\f6f0"; }
+
+.fa-q::before {
+  content: "\51"; }
+
+.fa-g::before {
+  content: "\47"; }
+
+.fa-notes-medical::before {
+  content: "\f481"; }
+
+.fa-temperature-half::before {
+  content: "\f2c9"; }
+
+.fa-temperature-2::before {
+  content: "\f2c9"; }
+
+.fa-thermometer-2::before {
+  content: "\f2c9"; }
+
+.fa-thermometer-half::before {
+  content: "\f2c9"; }
+
+.fa-dong-sign::before {
+  content: "\e169"; }
+
+.fa-capsules::before {
+  content: "\f46b"; }
+
+.fa-poo-storm::before {
+  content: "\f75a"; }
+
+.fa-poo-bolt::before {
+  content: "\f75a"; }
+
+.fa-face-frown-open::before {
+  content: "\f57a"; }
+
+.fa-frown-open::before {
+  content: "\f57a"; }
+
+.fa-hand-point-up::before {
+  content: "\f0a6"; }
+
+.fa-money-bill::before {
+  content: "\f0d6"; }
+
+.fa-bookmark::before {
+  content: "\f02e"; }
+
+.fa-align-justify::before {
+  content: "\f039"; }
+
+.fa-umbrella-beach::before {
+  content: "\f5ca"; }
+
+.fa-helmet-un::before {
+  content: "\e503"; }
+
+.fa-bullseye::before {
+  content: "\f140"; }
+
+.fa-bacon::before {
+  content: "\f7e5"; }
+
+.fa-hand-point-down::before {
+  content: "\f0a7"; }
+
+.fa-arrow-up-from-bracket::before {
+  content: "\e09a"; }
+
+.fa-folder::before {
+  content: "\f07b"; }
+
+.fa-folder-blank::before {
+  content: "\f07b"; }
+
+.fa-file-waveform::before {
+  content: "\f478"; }
+
+.fa-file-medical-alt::before {
+  content: "\f478"; }
+
+.fa-radiation::before {
+  content: "\f7b9"; }
+
+.fa-chart-simple::before {
+  content: "\e473"; }
+
+.fa-mars-stroke::before {
+  content: "\f229"; }
+
+.fa-vial::before {
+  content: "\f492"; }
+
+.fa-gauge::before {
+  content: "\f624"; }
+
+.fa-dashboard::before {
+  content: "\f624"; }
+
+.fa-gauge-med::before {
+  content: "\f624"; }
+
+.fa-tachometer-alt-average::before {
+  content: "\f624"; }
+
+.fa-wand-magic-sparkles::before {
+  content: "\e2ca"; }
+
+.fa-magic-wand-sparkles::before {
+  content: "\e2ca"; }
+
+.fa-e::before {
+  content: "\45"; }
+
+.fa-pen-clip::before {
+  content: "\f305"; }
+
+.fa-pen-alt::before {
+  content: "\f305"; }
+
+.fa-bridge-circle-exclamation::before {
+  content: "\e4ca"; }
+
+.fa-user::before {
+  content: "\f007"; }
+
+.fa-school-circle-check::before {
+  content: "\e56b"; }
+
+.fa-dumpster::before {
+  content: "\f793"; }
+
+.fa-van-shuttle::before {
+  content: "\f5b6"; }
+
+.fa-shuttle-van::before {
+  content: "\f5b6"; }
+
+.fa-building-user::before {
+  content: "\e4da"; }
+
+.fa-square-caret-left::before {
+  content: "\f191"; }
+
+.fa-caret-square-left::before {
+  content: "\f191"; }
+
+.fa-highlighter::before {
+  content: "\f591"; }
+
+.fa-key::before {
+  content: "\f084"; }
+
+.fa-bullhorn::before {
+  content: "\f0a1"; }
+
+.fa-globe::before {
+  content: "\f0ac"; }
+
+.fa-synagogue::before {
+  content: "\f69b"; }
+
+.fa-person-half-dress::before {
+  content: "\e548"; }
+
+.fa-road-bridge::before {
+  content: "\e563"; }
+
+.fa-location-arrow::before {
+  content: "\f124"; }
+
+.fa-c::before {
+  content: "\43"; }
+
+.fa-tablet-button::before {
+  content: "\f10a"; }
+
+.fa-building-lock::before {
+  content: "\e4d6"; }
+
+.fa-pizza-slice::before {
+  content: "\f818"; }
+
+.fa-money-bill-wave::before {
+  content: "\f53a"; }
+
+.fa-chart-area::before {
+  content: "\f1fe"; }
+
+.fa-area-chart::before {
+  content: "\f1fe"; }
+
+.fa-house-flag::before {
+  content: "\e50d"; }
+
+.fa-person-circle-minus::before {
+  content: "\e540"; }
+
+.fa-ban::before {
+  content: "\f05e"; }
+
+.fa-cancel::before {
+  content: "\f05e"; }
+
+.fa-camera-rotate::before {
+  content: "\e0d8"; }
+
+.fa-spray-can-sparkles::before {
+  content: "\f5d0"; }
+
+.fa-air-freshener::before {
+  content: "\f5d0"; }
+
+.fa-star::before {
+  content: "\f005"; }
+
+.fa-repeat::before {
+  content: "\f363"; }
+
+.fa-cross::before {
+  content: "\f654"; }
+
+.fa-box::before {
+  content: "\f466"; }
+
+.fa-venus-mars::before {
+  content: "\f228"; }
+
+.fa-arrow-pointer::before {
+  content: "\f245"; }
+
+.fa-mouse-pointer::before {
+  content: "\f245"; }
+
+.fa-maximize::before {
+  content: "\f31e"; }
+
+.fa-expand-arrows-alt::before {
+  content: "\f31e"; }
+
+.fa-charging-station::before {
+  content: "\f5e7"; }
+
+.fa-shapes::before {
+  content: "\f61f"; }
+
+.fa-triangle-circle-square::before {
+  content: "\f61f"; }
+
+.fa-shuffle::before {
+  content: "\f074"; }
+
+.fa-random::before {
+  content: "\f074"; }
+
+.fa-person-running::before {
+  content: "\f70c"; }
+
+.fa-running::before {
+  content: "\f70c"; }
+
+.fa-mobile-retro::before {
+  content: "\e527"; }
+
+.fa-grip-lines-vertical::before {
+  content: "\f7a5"; }
+
+.fa-spider::before {
+  content: "\f717"; }
+
+.fa-hands-bound::before {
+  content: "\e4f9"; }
+
+.fa-file-invoice-dollar::before {
+  content: "\f571"; }
+
+.fa-plane-circle-exclamation::before {
+  content: "\e556"; }
+
+.fa-x-ray::before {
+  content: "\f497"; }
+
+.fa-spell-check::before {
+  content: "\f891"; }
+
+.fa-slash::before {
+  content: "\f715"; }
+
+.fa-computer-mouse::before {
+  content: "\f8cc"; }
+
+.fa-mouse::before {
+  content: "\f8cc"; }
+
+.fa-arrow-right-to-bracket::before {
+  content: "\f090"; }
+
+.fa-sign-in::before {
+  content: "\f090"; }
+
+.fa-shop-slash::before {
+  content: "\e070"; }
+
+.fa-store-alt-slash::before {
+  content: "\e070"; }
+
+.fa-server::before {
+  content: "\f233"; }
+
+.fa-virus-covid-slash::before {
+  content: "\e4a9"; }
+
+.fa-shop-lock::before {
+  content: "\e4a5"; }
+
+.fa-hourglass-start::before {
+  content: "\f251"; }
+
+.fa-hourglass-1::before {
+  content: "\f251"; }
+
+.fa-blender-phone::before {
+  content: "\f6b6"; }
+
+.fa-building-wheat::before {
+  content: "\e4db"; }
+
+.fa-person-breastfeeding::before {
+  content: "\e53a"; }
+
+.fa-right-to-bracket::before {
+  content: "\f2f6"; }
+
+.fa-sign-in-alt::before {
+  content: "\f2f6"; }
+
+.fa-venus::before {
+  content: "\f221"; }
+
+.fa-passport::before {
+  content: "\f5ab"; }
+
+.fa-heart-pulse::before {
+  content: "\f21e"; }
+
+.fa-heartbeat::before {
+  content: "\f21e"; }
+
+.fa-people-carry-box::before {
+  content: "\f4ce"; }
+
+.fa-people-carry::before {
+  content: "\f4ce"; }
+
+.fa-temperature-high::before {
+  content: "\f769"; }
+
+.fa-microchip::before {
+  content: "\f2db"; }
+
+.fa-crown::before {
+  content: "\f521"; }
+
+.fa-weight-hanging::before {
+  content: "\f5cd"; }
+
+.fa-xmarks-lines::before {
+  content: "\e59a"; }
+
+.fa-file-prescription::before {
+  content: "\f572"; }
+
+.fa-weight-scale::before {
+  content: "\f496"; }
+
+.fa-weight::before {
+  content: "\f496"; }
+
+.fa-user-group::before {
+  content: "\f500"; }
+
+.fa-user-friends::before {
+  content: "\f500"; }
+
+.fa-arrow-up-a-z::before {
+  content: "\f15e"; }
+
+.fa-sort-alpha-up::before {
+  content: "\f15e"; }
+
+.fa-chess-knight::before {
+  content: "\f441"; }
+
+.fa-face-laugh-squint::before {
+  content: "\f59b"; }
+
+.fa-laugh-squint::before {
+  content: "\f59b"; }
+
+.fa-wheelchair::before {
+  content: "\f193"; }
+
+.fa-circle-arrow-up::before {
+  content: "\f0aa"; }
+
+.fa-arrow-circle-up::before {
+  content: "\f0aa"; }
+
+.fa-toggle-on::before {
+  content: "\f205"; }
+
+.fa-person-walking::before {
+  content: "\f554"; }
+
+.fa-walking::before {
+  content: "\f554"; }
+
+.fa-l::before {
+  content: "\4c"; }
+
+.fa-fire::before {
+  content: "\f06d"; }
+
+.fa-bed-pulse::before {
+  content: "\f487"; }
+
+.fa-procedures::before {
+  content: "\f487"; }
+
+.fa-shuttle-space::before {
+  content: "\f197"; }
+
+.fa-space-shuttle::before {
+  content: "\f197"; }
+
+.fa-face-laugh::before {
+  content: "\f599"; }
+
+.fa-laugh::before {
+  content: "\f599"; }
+
+.fa-folder-open::before {
+  content: "\f07c"; }
+
+.fa-heart-circle-plus::before {
+  content: "\e500"; }
+
+.fa-code-fork::before {
+  content: "\e13b"; }
+
+.fa-city::before {
+  content: "\f64f"; }
+
+.fa-microphone-lines::before {
+  content: "\f3c9"; }
+
+.fa-microphone-alt::before {
+  content: "\f3c9"; }
+
+.fa-pepper-hot::before {
+  content: "\f816"; }
+
+.fa-unlock::before {
+  content: "\f09c"; }
+
+.fa-colon-sign::before {
+  content: "\e140"; }
+
+.fa-headset::before {
+  content: "\f590"; }
+
+.fa-store-slash::before {
+  content: "\e071"; }
+
+.fa-road-circle-xmark::before {
+  content: "\e566"; }
+
+.fa-user-minus::before {
+  content: "\f503"; }
+
+.fa-mars-stroke-up::before {
+  content: "\f22a"; }
+
+.fa-mars-stroke-v::before {
+  content: "\f22a"; }
+
+.fa-champagne-glasses::before {
+  content: "\f79f"; }
+
+.fa-glass-cheers::before {
+  content: "\f79f"; }
+
+.fa-clipboard::before {
+  content: "\f328"; }
+
+.fa-house-circle-exclamation::before {
+  content: "\e50a"; }
+
+.fa-file-arrow-up::before {
+  content: "\f574"; }
+
+.fa-file-upload::before {
+  content: "\f574"; }
+
+.fa-wifi::before {
+  content: "\f1eb"; }
+
+.fa-wifi-3::before {
+  content: "\f1eb"; }
+
+.fa-wifi-strong::before {
+  content: "\f1eb"; }
+
+.fa-bath::before {
+  content: "\f2cd"; }
+
+.fa-bathtub::before {
+  content: "\f2cd"; }
+
+.fa-underline::before {
+  content: "\f0cd"; }
+
+.fa-user-pen::before {
+  content: "\f4ff"; }
+
+.fa-user-edit::before {
+  content: "\f4ff"; }
+
+.fa-signature::before {
+  content: "\f5b7"; }
+
+.fa-stroopwafel::before {
+  content: "\f551"; }
+
+.fa-bold::before {
+  content: "\f032"; }
+
+.fa-anchor-lock::before {
+  content: "\e4ad"; }
+
+.fa-building-ngo::before {
+  content: "\e4d7"; }
+
+.fa-manat-sign::before {
+  content: "\e1d5"; }
+
+.fa-not-equal::before {
+  content: "\f53e"; }
+
+.fa-border-top-left::before {
+  content: "\f853"; }
+
+.fa-border-style::before {
+  content: "\f853"; }
+
+.fa-map-location-dot::before {
+  content: "\f5a0"; }
+
+.fa-map-marked-alt::before {
+  content: "\f5a0"; }
+
+.fa-jedi::before {
+  content: "\f669"; }
+
+.fa-square-poll-vertical::before {
+  content: "\f681"; }
+
+.fa-poll::before {
+  content: "\f681"; }
+
+.fa-mug-hot::before {
+  content: "\f7b6"; }
+
+.fa-car-battery::before {
+  content: "\f5df"; }
+
+.fa-battery-car::before {
+  content: "\f5df"; }
+
+.fa-gift::before {
+  content: "\f06b"; }
+
+.fa-dice-two::before {
+  content: "\f528"; }
+
+.fa-chess-queen::before {
+  content: "\f445"; }
+
+.fa-glasses::before {
+  content: "\f530"; }
+
+.fa-chess-board::before {
+  content: "\f43c"; }
+
+.fa-building-circle-check::before {
+  content: "\e4d2"; }
+
+.fa-person-chalkboard::before {
+  content: "\e53d"; }
+
+.fa-mars-stroke-right::before {
+  content: "\f22b"; }
+
+.fa-mars-stroke-h::before {
+  content: "\f22b"; }
+
+.fa-hand-back-fist::before {
+  content: "\f255"; }
+
+.fa-hand-rock::before {
+  content: "\f255"; }
+
+.fa-square-caret-up::before {
+  content: "\f151"; }
+
+.fa-caret-square-up::before {
+  content: "\f151"; }
+
+.fa-cloud-showers-water::before {
+  content: "\e4e4"; }
+
+.fa-chart-bar::before {
+  content: "\f080"; }
+
+.fa-bar-chart::before {
+  content: "\f080"; }
+
+.fa-hands-bubbles::before {
+  content: "\e05e"; }
+
+.fa-hands-wash::before {
+  content: "\e05e"; }
+
+.fa-less-than-equal::before {
+  content: "\f537"; }
+
+.fa-train::before {
+  content: "\f238"; }
+
+.fa-eye-low-vision::before {
+  content: "\f2a8"; }
+
+.fa-low-vision::before {
+  content: "\f2a8"; }
+
+.fa-crow::before {
+  content: "\f520"; }
+
+.fa-sailboat::before {
+  content: "\e445"; }
+
+.fa-window-restore::before {
+  content: "\f2d2"; }
+
+.fa-square-plus::before {
+  content: "\f0fe"; }
+
+.fa-plus-square::before {
+  content: "\f0fe"; }
+
+.fa-torii-gate::before {
+  content: "\f6a1"; }
+
+.fa-frog::before {
+  content: "\f52e"; }
+
+.fa-bucket::before {
+  content: "\e4cf"; }
+
+.fa-image::before {
+  content: "\f03e"; }
+
+.fa-microphone::before {
+  content: "\f130"; }
+
+.fa-cow::before {
+  content: "\f6c8"; }
+
+.fa-caret-up::before {
+  content: "\f0d8"; }
+
+.fa-screwdriver::before {
+  content: "\f54a"; }
+
+.fa-folder-closed::before {
+  content: "\e185"; }
+
+.fa-house-tsunami::before {
+  content: "\e515"; }
+
+.fa-square-nfi::before {
+  content: "\e576"; }
+
+.fa-arrow-up-from-ground-water::before {
+  content: "\e4b5"; }
+
+.fa-martini-glass::before {
+  content: "\f57b"; }
+
+.fa-glass-martini-alt::before {
+  content: "\f57b"; }
+
+.fa-rotate-left::before {
+  content: "\f2ea"; }
+
+.fa-rotate-back::before {
+  content: "\f2ea"; }
+
+.fa-rotate-backward::before {
+  content: "\f2ea"; }
+
+.fa-undo-alt::before {
+  content: "\f2ea"; }
+
+.fa-table-columns::before {
+  content: "\f0db"; }
+
+.fa-columns::before {
+  content: "\f0db"; }
+
+.fa-lemon::before {
+  content: "\f094"; }
+
+.fa-head-side-mask::before {
+  content: "\e063"; }
+
+.fa-handshake::before {
+  content: "\f2b5"; }
+
+.fa-gem::before {
+  content: "\f3a5"; }
+
+.fa-dolly::before {
+  content: "\f472"; }
+
+.fa-dolly-box::before {
+  content: "\f472"; }
+
+.fa-smoking::before {
+  content: "\f48d"; }
+
+.fa-minimize::before {
+  content: "\f78c"; }
+
+.fa-compress-arrows-alt::before {
+  content: "\f78c"; }
+
+.fa-monument::before {
+  content: "\f5a6"; }
+
+.fa-snowplow::before {
+  content: "\f7d2"; }
+
+.fa-angles-right::before {
+  content: "\f101"; }
+
+.fa-angle-double-right::before {
+  content: "\f101"; }
+
+.fa-cannabis::before {
+  content: "\f55f"; }
+
+.fa-circle-play::before {
+  content: "\f144"; }
+
+.fa-play-circle::before {
+  content: "\f144"; }
+
+.fa-tablets::before {
+  content: "\f490"; }
+
+.fa-ethernet::before {
+  content: "\f796"; }
+
+.fa-euro-sign::before {
+  content: "\f153"; }
+
+.fa-eur::before {
+  content: "\f153"; }
+
+.fa-euro::before {
+  content: "\f153"; }
+
+.fa-chair::before {
+  content: "\f6c0"; }
+
+.fa-circle-check::before {
+  content: "\f058"; }
+
+.fa-check-circle::before {
+  content: "\f058"; }
+
+.fa-circle-stop::before {
+  content: "\f28d"; }
+
+.fa-stop-circle::before {
+  content: "\f28d"; }
+
+.fa-compass-drafting::before {
+  content: "\f568"; }
+
+.fa-drafting-compass::before {
+  content: "\f568"; }
+
+.fa-plate-wheat::before {
+  content: "\e55a"; }
+
+.fa-icicles::before {
+  content: "\f7ad"; }
+
+.fa-person-shelter::before {
+  content: "\e54f"; }
+
+.fa-neuter::before {
+  content: "\f22c"; }
+
+.fa-id-badge::before {
+  content: "\f2c1"; }
+
+.fa-marker::before {
+  content: "\f5a1"; }
+
+.fa-face-laugh-beam::before {
+  content: "\f59a"; }
+
+.fa-laugh-beam::before {
+  content: "\f59a"; }
+
+.fa-helicopter-symbol::before {
+  content: "\e502"; }
+
+.fa-universal-access::before {
+  content: "\f29a"; }
+
+.fa-circle-chevron-up::before {
+  content: "\f139"; }
+
+.fa-chevron-circle-up::before {
+  content: "\f139"; }
+
+.fa-lari-sign::before {
+  content: "\e1c8"; }
+
+.fa-volcano::before {
+  content: "\f770"; }
+
+.fa-person-walking-dashed-line-arrow-right::before {
+  content: "\e553"; }
+
+.fa-sterling-sign::before {
+  content: "\f154"; }
+
+.fa-gbp::before {
+  content: "\f154"; }
+
+.fa-pound-sign::before {
+  content: "\f154"; }
+
+.fa-viruses::before {
+  content: "\e076"; }
+
+.fa-square-person-confined::before {
+  content: "\e577"; }
+
+.fa-user-tie::before {
+  content: "\f508"; }
+
+.fa-arrow-down-long::before {
+  content: "\f175"; }
+
+.fa-long-arrow-down::before {
+  content: "\f175"; }
+
+.fa-tent-arrow-down-to-line::before {
+  content: "\e57e"; }
+
+.fa-certificate::before {
+  content: "\f0a3"; }
+
+.fa-reply-all::before {
+  content: "\f122"; }
+
+.fa-mail-reply-all::before {
+  content: "\f122"; }
+
+.fa-suitcase::before {
+  content: "\f0f2"; }
+
+.fa-person-skating::before {
+  content: "\f7c5"; }
+
+.fa-skating::before {
+  content: "\f7c5"; }
+
+.fa-filter-circle-dollar::before {
+  content: "\f662"; }
+
+.fa-funnel-dollar::before {
+  content: "\f662"; }
+
+.fa-camera-retro::before {
+  content: "\f083"; }
+
+.fa-circle-arrow-down::before {
+  content: "\f0ab"; }
+
+.fa-arrow-circle-down::before {
+  content: "\f0ab"; }
+
+.fa-file-import::before {
+  content: "\f56f"; }
+
+.fa-arrow-right-to-file::before {
+  content: "\f56f"; }
+
+.fa-square-arrow-up-right::before {
+  content: "\f14c"; }
+
+.fa-external-link-square::before {
+  content: "\f14c"; }
+
+.fa-box-open::before {
+  content: "\f49e"; }
+
+.fa-scroll::before {
+  content: "\f70e"; }
+
+.fa-spa::before {
+  content: "\f5bb"; }
+
+.fa-location-pin-lock::before {
+  content: "\e51f"; }
+
+.fa-pause::before {
+  content: "\f04c"; }
+
+.fa-hill-avalanche::before {
+  content: "\e507"; }
+
+.fa-temperature-empty::before {
+  content: "\f2cb"; }
+
+.fa-temperature-0::before {
+  content: "\f2cb"; }
+
+.fa-thermometer-0::before {
+  content: "\f2cb"; }
+
+.fa-thermometer-empty::before {
+  content: "\f2cb"; }
+
+.fa-bomb::before {
+  content: "\f1e2"; }
+
+.fa-registered::before {
+  content: "\f25d"; }
+
+.fa-address-card::before {
+  content: "\f2bb"; }
+
+.fa-contact-card::before {
+  content: "\f2bb"; }
+
+.fa-vcard::before {
+  content: "\f2bb"; }
+
+.fa-scale-unbalanced-flip::before {
+  content: "\f516"; }
+
+.fa-balance-scale-right::before {
+  content: "\f516"; }
+
+.fa-subscript::before {
+  content: "\f12c"; }
+
+.fa-diamond-turn-right::before {
+  content: "\f5eb"; }
+
+.fa-directions::before {
+  content: "\f5eb"; }
+
+.fa-burst::before {
+  content: "\e4dc"; }
+
+.fa-house-laptop::before {
+  content: "\e066"; }
+
+.fa-laptop-house::before {
+  content: "\e066"; }
+
+.fa-face-tired::before {
+  content: "\f5c8"; }
+
+.fa-tired::before {
+  content: "\f5c8"; }
+
+.fa-money-bills::before {
+  content: "\e1f3"; }
+
+.fa-smog::before {
+  content: "\f75f"; }
+
+.fa-crutch::before {
+  content: "\f7f7"; }
+
+.fa-cloud-arrow-up::before {
+  content: "\f0ee"; }
+
+.fa-cloud-upload::before {
+  content: "\f0ee"; }
+
+.fa-cloud-upload-alt::before {
+  content: "\f0ee"; }
+
+.fa-palette::before {
+  content: "\f53f"; }
+
+.fa-arrows-turn-right::before {
+  content: "\e4c0"; }
+
+.fa-vest::before {
+  content: "\e085"; }
+
+.fa-ferry::before {
+  content: "\e4ea"; }
+
+.fa-arrows-down-to-people::before {
+  content: "\e4b9"; }
+
+.fa-seedling::before {
+  content: "\f4d8"; }
+
+.fa-sprout::before {
+  content: "\f4d8"; }
+
+.fa-left-right::before {
+  content: "\f337"; }
+
+.fa-arrows-alt-h::before {
+  content: "\f337"; }
+
+.fa-boxes-packing::before {
+  content: "\e4c7"; }
+
+.fa-circle-arrow-left::before {
+  content: "\f0a8"; }
+
+.fa-arrow-circle-left::before {
+  content: "\f0a8"; }
+
+.fa-group-arrows-rotate::before {
+  content: "\e4f6"; }
+
+.fa-bowl-food::before {
+  content: "\e4c6"; }
+
+.fa-candy-cane::before {
+  content: "\f786"; }
+
+.fa-arrow-down-wide-short::before {
+  content: "\f160"; }
+
+.fa-sort-amount-asc::before {
+  content: "\f160"; }
+
+.fa-sort-amount-down::before {
+  content: "\f160"; }
+
+.fa-cloud-bolt::before {
+  content: "\f76c"; }
+
+.fa-thunderstorm::before {
+  content: "\f76c"; }
+
+.fa-text-slash::before {
+  content: "\f87d"; }
+
+.fa-remove-format::before {
+  content: "\f87d"; }
+
+.fa-face-smile-wink::before {
+  content: "\f4da"; }
+
+.fa-smile-wink::before {
+  content: "\f4da"; }
+
+.fa-file-word::before {
+  content: "\f1c2"; }
+
+.fa-file-powerpoint::before {
+  content: "\f1c4"; }
+
+.fa-arrows-left-right::before {
+  content: "\f07e"; }
+
+.fa-arrows-h::before {
+  content: "\f07e"; }
+
+.fa-house-lock::before {
+  content: "\e510"; }
+
+.fa-cloud-arrow-down::before {
+  content: "\f0ed"; }
+
+.fa-cloud-download::before {
+  content: "\f0ed"; }
+
+.fa-cloud-download-alt::before {
+  content: "\f0ed"; }
+
+.fa-children::before {
+  content: "\e4e1"; }
+
+.fa-chalkboard::before {
+  content: "\f51b"; }
+
+.fa-blackboard::before {
+  content: "\f51b"; }
+
+.fa-user-large-slash::before {
+  content: "\f4fa"; }
+
+.fa-user-alt-slash::before {
+  content: "\f4fa"; }
+
+.fa-envelope-open::before {
+  content: "\f2b6"; }
+
+.fa-handshake-simple-slash::before {
+  content: "\e05f"; }
+
+.fa-handshake-alt-slash::before {
+  content: "\e05f"; }
+
+.fa-mattress-pillow::before {
+  content: "\e525"; }
+
+.fa-guarani-sign::before {
+  content: "\e19a"; }
+
+.fa-arrows-rotate::before {
+  content: "\f021"; }
+
+.fa-refresh::before {
+  content: "\f021"; }
+
+.fa-sync::before {
+  content: "\f021"; }
+
+.fa-fire-extinguisher::before {
+  content: "\f134"; }
+
+.fa-cruzeiro-sign::before {
+  content: "\e152"; }
+
+.fa-greater-than-equal::before {
+  content: "\f532"; }
+
+.fa-shield-halved::before {
+  content: "\f3ed"; }
+
+.fa-shield-alt::before {
+  content: "\f3ed"; }
+
+.fa-book-atlas::before {
+  content: "\f558"; }
+
+.fa-atlas::before {
+  content: "\f558"; }
+
+.fa-virus::before {
+  content: "\e074"; }
+
+.fa-envelope-circle-check::before {
+  content: "\e4e8"; }
+
+.fa-layer-group::before {
+  content: "\f5fd"; }
+
+.fa-arrows-to-dot::before {
+  content: "\e4be"; }
+
+.fa-archway::before {
+  content: "\f557"; }
+
+.fa-heart-circle-check::before {
+  content: "\e4fd"; }
+
+.fa-house-chimney-crack::before {
+  content: "\f6f1"; }
+
+.fa-house-damage::before {
+  content: "\f6f1"; }
+
+.fa-file-zipper::before {
+  content: "\f1c6"; }
+
+.fa-file-archive::before {
+  content: "\f1c6"; }
+
+.fa-square::before {
+  content: "\f0c8"; }
+
+.fa-martini-glass-empty::before {
+  content: "\f000"; }
+
+.fa-glass-martini::before {
+  content: "\f000"; }
+
+.fa-couch::before {
+  content: "\f4b8"; }
+
+.fa-cedi-sign::before {
+  content: "\e0df"; }
+
+.fa-italic::before {
+  content: "\f033"; }
+
+.fa-table-cells-column-lock::before {
+  content: "\e678"; }
+
+.fa-church::before {
+  content: "\f51d"; }
+
+.fa-comments-dollar::before {
+  content: "\f653"; }
+
+.fa-democrat::before {
+  content: "\f747"; }
+
+.fa-z::before {
+  content: "\5a"; }
+
+.fa-person-skiing::before {
+  content: "\f7c9"; }
+
+.fa-skiing::before {
+  content: "\f7c9"; }
+
+.fa-road-lock::before {
+  content: "\e567"; }
+
+.fa-a::before {
+  content: "\41"; }
+
+.fa-temperature-arrow-down::before {
+  content: "\e03f"; }
+
+.fa-temperature-down::before {
+  content: "\e03f"; }
+
+.fa-feather-pointed::before {
+  content: "\f56b"; }
+
+.fa-feather-alt::before {
+  content: "\f56b"; }
+
+.fa-p::before {
+  content: "\50"; }
+
+.fa-snowflake::before {
+  content: "\f2dc"; }
+
+.fa-newspaper::before {
+  content: "\f1ea"; }
+
+.fa-rectangle-ad::before {
+  content: "\f641"; }
+
+.fa-ad::before {
+  content: "\f641"; }
+
+.fa-circle-arrow-right::before {
+  content: "\f0a9"; }
+
+.fa-arrow-circle-right::before {
+  content: "\f0a9"; }
+
+.fa-filter-circle-xmark::before {
+  content: "\e17b"; }
+
+.fa-locust::before {
+  content: "\e520"; }
+
+.fa-sort::before {
+  content: "\f0dc"; }
+
+.fa-unsorted::before {
+  content: "\f0dc"; }
+
+.fa-list-ol::before {
+  content: "\f0cb"; }
+
+.fa-list-1-2::before {
+  content: "\f0cb"; }
+
+.fa-list-numeric::before {
+  content: "\f0cb"; }
+
+.fa-person-dress-burst::before {
+  content: "\e544"; }
+
+.fa-money-check-dollar::before {
+  content: "\f53d"; }
+
+.fa-money-check-alt::before {
+  content: "\f53d"; }
+
+.fa-vector-square::before {
+  content: "\f5cb"; }
+
+.fa-bread-slice::before {
+  content: "\f7ec"; }
+
+.fa-language::before {
+  content: "\f1ab"; }
+
+.fa-face-kiss-wink-heart::before {
+  content: "\f598"; }
+
+.fa-kiss-wink-heart::before {
+  content: "\f598"; }
+
+.fa-filter::before {
+  content: "\f0b0"; }
+
+.fa-question::before {
+  content: "\3f"; }
+
+.fa-file-signature::before {
+  content: "\f573"; }
+
+.fa-up-down-left-right::before {
+  content: "\f0b2"; }
+
+.fa-arrows-alt::before {
+  content: "\f0b2"; }
+
+.fa-house-chimney-user::before {
+  content: "\e065"; }
+
+.fa-hand-holding-heart::before {
+  content: "\f4be"; }
+
+.fa-puzzle-piece::before {
+  content: "\f12e"; }
+
+.fa-money-check::before {
+  content: "\f53c"; }
+
+.fa-star-half-stroke::before {
+  content: "\f5c0"; }
+
+.fa-star-half-alt::before {
+  content: "\f5c0"; }
+
+.fa-code::before {
+  content: "\f121"; }
+
+.fa-whiskey-glass::before {
+  content: "\f7a0"; }
+
+.fa-glass-whiskey::before {
+  content: "\f7a0"; }
+
+.fa-building-circle-exclamation::before {
+  content: "\e4d3"; }
+
+.fa-magnifying-glass-chart::before {
+  content: "\e522"; }
+
+.fa-arrow-up-right-from-square::before {
+  content: "\f08e"; }
+
+.fa-external-link::before {
+  content: "\f08e"; }
+
+.fa-cubes-stacked::before {
+  content: "\e4e6"; }
+
+.fa-won-sign::before {
+  content: "\f159"; }
+
+.fa-krw::before {
+  content: "\f159"; }
+
+.fa-won::before {
+  content: "\f159"; }
+
+.fa-virus-covid::before {
+  content: "\e4a8"; }
+
+.fa-austral-sign::before {
+  content: "\e0a9"; }
+
+.fa-f::before {
+  content: "\46"; }
+
+.fa-leaf::before {
+  content: "\f06c"; }
+
+.fa-road::before {
+  content: "\f018"; }
+
+.fa-taxi::before {
+  content: "\f1ba"; }
+
+.fa-cab::before {
+  content: "\f1ba"; }
+
+.fa-person-circle-plus::before {
+  content: "\e541"; }
+
+.fa-chart-pie::before {
+  content: "\f200"; }
+
+.fa-pie-chart::before {
+  content: "\f200"; }
+
+.fa-bolt-lightning::before {
+  content: "\e0b7"; }
+
+.fa-sack-xmark::before {
+  content: "\e56a"; }
+
+.fa-file-excel::before {
+  content: "\f1c3"; }
+
+.fa-file-contract::before {
+  content: "\f56c"; }
+
+.fa-fish-fins::before {
+  content: "\e4f2"; }
+
+.fa-building-flag::before {
+  content: "\e4d5"; }
+
+.fa-face-grin-beam::before {
+  content: "\f582"; }
+
+.fa-grin-beam::before {
+  content: "\f582"; }
+
+.fa-object-ungroup::before {
+  content: "\f248"; }
+
+.fa-poop::before {
+  content: "\f619"; }
+
+.fa-location-pin::before {
+  content: "\f041"; }
+
+.fa-map-marker::before {
+  content: "\f041"; }
+
+.fa-kaaba::before {
+  content: "\f66b"; }
+
+.fa-toilet-paper::before {
+  content: "\f71e"; }
+
+.fa-helmet-safety::before {
+  content: "\f807"; }
+
+.fa-hard-hat::before {
+  content: "\f807"; }
+
+.fa-hat-hard::before {
+  content: "\f807"; }
+
+.fa-eject::before {
+  content: "\f052"; }
+
+.fa-circle-right::before {
+  content: "\f35a"; }
+
+.fa-arrow-alt-circle-right::before {
+  content: "\f35a"; }
+
+.fa-plane-circle-check::before {
+  content: "\e555"; }
+
+.fa-face-rolling-eyes::before {
+  content: "\f5a5"; }
+
+.fa-meh-rolling-eyes::before {
+  content: "\f5a5"; }
+
+.fa-object-group::before {
+  content: "\f247"; }
+
+.fa-chart-line::before {
+  content: "\f201"; }
+
+.fa-line-chart::before {
+  content: "\f201"; }
+
+.fa-mask-ventilator::before {
+  content: "\e524"; }
+
+.fa-arrow-right::before {
+  content: "\f061"; }
+
+.fa-signs-post::before {
+  content: "\f277"; }
+
+.fa-map-signs::before {
+  content: "\f277"; }
+
+.fa-cash-register::before {
+  content: "\f788"; }
+
+.fa-person-circle-question::before {
+  content: "\e542"; }
+
+.fa-h::before {
+  content: "\48"; }
+
+.fa-tarp::before {
+  content: "\e57b"; }
+
+.fa-screwdriver-wrench::before {
+  content: "\f7d9"; }
+
+.fa-tools::before {
+  content: "\f7d9"; }
+
+.fa-arrows-to-eye::before {
+  content: "\e4bf"; }
+
+.fa-plug-circle-bolt::before {
+  content: "\e55b"; }
+
+.fa-heart::before {
+  content: "\f004"; }
+
+.fa-mars-and-venus::before {
+  content: "\f224"; }
+
+.fa-house-user::before {
+  content: "\e1b0"; }
+
+.fa-home-user::before {
+  content: "\e1b0"; }
+
+.fa-dumpster-fire::before {
+  content: "\f794"; }
+
+.fa-house-crack::before {
+  content: "\e3b1"; }
+
+.fa-martini-glass-citrus::before {
+  content: "\f561"; }
+
+.fa-cocktail::before {
+  content: "\f561"; }
+
+.fa-face-surprise::before {
+  content: "\f5c2"; }
+
+.fa-surprise::before {
+  content: "\f5c2"; }
+
+.fa-bottle-water::before {
+  content: "\e4c5"; }
+
+.fa-circle-pause::before {
+  content: "\f28b"; }
+
+.fa-pause-circle::before {
+  content: "\f28b"; }
+
+.fa-toilet-paper-slash::before {
+  content: "\e072"; }
+
+.fa-apple-whole::before {
+  content: "\f5d1"; }
+
+.fa-apple-alt::before {
+  content: "\f5d1"; }
+
+.fa-kitchen-set::before {
+  content: "\e51a"; }
+
+.fa-r::before {
+  content: "\52"; }
+
+.fa-temperature-quarter::before {
+  content: "\f2ca"; }
+
+.fa-temperature-1::before {
+  content: "\f2ca"; }
+
+.fa-thermometer-1::before {
+  content: "\f2ca"; }
+
+.fa-thermometer-quarter::before {
+  content: "\f2ca"; }
+
+.fa-cube::before {
+  content: "\f1b2"; }
+
+.fa-bitcoin-sign::before {
+  content: "\e0b4"; }
+
+.fa-shield-dog::before {
+  content: "\e573"; }
+
+.fa-solar-panel::before {
+  content: "\f5ba"; }
+
+.fa-lock-open::before {
+  content: "\f3c1"; }
+
+.fa-elevator::before {
+  content: "\e16d"; }
+
+.fa-money-bill-transfer::before {
+  content: "\e528"; }
+
+.fa-money-bill-trend-up::before {
+  content: "\e529"; }
+
+.fa-house-flood-water-circle-arrow-right::before {
+  content: "\e50f"; }
+
+.fa-square-poll-horizontal::before {
+  content: "\f682"; }
+
+.fa-poll-h::before {
+  content: "\f682"; }
+
+.fa-circle::before {
+  content: "\f111"; }
+
+.fa-backward-fast::before {
+  content: "\f049"; }
+
+.fa-fast-backward::before {
+  content: "\f049"; }
+
+.fa-recycle::before {
+  content: "\f1b8"; }
+
+.fa-user-astronaut::before {
+  content: "\f4fb"; }
+
+.fa-plane-slash::before {
+  content: "\e069"; }
+
+.fa-trademark::before {
+  content: "\f25c"; }
+
+.fa-basketball::before {
+  content: "\f434"; }
+
+.fa-basketball-ball::before {
+  content: "\f434"; }
+
+.fa-satellite-dish::before {
+  content: "\f7c0"; }
+
+.fa-circle-up::before {
+  content: "\f35b"; }
+
+.fa-arrow-alt-circle-up::before {
+  content: "\f35b"; }
+
+.fa-mobile-screen-button::before {
+  content: "\f3cd"; }
+
+.fa-mobile-alt::before {
+  content: "\f3cd"; }
+
+.fa-volume-high::before {
+  content: "\f028"; }
+
+.fa-volume-up::before {
+  content: "\f028"; }
+
+.fa-users-rays::before {
+  content: "\e593"; }
+
+.fa-wallet::before {
+  content: "\f555"; }
+
+.fa-clipboard-check::before {
+  content: "\f46c"; }
+
+.fa-file-audio::before {
+  content: "\f1c7"; }
+
+.fa-burger::before {
+  content: "\f805"; }
+
+.fa-hamburger::before {
+  content: "\f805"; }
+
+.fa-wrench::before {
+  content: "\f0ad"; }
+
+.fa-bugs::before {
+  content: "\e4d0"; }
+
+.fa-rupee-sign::before {
+  content: "\f156"; }
+
+.fa-rupee::before {
+  content: "\f156"; }
+
+.fa-file-image::before {
+  content: "\f1c5"; }
+
+.fa-circle-question::before {
+  content: "\f059"; }
+
+.fa-question-circle::before {
+  content: "\f059"; }
+
+.fa-plane-departure::before {
+  content: "\f5b0"; }
+
+.fa-handshake-slash::before {
+  content: "\e060"; }
+
+.fa-book-bookmark::before {
+  content: "\e0bb"; }
+
+.fa-code-branch::before {
+  content: "\f126"; }
+
+.fa-hat-cowboy::before {
+  content: "\f8c0"; }
+
+.fa-bridge::before {
+  content: "\e4c8"; }
+
+.fa-phone-flip::before {
+  content: "\f879"; }
+
+.fa-phone-alt::before {
+  content: "\f879"; }
+
+.fa-truck-front::before {
+  content: "\e2b7"; }
+
+.fa-cat::before {
+  content: "\f6be"; }
+
+.fa-anchor-circle-exclamation::before {
+  content: "\e4ab"; }
+
+.fa-truck-field::before {
+  content: "\e58d"; }
+
+.fa-route::before {
+  content: "\f4d7"; }
+
+.fa-clipboard-question::before {
+  content: "\e4e3"; }
+
+.fa-panorama::before {
+  content: "\e209"; }
+
+.fa-comment-medical::before {
+  content: "\f7f5"; }
+
+.fa-teeth-open::before {
+  content: "\f62f"; }
+
+.fa-file-circle-minus::before {
+  content: "\e4ed"; }
+
+.fa-tags::before {
+  content: "\f02c"; }
+
+.fa-wine-glass::before {
+  content: "\f4e3"; }
+
+.fa-forward-fast::before {
+  content: "\f050"; }
+
+.fa-fast-forward::before {
+  content: "\f050"; }
+
+.fa-face-meh-blank::before {
+  content: "\f5a4"; }
+
+.fa-meh-blank::before {
+  content: "\f5a4"; }
+
+.fa-square-parking::before {
+  content: "\f540"; }
+
+.fa-parking::before {
+  content: "\f540"; }
+
+.fa-house-signal::before {
+  content: "\e012"; }
+
+.fa-bars-progress::before {
+  content: "\f828"; }
+
+.fa-tasks-alt::before {
+  content: "\f828"; }
+
+.fa-faucet-drip::before {
+  content: "\e006"; }
+
+.fa-cart-flatbed::before {
+  content: "\f474"; }
+
+.fa-dolly-flatbed::before {
+  content: "\f474"; }
+
+.fa-ban-smoking::before {
+  content: "\f54d"; }
+
+.fa-smoking-ban::before {
+  content: "\f54d"; }
+
+.fa-terminal::before {
+  content: "\f120"; }
+
+.fa-mobile-button::before {
+  content: "\f10b"; }
+
+.fa-house-medical-flag::before {
+  content: "\e514"; }
+
+.fa-basket-shopping::before {
+  content: "\f291"; }
+
+.fa-shopping-basket::before {
+  content: "\f291"; }
+
+.fa-tape::before {
+  content: "\f4db"; }
+
+.fa-bus-simple::before {
+  content: "\f55e"; }
+
+.fa-bus-alt::before {
+  content: "\f55e"; }
+
+.fa-eye::before {
+  content: "\f06e"; }
+
+.fa-face-sad-cry::before {
+  content: "\f5b3"; }
+
+.fa-sad-cry::before {
+  content: "\f5b3"; }
+
+.fa-audio-description::before {
+  content: "\f29e"; }
+
+.fa-person-military-to-person::before {
+  content: "\e54c"; }
+
+.fa-file-shield::before {
+  content: "\e4f0"; }
+
+.fa-user-slash::before {
+  content: "\f506"; }
+
+.fa-pen::before {
+  content: "\f304"; }
+
+.fa-tower-observation::before {
+  content: "\e586"; }
+
+.fa-file-code::before {
+  content: "\f1c9"; }
+
+.fa-signal::before {
+  content: "\f012"; }
+
+.fa-signal-5::before {
+  content: "\f012"; }
+
+.fa-signal-perfect::before {
+  content: "\f012"; }
+
+.fa-bus::before {
+  content: "\f207"; }
+
+.fa-heart-circle-xmark::before {
+  content: "\e501"; }
+
+.fa-house-chimney::before {
+  content: "\e3af"; }
+
+.fa-home-lg::before {
+  content: "\e3af"; }
+
+.fa-window-maximize::before {
+  content: "\f2d0"; }
+
+.fa-face-frown::before {
+  content: "\f119"; }
+
+.fa-frown::before {
+  content: "\f119"; }
+
+.fa-prescription::before {
+  content: "\f5b1"; }
+
+.fa-shop::before {
+  content: "\f54f"; }
+
+.fa-store-alt::before {
+  content: "\f54f"; }
+
+.fa-floppy-disk::before {
+  content: "\f0c7"; }
+
+.fa-save::before {
+  content: "\f0c7"; }
+
+.fa-vihara::before {
+  content: "\f6a7"; }
+
+.fa-scale-unbalanced::before {
+  content: "\f515"; }
+
+.fa-balance-scale-left::before {
+  content: "\f515"; }
+
+.fa-sort-up::before {
+  content: "\f0de"; }
+
+.fa-sort-asc::before {
+  content: "\f0de"; }
+
+.fa-comment-dots::before {
+  content: "\f4ad"; }
+
+.fa-commenting::before {
+  content: "\f4ad"; }
+
+.fa-plant-wilt::before {
+  content: "\e5aa"; }
+
+.fa-diamond::before {
+  content: "\f219"; }
+
+.fa-face-grin-squint::before {
+  content: "\f585"; }
+
+.fa-grin-squint::before {
+  content: "\f585"; }
+
+.fa-hand-holding-dollar::before {
+  content: "\f4c0"; }
+
+.fa-hand-holding-usd::before {
+  content: "\f4c0"; }
+
+.fa-bacterium::before {
+  content: "\e05a"; }
+
+.fa-hand-pointer::before {
+  content: "\f25a"; }
+
+.fa-drum-steelpan::before {
+  content: "\f56a"; }
+
+.fa-hand-scissors::before {
+  content: "\f257"; }
+
+.fa-hands-praying::before {
+  content: "\f684"; }
+
+.fa-praying-hands::before {
+  content: "\f684"; }
+
+.fa-arrow-rotate-right::before {
+  content: "\f01e"; }
+
+.fa-arrow-right-rotate::before {
+  content: "\f01e"; }
+
+.fa-arrow-rotate-forward::before {
+  content: "\f01e"; }
+
+.fa-redo::before {
+  content: "\f01e"; }
+
+.fa-biohazard::before {
+  content: "\f780"; }
+
+.fa-location-crosshairs::before {
+  content: "\f601"; }
+
+.fa-location::before {
+  content: "\f601"; }
+
+.fa-mars-double::before {
+  content: "\f227"; }
+
+.fa-child-dress::before {
+  content: "\e59c"; }
+
+.fa-users-between-lines::before {
+  content: "\e591"; }
+
+.fa-lungs-virus::before {
+  content: "\e067"; }
+
+.fa-face-grin-tears::before {
+  content: "\f588"; }
+
+.fa-grin-tears::before {
+  content: "\f588"; }
+
+.fa-phone::before {
+  content: "\f095"; }
+
+.fa-calendar-xmark::before {
+  content: "\f273"; }
+
+.fa-calendar-times::before {
+  content: "\f273"; }
+
+.fa-child-reaching::before {
+  content: "\e59d"; }
+
+.fa-head-side-virus::before {
+  content: "\e064"; }
+
+.fa-user-gear::before {
+  content: "\f4fe"; }
+
+.fa-user-cog::before {
+  content: "\f4fe"; }
+
+.fa-arrow-up-1-9::before {
+  content: "\f163"; }
+
+.fa-sort-numeric-up::before {
+  content: "\f163"; }
+
+.fa-door-closed::before {
+  content: "\f52a"; }
+
+.fa-shield-virus::before {
+  content: "\e06c"; }
+
+.fa-dice-six::before {
+  content: "\f526"; }
+
+.fa-mosquito-net::before {
+  content: "\e52c"; }
+
+.fa-bridge-water::before {
+  content: "\e4ce"; }
+
+.fa-person-booth::before {
+  content: "\f756"; }
+
+.fa-text-width::before {
+  content: "\f035"; }
+
+.fa-hat-wizard::before {
+  content: "\f6e8"; }
+
+.fa-pen-fancy::before {
+  content: "\f5ac"; }
+
+.fa-person-digging::before {
+  content: "\f85e"; }
+
+.fa-digging::before {
+  content: "\f85e"; }
+
+.fa-trash::before {
+  content: "\f1f8"; }
+
+.fa-gauge-simple::before {
+  content: "\f629"; }
+
+.fa-gauge-simple-med::before {
+  content: "\f629"; }
+
+.fa-tachometer-average::before {
+  content: "\f629"; }
+
+.fa-book-medical::before {
+  content: "\f7e6"; }
+
+.fa-poo::before {
+  content: "\f2fe"; }
+
+.fa-quote-right::before {
+  content: "\f10e"; }
+
+.fa-quote-right-alt::before {
+  content: "\f10e"; }
+
+.fa-shirt::before {
+  content: "\f553"; }
+
+.fa-t-shirt::before {
+  content: "\f553"; }
+
+.fa-tshirt::before {
+  content: "\f553"; }
+
+.fa-cubes::before {
+  content: "\f1b3"; }
+
+.fa-divide::before {
+  content: "\f529"; }
+
+.fa-tenge-sign::before {
+  content: "\f7d7"; }
+
+.fa-tenge::before {
+  content: "\f7d7"; }
+
+.fa-headphones::before {
+  content: "\f025"; }
+
+.fa-hands-holding::before {
+  content: "\f4c2"; }
+
+.fa-hands-clapping::before {
+  content: "\e1a8"; }
+
+.fa-republican::before {
+  content: "\f75e"; }
+
+.fa-arrow-left::before {
+  content: "\f060"; }
+
+.fa-person-circle-xmark::before {
+  content: "\e543"; }
+
+.fa-ruler::before {
+  content: "\f545"; }
+
+.fa-align-left::before {
+  content: "\f036"; }
+
+.fa-dice-d6::before {
+  content: "\f6d1"; }
+
+.fa-restroom::before {
+  content: "\f7bd"; }
+
+.fa-j::before {
+  content: "\4a"; }
+
+.fa-users-viewfinder::before {
+  content: "\e595"; }
+
+.fa-file-video::before {
+  content: "\f1c8"; }
+
+.fa-up-right-from-square::before {
+  content: "\f35d"; }
+
+.fa-external-link-alt::before {
+  content: "\f35d"; }
+
+.fa-table-cells::before {
+  content: "\f00a"; }
+
+.fa-th::before {
+  content: "\f00a"; }
+
+.fa-file-pdf::before {
+  content: "\f1c1"; }
+
+.fa-book-bible::before {
+  content: "\f647"; }
+
+.fa-bible::before {
+  content: "\f647"; }
+
+.fa-o::before {
+  content: "\4f"; }
+
+.fa-suitcase-medical::before {
+  content: "\f0fa"; }
+
+.fa-medkit::before {
+  content: "\f0fa"; }
+
+.fa-user-secret::before {
+  content: "\f21b"; }
+
+.fa-otter::before {
+  content: "\f700"; }
+
+.fa-person-dress::before {
+  content: "\f182"; }
+
+.fa-female::before {
+  content: "\f182"; }
+
+.fa-comment-dollar::before {
+  content: "\f651"; }
+
+.fa-business-time::before {
+  content: "\f64a"; }
+
+.fa-briefcase-clock::before {
+  content: "\f64a"; }
+
+.fa-table-cells-large::before {
+  content: "\f009"; }
+
+.fa-th-large::before {
+  content: "\f009"; }
+
+.fa-book-tanakh::before {
+  content: "\f827"; }
+
+.fa-tanakh::before {
+  content: "\f827"; }
+
+.fa-phone-volume::before {
+  content: "\f2a0"; }
+
+.fa-volume-control-phone::before {
+  content: "\f2a0"; }
+
+.fa-hat-cowboy-side::before {
+  content: "\f8c1"; }
+
+.fa-clipboard-user::before {
+  content: "\f7f3"; }
+
+.fa-child::before {
+  content: "\f1ae"; }
+
+.fa-lira-sign::before {
+  content: "\f195"; }
+
+.fa-satellite::before {
+  content: "\f7bf"; }
+
+.fa-plane-lock::before {
+  content: "\e558"; }
+
+.fa-tag::before {
+  content: "\f02b"; }
+
+.fa-comment::before {
+  content: "\f075"; }
+
+.fa-cake-candles::before {
+  content: "\f1fd"; }
+
+.fa-birthday-cake::before {
+  content: "\f1fd"; }
+
+.fa-cake::before {
+  content: "\f1fd"; }
+
+.fa-envelope::before {
+  content: "\f0e0"; }
+
+.fa-angles-up::before {
+  content: "\f102"; }
+
+.fa-angle-double-up::before {
+  content: "\f102"; }
+
+.fa-paperclip::before {
+  content: "\f0c6"; }
+
+.fa-arrow-right-to-city::before {
+  content: "\e4b3"; }
+
+.fa-ribbon::before {
+  content: "\f4d6"; }
+
+.fa-lungs::before {
+  content: "\f604"; }
+
+.fa-arrow-up-9-1::before {
+  content: "\f887"; }
+
+.fa-sort-numeric-up-alt::before {
+  content: "\f887"; }
+
+.fa-litecoin-sign::before {
+  content: "\e1d3"; }
+
+.fa-border-none::before {
+  content: "\f850"; }
+
+.fa-circle-nodes::before {
+  content: "\e4e2"; }
+
+.fa-parachute-box::before {
+  content: "\f4cd"; }
+
+.fa-indent::before {
+  content: "\f03c"; }
+
+.fa-truck-field-un::before {
+  content: "\e58e"; }
+
+.fa-hourglass::before {
+  content: "\f254"; }
+
+.fa-hourglass-empty::before {
+  content: "\f254"; }
+
+.fa-mountain::before {
+  content: "\f6fc"; }
+
+.fa-user-doctor::before {
+  content: "\f0f0"; }
+
+.fa-user-md::before {
+  content: "\f0f0"; }
+
+.fa-circle-info::before {
+  content: "\f05a"; }
+
+.fa-info-circle::before {
+  content: "\f05a"; }
+
+.fa-cloud-meatball::before {
+  content: "\f73b"; }
+
+.fa-camera::before {
+  content: "\f030"; }
+
+.fa-camera-alt::before {
+  content: "\f030"; }
+
+.fa-square-virus::before {
+  content: "\e578"; }
+
+.fa-meteor::before {
+  content: "\f753"; }
+
+.fa-car-on::before {
+  content: "\e4dd"; }
+
+.fa-sleigh::before {
+  content: "\f7cc"; }
+
+.fa-arrow-down-1-9::before {
+  content: "\f162"; }
+
+.fa-sort-numeric-asc::before {
+  content: "\f162"; }
+
+.fa-sort-numeric-down::before {
+  content: "\f162"; }
+
+.fa-hand-holding-droplet::before {
+  content: "\f4c1"; }
+
+.fa-hand-holding-water::before {
+  content: "\f4c1"; }
+
+.fa-water::before {
+  content: "\f773"; }
+
+.fa-calendar-check::before {
+  content: "\f274"; }
+
+.fa-braille::before {
+  content: "\f2a1"; }
+
+.fa-prescription-bottle-medical::before {
+  content: "\f486"; }
+
+.fa-prescription-bottle-alt::before {
+  content: "\f486"; }
+
+.fa-landmark::before {
+  content: "\f66f"; }
+
+.fa-truck::before {
+  content: "\f0d1"; }
+
+.fa-crosshairs::before {
+  content: "\f05b"; }
+
+.fa-person-cane::before {
+  content: "\e53c"; }
+
+.fa-tent::before {
+  content: "\e57d"; }
+
+.fa-vest-patches::before {
+  content: "\e086"; }
+
+.fa-check-double::before {
+  content: "\f560"; }
+
+.fa-arrow-down-a-z::before {
+  content: "\f15d"; }
+
+.fa-sort-alpha-asc::before {
+  content: "\f15d"; }
+
+.fa-sort-alpha-down::before {
+  content: "\f15d"; }
+
+.fa-money-bill-wheat::before {
+  content: "\e52a"; }
+
+.fa-cookie::before {
+  content: "\f563"; }
+
+.fa-arrow-rotate-left::before {
+  content: "\f0e2"; }
+
+.fa-arrow-left-rotate::before {
+  content: "\f0e2"; }
+
+.fa-arrow-rotate-back::before {
+  content: "\f0e2"; }
+
+.fa-arrow-rotate-backward::before {
+  content: "\f0e2"; }
+
+.fa-undo::before {
+  content: "\f0e2"; }
+
+.fa-hard-drive::before {
+  content: "\f0a0"; }
+
+.fa-hdd::before {
+  content: "\f0a0"; }
+
+.fa-face-grin-squint-tears::before {
+  content: "\f586"; }
+
+.fa-grin-squint-tears::before {
+  content: "\f586"; }
+
+.fa-dumbbell::before {
+  content: "\f44b"; }
+
+.fa-rectangle-list::before {
+  content: "\f022"; }
+
+.fa-list-alt::before {
+  content: "\f022"; }
+
+.fa-tarp-droplet::before {
+  content: "\e57c"; }
+
+.fa-house-medical-circle-check::before {
+  content: "\e511"; }
+
+.fa-person-skiing-nordic::before {
+  content: "\f7ca"; }
+
+.fa-skiing-nordic::before {
+  content: "\f7ca"; }
+
+.fa-calendar-plus::before {
+  content: "\f271"; }
+
+.fa-plane-arrival::before {
+  content: "\f5af"; }
+
+.fa-circle-left::before {
+  content: "\f359"; }
+
+.fa-arrow-alt-circle-left::before {
+  content: "\f359"; }
+
+.fa-train-subway::before {
+  content: "\f239"; }
+
+.fa-subway::before {
+  content: "\f239"; }
+
+.fa-chart-gantt::before {
+  content: "\e0e4"; }
+
+.fa-indian-rupee-sign::before {
+  content: "\e1bc"; }
+
+.fa-indian-rupee::before {
+  content: "\e1bc"; }
+
+.fa-inr::before {
+  content: "\e1bc"; }
+
+.fa-crop-simple::before {
+  content: "\f565"; }
+
+.fa-crop-alt::before {
+  content: "\f565"; }
+
+.fa-money-bill-1::before {
+  content: "\f3d1"; }
+
+.fa-money-bill-alt::before {
+  content: "\f3d1"; }
+
+.fa-left-long::before {
+  content: "\f30a"; }
+
+.fa-long-arrow-alt-left::before {
+  content: "\f30a"; }
+
+.fa-dna::before {
+  content: "\f471"; }
+
+.fa-virus-slash::before {
+  content: "\e075"; }
+
+.fa-minus::before {
+  content: "\f068"; }
+
+.fa-subtract::before {
+  content: "\f068"; }
+
+.fa-chess::before {
+  content: "\f439"; }
+
+.fa-arrow-left-long::before {
+  content: "\f177"; }
+
+.fa-long-arrow-left::before {
+  content: "\f177"; }
+
+.fa-plug-circle-check::before {
+  content: "\e55c"; }
+
+.fa-street-view::before {
+  content: "\f21d"; }
+
+.fa-franc-sign::before {
+  content: "\e18f"; }
+
+.fa-volume-off::before {
+  content: "\f026"; }
+
+.fa-hands-asl-interpreting::before {
+  content: "\f2a3"; }
+
+.fa-american-sign-language-interpreting::before {
+  content: "\f2a3"; }
+
+.fa-asl-interpreting::before {
+  content: "\f2a3"; }
+
+.fa-hands-american-sign-language-interpreting::before {
+  content: "\f2a3"; }
+
+.fa-gear::before {
+  content: "\f013"; }
+
+.fa-cog::before {
+  content: "\f013"; }
+
+.fa-droplet-slash::before {
+  content: "\f5c7"; }
+
+.fa-tint-slash::before {
+  content: "\f5c7"; }
+
+.fa-mosque::before {
+  content: "\f678"; }
+
+.fa-mosquito::before {
+  content: "\e52b"; }
+
+.fa-star-of-david::before {
+  content: "\f69a"; }
+
+.fa-person-military-rifle::before {
+  content: "\e54b"; }
+
+.fa-cart-shopping::before {
+  content: "\f07a"; }
+
+.fa-shopping-cart::before {
+  content: "\f07a"; }
+
+.fa-vials::before {
+  content: "\f493"; }
+
+.fa-plug-circle-plus::before {
+  content: "\e55f"; }
+
+.fa-place-of-worship::before {
+  content: "\f67f"; }
+
+.fa-grip-vertical::before {
+  content: "\f58e"; }
+
+.fa-arrow-turn-up::before {
+  content: "\f148"; }
+
+.fa-level-up::before {
+  content: "\f148"; }
+
+.fa-u::before {
+  content: "\55"; }
+
+.fa-square-root-variable::before {
+  content: "\f698"; }
+
+.fa-square-root-alt::before {
+  content: "\f698"; }
+
+.fa-clock::before {
+  content: "\f017"; }
+
+.fa-clock-four::before {
+  content: "\f017"; }
+
+.fa-backward-step::before {
+  content: "\f048"; }
+
+.fa-step-backward::before {
+  content: "\f048"; }
+
+.fa-pallet::before {
+  content: "\f482"; }
+
+.fa-faucet::before {
+  content: "\e005"; }
+
+.fa-baseball-bat-ball::before {
+  content: "\f432"; }
+
+.fa-s::before {
+  content: "\53"; }
+
+.fa-timeline::before {
+  content: "\e29c"; }
+
+.fa-keyboard::before {
+  content: "\f11c"; }
+
+.fa-caret-down::before {
+  content: "\f0d7"; }
+
+.fa-house-chimney-medical::before {
+  content: "\f7f2"; }
+
+.fa-clinic-medical::before {
+  content: "\f7f2"; }
+
+.fa-temperature-three-quarters::before {
+  content: "\f2c8"; }
+
+.fa-temperature-3::before {
+  content: "\f2c8"; }
+
+.fa-thermometer-3::before {
+  content: "\f2c8"; }
+
+.fa-thermometer-three-quarters::before {
+  content: "\f2c8"; }
+
+.fa-mobile-screen::before {
+  content: "\f3cf"; }
+
+.fa-mobile-android-alt::before {
+  content: "\f3cf"; }
+
+.fa-plane-up::before {
+  content: "\e22d"; }
+
+.fa-piggy-bank::before {
+  content: "\f4d3"; }
+
+.fa-battery-half::before {
+  content: "\f242"; }
+
+.fa-battery-3::before {
+  content: "\f242"; }
+
+.fa-mountain-city::before {
+  content: "\e52e"; }
+
+.fa-coins::before {
+  content: "\f51e"; }
+
+.fa-khanda::before {
+  content: "\f66d"; }
+
+.fa-sliders::before {
+  content: "\f1de"; }
+
+.fa-sliders-h::before {
+  content: "\f1de"; }
+
+.fa-folder-tree::before {
+  content: "\f802"; }
+
+.fa-network-wired::before {
+  content: "\f6ff"; }
+
+.fa-map-pin::before {
+  content: "\f276"; }
+
+.fa-hamsa::before {
+  content: "\f665"; }
+
+.fa-cent-sign::before {
+  content: "\e3f5"; }
+
+.fa-flask::before {
+  content: "\f0c3"; }
+
+.fa-person-pregnant::before {
+  content: "\e31e"; }
+
+.fa-wand-sparkles::before {
+  content: "\f72b"; }
+
+.fa-ellipsis-vertical::before {
+  content: "\f142"; }
+
+.fa-ellipsis-v::before {
+  content: "\f142"; }
+
+.fa-ticket::before {
+  content: "\f145"; }
+
+.fa-power-off::before {
+  content: "\f011"; }
+
+.fa-right-long::before {
+  content: "\f30b"; }
+
+.fa-long-arrow-alt-right::before {
+  content: "\f30b"; }
+
+.fa-flag-usa::before {
+  content: "\f74d"; }
+
+.fa-laptop-file::before {
+  content: "\e51d"; }
+
+.fa-tty::before {
+  content: "\f1e4"; }
+
+.fa-teletype::before {
+  content: "\f1e4"; }
+
+.fa-diagram-next::before {
+  content: "\e476"; }
+
+.fa-person-rifle::before {
+  content: "\e54e"; }
+
+.fa-house-medical-circle-exclamation::before {
+  content: "\e512"; }
+
+.fa-closed-captioning::before {
+  content: "\f20a"; }
+
+.fa-person-hiking::before {
+  content: "\f6ec"; }
+
+.fa-hiking::before {
+  content: "\f6ec"; }
+
+.fa-venus-double::before {
+  content: "\f226"; }
+
+.fa-images::before {
+  content: "\f302"; }
+
+.fa-calculator::before {
+  content: "\f1ec"; }
+
+.fa-people-pulling::before {
+  content: "\e535"; }
+
+.fa-n::before {
+  content: "\4e"; }
+
+.fa-cable-car::before {
+  content: "\f7da"; }
+
+.fa-tram::before {
+  content: "\f7da"; }
+
+.fa-cloud-rain::before {
+  content: "\f73d"; }
+
+.fa-building-circle-xmark::before {
+  content: "\e4d4"; }
+
+.fa-ship::before {
+  content: "\f21a"; }
+
+.fa-arrows-down-to-line::before {
+  content: "\e4b8"; }
+
+.fa-download::before {
+  content: "\f019"; }
+
+.fa-face-grin::before {
+  content: "\f580"; }
+
+.fa-grin::before {
+  content: "\f580"; }
+
+.fa-delete-left::before {
+  content: "\f55a"; }
+
+.fa-backspace::before {
+  content: "\f55a"; }
+
+.fa-eye-dropper::before {
+  content: "\f1fb"; }
+
+.fa-eye-dropper-empty::before {
+  content: "\f1fb"; }
+
+.fa-eyedropper::before {
+  content: "\f1fb"; }
+
+.fa-file-circle-check::before {
+  content: "\e5a0"; }
+
+.fa-forward::before {
+  content: "\f04e"; }
+
+.fa-mobile::before {
+  content: "\f3ce"; }
+
+.fa-mobile-android::before {
+  content: "\f3ce"; }
+
+.fa-mobile-phone::before {
+  content: "\f3ce"; }
+
+.fa-face-meh::before {
+  content: "\f11a"; }
+
+.fa-meh::before {
+  content: "\f11a"; }
+
+.fa-align-center::before {
+  content: "\f037"; }
+
+.fa-book-skull::before {
+  content: "\f6b7"; }
+
+.fa-book-dead::before {
+  content: "\f6b7"; }
+
+.fa-id-card::before {
+  content: "\f2c2"; }
+
+.fa-drivers-license::before {
+  content: "\f2c2"; }
+
+.fa-outdent::before {
+  content: "\f03b"; }
+
+.fa-dedent::before {
+  content: "\f03b"; }
+
+.fa-heart-circle-exclamation::before {
+  content: "\e4fe"; }
+
+.fa-house::before {
+  content: "\f015"; }
+
+.fa-home::before {
+  content: "\f015"; }
+
+.fa-home-alt::before {
+  content: "\f015"; }
+
+.fa-home-lg-alt::before {
+  content: "\f015"; }
+
+.fa-calendar-week::before {
+  content: "\f784"; }
+
+.fa-laptop-medical::before {
+  content: "\f812"; }
+
+.fa-b::before {
+  content: "\42"; }
+
+.fa-file-medical::before {
+  content: "\f477"; }
+
+.fa-dice-one::before {
+  content: "\f525"; }
+
+.fa-kiwi-bird::before {
+  content: "\f535"; }
+
+.fa-arrow-right-arrow-left::before {
+  content: "\f0ec"; }
+
+.fa-exchange::before {
+  content: "\f0ec"; }
+
+.fa-rotate-right::before {
+  content: "\f2f9"; }
+
+.fa-redo-alt::before {
+  content: "\f2f9"; }
+
+.fa-rotate-forward::before {
+  content: "\f2f9"; }
+
+.fa-utensils::before {
+  content: "\f2e7"; }
+
+.fa-cutlery::before {
+  content: "\f2e7"; }
+
+.fa-arrow-up-wide-short::before {
+  content: "\f161"; }
+
+.fa-sort-amount-up::before {
+  content: "\f161"; }
+
+.fa-mill-sign::before {
+  content: "\e1ed"; }
+
+.fa-bowl-rice::before {
+  content: "\e2eb"; }
+
+.fa-skull::before {
+  content: "\f54c"; }
+
+.fa-tower-broadcast::before {
+  content: "\f519"; }
+
+.fa-broadcast-tower::before {
+  content: "\f519"; }
+
+.fa-truck-pickup::before {
+  content: "\f63c"; }
+
+.fa-up-long::before {
+  content: "\f30c"; }
+
+.fa-long-arrow-alt-up::before {
+  content: "\f30c"; }
+
+.fa-stop::before {
+  content: "\f04d"; }
+
+.fa-code-merge::before {
+  content: "\f387"; }
+
+.fa-upload::before {
+  content: "\f093"; }
+
+.fa-hurricane::before {
+  content: "\f751"; }
+
+.fa-mound::before {
+  content: "\e52d"; }
+
+.fa-toilet-portable::before {
+  content: "\e583"; }
+
+.fa-compact-disc::before {
+  content: "\f51f"; }
+
+.fa-file-arrow-down::before {
+  content: "\f56d"; }
+
+.fa-file-download::before {
+  content: "\f56d"; }
+
+.fa-caravan::before {
+  content: "\f8ff"; }
+
+.fa-shield-cat::before {
+  content: "\e572"; }
+
+.fa-bolt::before {
+  content: "\f0e7"; }
+
+.fa-zap::before {
+  content: "\f0e7"; }
+
+.fa-glass-water::before {
+  content: "\e4f4"; }
+
+.fa-oil-well::before {
+  content: "\e532"; }
+
+.fa-vault::before {
+  content: "\e2c5"; }
+
+.fa-mars::before {
+  content: "\f222"; }
+
+.fa-toilet::before {
+  content: "\f7d8"; }
+
+.fa-plane-circle-xmark::before {
+  content: "\e557"; }
+
+.fa-yen-sign::before {
+  content: "\f157"; }
+
+.fa-cny::before {
+  content: "\f157"; }
+
+.fa-jpy::before {
+  content: "\f157"; }
+
+.fa-rmb::before {
+  content: "\f157"; }
+
+.fa-yen::before {
+  content: "\f157"; }
+
+.fa-ruble-sign::before {
+  content: "\f158"; }
+
+.fa-rouble::before {
+  content: "\f158"; }
+
+.fa-rub::before {
+  content: "\f158"; }
+
+.fa-ruble::before {
+  content: "\f158"; }
+
+.fa-sun::before {
+  content: "\f185"; }
+
+.fa-guitar::before {
+  content: "\f7a6"; }
+
+.fa-face-laugh-wink::before {
+  content: "\f59c"; }
+
+.fa-laugh-wink::before {
+  content: "\f59c"; }
+
+.fa-horse-head::before {
+  content: "\f7ab"; }
+
+.fa-bore-hole::before {
+  content: "\e4c3"; }
+
+.fa-industry::before {
+  content: "\f275"; }
+
+.fa-circle-down::before {
+  content: "\f358"; }
+
+.fa-arrow-alt-circle-down::before {
+  content: "\f358"; }
+
+.fa-arrows-turn-to-dots::before {
+  content: "\e4c1"; }
+
+.fa-florin-sign::before {
+  content: "\e184"; }
+
+.fa-arrow-down-short-wide::before {
+  content: "\f884"; }
+
+.fa-sort-amount-desc::before {
+  content: "\f884"; }
+
+.fa-sort-amount-down-alt::before {
+  content: "\f884"; }
+
+.fa-less-than::before {
+  content: "\3c"; }
+
+.fa-angle-down::before {
+  content: "\f107"; }
+
+.fa-car-tunnel::before {
+  content: "\e4de"; }
+
+.fa-head-side-cough::before {
+  content: "\e061"; }
+
+.fa-grip-lines::before {
+  content: "\f7a4"; }
+
+.fa-thumbs-down::before {
+  content: "\f165"; }
+
+.fa-user-lock::before {
+  content: "\f502"; }
+
+.fa-arrow-right-long::before {
+  content: "\f178"; }
+
+.fa-long-arrow-right::before {
+  content: "\f178"; }
+
+.fa-anchor-circle-xmark::before {
+  content: "\e4ac"; }
+
+.fa-ellipsis::before {
+  content: "\f141"; }
+
+.fa-ellipsis-h::before {
+  content: "\f141"; }
+
+.fa-chess-pawn::before {
+  content: "\f443"; }
+
+.fa-kit-medical::before {
+  content: "\f479"; }
+
+.fa-first-aid::before {
+  content: "\f479"; }
+
+.fa-person-through-window::before {
+  content: "\e5a9"; }
+
+.fa-toolbox::before {
+  content: "\f552"; }
+
+.fa-hands-holding-circle::before {
+  content: "\e4fb"; }
+
+.fa-bug::before {
+  content: "\f188"; }
+
+.fa-credit-card::before {
+  content: "\f09d"; }
+
+.fa-credit-card-alt::before {
+  content: "\f09d"; }
+
+.fa-car::before {
+  content: "\f1b9"; }
+
+.fa-automobile::before {
+  content: "\f1b9"; }
+
+.fa-hand-holding-hand::before {
+  content: "\e4f7"; }
+
+.fa-book-open-reader::before {
+  content: "\f5da"; }
+
+.fa-book-reader::before {
+  content: "\f5da"; }
+
+.fa-mountain-sun::before {
+  content: "\e52f"; }
+
+.fa-arrows-left-right-to-line::before {
+  content: "\e4ba"; }
+
+.fa-dice-d20::before {
+  content: "\f6cf"; }
+
+.fa-truck-droplet::before {
+  content: "\e58c"; }
+
+.fa-file-circle-xmark::before {
+  content: "\e5a1"; }
+
+.fa-temperature-arrow-up::before {
+  content: "\e040"; }
+
+.fa-temperature-up::before {
+  content: "\e040"; }
+
+.fa-medal::before {
+  content: "\f5a2"; }
+
+.fa-bed::before {
+  content: "\f236"; }
+
+.fa-square-h::before {
+  content: "\f0fd"; }
+
+.fa-h-square::before {
+  content: "\f0fd"; }
+
+.fa-podcast::before {
+  content: "\f2ce"; }
+
+.fa-temperature-full::before {
+  content: "\f2c7"; }
+
+.fa-temperature-4::before {
+  content: "\f2c7"; }
+
+.fa-thermometer-4::before {
+  content: "\f2c7"; }
+
+.fa-thermometer-full::before {
+  content: "\f2c7"; }
+
+.fa-bell::before {
+  content: "\f0f3"; }
+
+.fa-superscript::before {
+  content: "\f12b"; }
+
+.fa-plug-circle-xmark::before {
+  content: "\e560"; }
+
+.fa-star-of-life::before {
+  content: "\f621"; }
+
+.fa-phone-slash::before {
+  content: "\f3dd"; }
+
+.fa-paint-roller::before {
+  content: "\f5aa"; }
+
+.fa-handshake-angle::before {
+  content: "\f4c4"; }
+
+.fa-hands-helping::before {
+  content: "\f4c4"; }
+
+.fa-location-dot::before {
+  content: "\f3c5"; }
+
+.fa-map-marker-alt::before {
+  content: "\f3c5"; }
+
+.fa-file::before {
+  content: "\f15b"; }
+
+.fa-greater-than::before {
+  content: "\3e"; }
+
+.fa-person-swimming::before {
+  content: "\f5c4"; }
+
+.fa-swimmer::before {
+  content: "\f5c4"; }
+
+.fa-arrow-down::before {
+  content: "\f063"; }
+
+.fa-droplet::before {
+  content: "\f043"; }
+
+.fa-tint::before {
+  content: "\f043"; }
+
+.fa-eraser::before {
+  content: "\f12d"; }
+
+.fa-earth-americas::before {
+  content: "\f57d"; }
+
+.fa-earth::before {
+  content: "\f57d"; }
+
+.fa-earth-america::before {
+  content: "\f57d"; }
+
+.fa-globe-americas::before {
+  content: "\f57d"; }
+
+.fa-person-burst::before {
+  content: "\e53b"; }
+
+.fa-dove::before {
+  content: "\f4ba"; }
+
+.fa-battery-empty::before {
+  content: "\f244"; }
+
+.fa-battery-0::before {
+  content: "\f244"; }
+
+.fa-socks::before {
+  content: "\f696"; }
+
+.fa-inbox::before {
+  content: "\f01c"; }
+
+.fa-section::before {
+  content: "\e447"; }
+
+.fa-gauge-high::before {
+  content: "\f625"; }
+
+.fa-tachometer-alt::before {
+  content: "\f625"; }
+
+.fa-tachometer-alt-fast::before {
+  content: "\f625"; }
+
+.fa-envelope-open-text::before {
+  content: "\f658"; }
+
+.fa-hospital::before {
+  content: "\f0f8"; }
+
+.fa-hospital-alt::before {
+  content: "\f0f8"; }
+
+.fa-hospital-wide::before {
+  content: "\f0f8"; }
+
+.fa-wine-bottle::before {
+  content: "\f72f"; }
+
+.fa-chess-rook::before {
+  content: "\f447"; }
+
+.fa-bars-staggered::before {
+  content: "\f550"; }
+
+.fa-reorder::before {
+  content: "\f550"; }
+
+.fa-stream::before {
+  content: "\f550"; }
+
+.fa-dharmachakra::before {
+  content: "\f655"; }
+
+.fa-hotdog::before {
+  content: "\f80f"; }
+
+.fa-person-walking-with-cane::before {
+  content: "\f29d"; }
+
+.fa-blind::before {
+  content: "\f29d"; }
+
+.fa-drum::before {
+  content: "\f569"; }
+
+.fa-ice-cream::before {
+  content: "\f810"; }
+
+.fa-heart-circle-bolt::before {
+  content: "\e4fc"; }
+
+.fa-fax::before {
+  content: "\f1ac"; }
+
+.fa-paragraph::before {
+  content: "\f1dd"; }
+
+.fa-check-to-slot::before {
+  content: "\f772"; }
+
+.fa-vote-yea::before {
+  content: "\f772"; }
+
+.fa-star-half::before {
+  content: "\f089"; }
+
+.fa-boxes-stacked::before {
+  content: "\f468"; }
+
+.fa-boxes::before {
+  content: "\f468"; }
+
+.fa-boxes-alt::before {
+  content: "\f468"; }
+
+.fa-link::before {
+  content: "\f0c1"; }
+
+.fa-chain::before {
+  content: "\f0c1"; }
+
+.fa-ear-listen::before {
+  content: "\f2a2"; }
+
+.fa-assistive-listening-systems::before {
+  content: "\f2a2"; }
+
+.fa-tree-city::before {
+  content: "\e587"; }
+
+.fa-play::before {
+  content: "\f04b"; }
+
+.fa-font::before {
+  content: "\f031"; }
+
+.fa-table-cells-row-lock::before {
+  content: "\e67a"; }
+
+.fa-rupiah-sign::before {
+  content: "\e23d"; }
+
+.fa-magnifying-glass::before {
+  content: "\f002"; }
+
+.fa-search::before {
+  content: "\f002"; }
+
+.fa-table-tennis-paddle-ball::before {
+  content: "\f45d"; }
+
+.fa-ping-pong-paddle-ball::before {
+  content: "\f45d"; }
+
+.fa-table-tennis::before {
+  content: "\f45d"; }
+
+.fa-person-dots-from-line::before {
+  content: "\f470"; }
+
+.fa-diagnoses::before {
+  content: "\f470"; }
+
+.fa-trash-can-arrow-up::before {
+  content: "\f82a"; }
+
+.fa-trash-restore-alt::before {
+  content: "\f82a"; }
+
+.fa-naira-sign::before {
+  content: "\e1f6"; }
+
+.fa-cart-arrow-down::before {
+  content: "\f218"; }
+
+.fa-walkie-talkie::before {
+  content: "\f8ef"; }
+
+.fa-file-pen::before {
+  content: "\f31c"; }
+
+.fa-file-edit::before {
+  content: "\f31c"; }
+
+.fa-receipt::before {
+  content: "\f543"; }
+
+.fa-square-pen::before {
+  content: "\f14b"; }
+
+.fa-pen-square::before {
+  content: "\f14b"; }
+
+.fa-pencil-square::before {
+  content: "\f14b"; }
+
+.fa-suitcase-rolling::before {
+  content: "\f5c1"; }
+
+.fa-person-circle-exclamation::before {
+  content: "\e53f"; }
+
+.fa-chevron-down::before {
+  content: "\f078"; }
+
+.fa-battery-full::before {
+  content: "\f240"; }
+
+.fa-battery::before {
+  content: "\f240"; }
+
+.fa-battery-5::before {
+  content: "\f240"; }
+
+.fa-skull-crossbones::before {
+  content: "\f714"; }
+
+.fa-code-compare::before {
+  content: "\e13a"; }
+
+.fa-list-ul::before {
+  content: "\f0ca"; }
+
+.fa-list-dots::before {
+  content: "\f0ca"; }
+
+.fa-school-lock::before {
+  content: "\e56f"; }
+
+.fa-tower-cell::before {
+  content: "\e585"; }
+
+.fa-down-long::before {
+  content: "\f309"; }
+
+.fa-long-arrow-alt-down::before {
+  content: "\f309"; }
+
+.fa-ranking-star::before {
+  content: "\e561"; }
+
+.fa-chess-king::before {
+  content: "\f43f"; }
+
+.fa-person-harassing::before {
+  content: "\e549"; }
+
+.fa-brazilian-real-sign::before {
+  content: "\e46c"; }
+
+.fa-landmark-dome::before {
+  content: "\f752"; }
+
+.fa-landmark-alt::before {
+  content: "\f752"; }
+
+.fa-arrow-up::before {
+  content: "\f062"; }
+
+.fa-tv::before {
+  content: "\f26c"; }
+
+.fa-television::before {
+  content: "\f26c"; }
+
+.fa-tv-alt::before {
+  content: "\f26c"; }
+
+.fa-shrimp::before {
+  content: "\e448"; }
+
+.fa-list-check::before {
+  content: "\f0ae"; }
+
+.fa-tasks::before {
+  content: "\f0ae"; }
+
+.fa-jug-detergent::before {
+  content: "\e519"; }
+
+.fa-circle-user::before {
+  content: "\f2bd"; }
+
+.fa-user-circle::before {
+  content: "\f2bd"; }
+
+.fa-user-shield::before {
+  content: "\f505"; }
+
+.fa-wind::before {
+  content: "\f72e"; }
+
+.fa-car-burst::before {
+  content: "\f5e1"; }
+
+.fa-car-crash::before {
+  content: "\f5e1"; }
+
+.fa-y::before {
+  content: "\59"; }
+
+.fa-person-snowboarding::before {
+  content: "\f7ce"; }
+
+.fa-snowboarding::before {
+  content: "\f7ce"; }
+
+.fa-truck-fast::before {
+  content: "\f48b"; }
+
+.fa-shipping-fast::before {
+  content: "\f48b"; }
+
+.fa-fish::before {
+  content: "\f578"; }
+
+.fa-user-graduate::before {
+  content: "\f501"; }
+
+.fa-circle-half-stroke::before {
+  content: "\f042"; }
+
+.fa-adjust::before {
+  content: "\f042"; }
+
+.fa-clapperboard::before {
+  content: "\e131"; }
+
+.fa-circle-radiation::before {
+  content: "\f7ba"; }
+
+.fa-radiation-alt::before {
+  content: "\f7ba"; }
+
+.fa-baseball::before {
+  content: "\f433"; }
+
+.fa-baseball-ball::before {
+  content: "\f433"; }
+
+.fa-jet-fighter-up::before {
+  content: "\e518"; }
+
+.fa-diagram-project::before {
+  content: "\f542"; }
+
+.fa-project-diagram::before {
+  content: "\f542"; }
+
+.fa-copy::before {
+  content: "\f0c5"; }
+
+.fa-volume-xmark::before {
+  content: "\f6a9"; }
+
+.fa-volume-mute::before {
+  content: "\f6a9"; }
+
+.fa-volume-times::before {
+  content: "\f6a9"; }
+
+.fa-hand-sparkles::before {
+  content: "\e05d"; }
+
+.fa-grip::before {
+  content: "\f58d"; }
+
+.fa-grip-horizontal::before {
+  content: "\f58d"; }
+
+.fa-share-from-square::before {
+  content: "\f14d"; }
+
+.fa-share-square::before {
+  content: "\f14d"; }
+
+.fa-child-combatant::before {
+  content: "\e4e0"; }
+
+.fa-child-rifle::before {
+  content: "\e4e0"; }
+
+.fa-gun::before {
+  content: "\e19b"; }
+
+.fa-square-phone::before {
+  content: "\f098"; }
+
+.fa-phone-square::before {
+  content: "\f098"; }
+
+.fa-plus::before {
+  content: "\2b"; }
+
+.fa-add::before {
+  content: "\2b"; }
+
+.fa-expand::before {
+  content: "\f065"; }
+
+.fa-computer::before {
+  content: "\e4e5"; }
+
+.fa-xmark::before {
+  content: "\f00d"; }
+
+.fa-close::before {
+  content: "\f00d"; }
+
+.fa-multiply::before {
+  content: "\f00d"; }
+
+.fa-remove::before {
+  content: "\f00d"; }
+
+.fa-times::before {
+  content: "\f00d"; }
+
+.fa-arrows-up-down-left-right::before {
+  content: "\f047"; }
+
+.fa-arrows::before {
+  content: "\f047"; }
+
+.fa-chalkboard-user::before {
+  content: "\f51c"; }
+
+.fa-chalkboard-teacher::before {
+  content: "\f51c"; }
+
+.fa-peso-sign::before {
+  content: "\e222"; }
+
+.fa-building-shield::before {
+  content: "\e4d8"; }
+
+.fa-baby::before {
+  content: "\f77c"; }
+
+.fa-users-line::before {
+  content: "\e592"; }
+
+.fa-quote-left::before {
+  content: "\f10d"; }
+
+.fa-quote-left-alt::before {
+  content: "\f10d"; }
+
+.fa-tractor::before {
+  content: "\f722"; }
+
+.fa-trash-arrow-up::before {
+  content: "\f829"; }
+
+.fa-trash-restore::before {
+  content: "\f829"; }
+
+.fa-arrow-down-up-lock::before {
+  content: "\e4b0"; }
+
+.fa-lines-leaning::before {
+  content: "\e51e"; }
+
+.fa-ruler-combined::before {
+  content: "\f546"; }
+
+.fa-copyright::before {
+  content: "\f1f9"; }
+
+.fa-equals::before {
+  content: "\3d"; }
+
+.fa-blender::before {
+  content: "\f517"; }
+
+.fa-teeth::before {
+  content: "\f62e"; }
+
+.fa-shekel-sign::before {
+  content: "\f20b"; }
+
+.fa-ils::before {
+  content: "\f20b"; }
+
+.fa-shekel::before {
+  content: "\f20b"; }
+
+.fa-sheqel::before {
+  content: "\f20b"; }
+
+.fa-sheqel-sign::before {
+  content: "\f20b"; }
+
+.fa-map::before {
+  content: "\f279"; }
+
+.fa-rocket::before {
+  content: "\f135"; }
+
+.fa-photo-film::before {
+  content: "\f87c"; }
+
+.fa-photo-video::before {
+  content: "\f87c"; }
+
+.fa-folder-minus::before {
+  content: "\f65d"; }
+
+.fa-store::before {
+  content: "\f54e"; }
+
+.fa-arrow-trend-up::before {
+  content: "\e098"; }
+
+.fa-plug-circle-minus::before {
+  content: "\e55e"; }
+
+.fa-sign-hanging::before {
+  content: "\f4d9"; }
+
+.fa-sign::before {
+  content: "\f4d9"; }
+
+.fa-bezier-curve::before {
+  content: "\f55b"; }
+
+.fa-bell-slash::before {
+  content: "\f1f6"; }
+
+.fa-tablet::before {
+  content: "\f3fb"; }
+
+.fa-tablet-android::before {
+  content: "\f3fb"; }
+
+.fa-school-flag::before {
+  content: "\e56e"; }
+
+.fa-fill::before {
+  content: "\f575"; }
+
+.fa-angle-up::before {
+  content: "\f106"; }
+
+.fa-drumstick-bite::before {
+  content: "\f6d7"; }
+
+.fa-holly-berry::before {
+  content: "\f7aa"; }
+
+.fa-chevron-left::before {
+  content: "\f053"; }
+
+.fa-bacteria::before {
+  content: "\e059"; }
+
+.fa-hand-lizard::before {
+  content: "\f258"; }
+
+.fa-notdef::before {
+  content: "\e1fe"; }
+
+.fa-disease::before {
+  content: "\f7fa"; }
+
+.fa-briefcase-medical::before {
+  content: "\f469"; }
+
+.fa-genderless::before {
+  content: "\f22d"; }
+
+.fa-chevron-right::before {
+  content: "\f054"; }
+
+.fa-retweet::before {
+  content: "\f079"; }
+
+.fa-car-rear::before {
+  content: "\f5de"; }
+
+.fa-car-alt::before {
+  content: "\f5de"; }
+
+.fa-pump-soap::before {
+  content: "\e06b"; }
+
+.fa-video-slash::before {
+  content: "\f4e2"; }
+
+.fa-battery-quarter::before {
+  content: "\f243"; }
+
+.fa-battery-2::before {
+  content: "\f243"; }
+
+.fa-radio::before {
+  content: "\f8d7"; }
+
+.fa-baby-carriage::before {
+  content: "\f77d"; }
+
+.fa-carriage-baby::before {
+  content: "\f77d"; }
+
+.fa-traffic-light::before {
+  content: "\f637"; }
+
+.fa-thermometer::before {
+  content: "\f491"; }
+
+.fa-vr-cardboard::before {
+  content: "\f729"; }
+
+.fa-hand-middle-finger::before {
+  content: "\f806"; }
+
+.fa-percent::before {
+  content: "\25"; }
+
+.fa-percentage::before {
+  content: "\25"; }
+
+.fa-truck-moving::before {
+  content: "\f4df"; }
+
+.fa-glass-water-droplet::before {
+  content: "\e4f5"; }
+
+.fa-display::before {
+  content: "\e163"; }
+
+.fa-face-smile::before {
+  content: "\f118"; }
+
+.fa-smile::before {
+  content: "\f118"; }
+
+.fa-thumbtack::before {
+  content: "\f08d"; }
+
+.fa-thumb-tack::before {
+  content: "\f08d"; }
+
+.fa-trophy::before {
+  content: "\f091"; }
+
+.fa-person-praying::before {
+  content: "\f683"; }
+
+.fa-pray::before {
+  content: "\f683"; }
+
+.fa-hammer::before {
+  content: "\f6e3"; }
+
+.fa-hand-peace::before {
+  content: "\f25b"; }
+
+.fa-rotate::before {
+  content: "\f2f1"; }
+
+.fa-sync-alt::before {
+  content: "\f2f1"; }
+
+.fa-spinner::before {
+  content: "\f110"; }
+
+.fa-robot::before {
+  content: "\f544"; }
+
+.fa-peace::before {
+  content: "\f67c"; }
+
+.fa-gears::before {
+  content: "\f085"; }
+
+.fa-cogs::before {
+  content: "\f085"; }
+
+.fa-warehouse::before {
+  content: "\f494"; }
+
+.fa-arrow-up-right-dots::before {
+  content: "\e4b7"; }
+
+.fa-splotch::before {
+  content: "\f5bc"; }
+
+.fa-face-grin-hearts::before {
+  content: "\f584"; }
+
+.fa-grin-hearts::before {
+  content: "\f584"; }
+
+.fa-dice-four::before {
+  content: "\f524"; }
+
+.fa-sim-card::before {
+  content: "\f7c4"; }
+
+.fa-transgender::before {
+  content: "\f225"; }
+
+.fa-transgender-alt::before {
+  content: "\f225"; }
+
+.fa-mercury::before {
+  content: "\f223"; }
+
+.fa-arrow-turn-down::before {
+  content: "\f149"; }
+
+.fa-level-down::before {
+  content: "\f149"; }
+
+.fa-person-falling-burst::before {
+  content: "\e547"; }
+
+.fa-award::before {
+  content: "\f559"; }
+
+.fa-ticket-simple::before {
+  content: "\f3ff"; }
+
+.fa-ticket-alt::before {
+  content: "\f3ff"; }
+
+.fa-building::before {
+  content: "\f1ad"; }
+
+.fa-angles-left::before {
+  content: "\f100"; }
+
+.fa-angle-double-left::before {
+  content: "\f100"; }
+
+.fa-qrcode::before {
+  content: "\f029"; }
+
+.fa-clock-rotate-left::before {
+  content: "\f1da"; }
+
+.fa-history::before {
+  content: "\f1da"; }
+
+.fa-face-grin-beam-sweat::before {
+  content: "\f583"; }
+
+.fa-grin-beam-sweat::before {
+  content: "\f583"; }
+
+.fa-file-export::before {
+  content: "\f56e"; }
+
+.fa-arrow-right-from-file::before {
+  content: "\f56e"; }
+
+.fa-shield::before {
+  content: "\f132"; }
+
+.fa-shield-blank::before {
+  content: "\f132"; }
+
+.fa-arrow-up-short-wide::before {
+  content: "\f885"; }
+
+.fa-sort-amount-up-alt::before {
+  content: "\f885"; }
+
+.fa-house-medical::before {
+  content: "\e3b2"; }
+
+.fa-golf-ball-tee::before {
+  content: "\f450"; }
+
+.fa-golf-ball::before {
+  content: "\f450"; }
+
+.fa-circle-chevron-left::before {
+  content: "\f137"; }
+
+.fa-chevron-circle-left::before {
+  content: "\f137"; }
+
+.fa-house-chimney-window::before {
+  content: "\e00d"; }
+
+.fa-pen-nib::before {
+  content: "\f5ad"; }
+
+.fa-tent-arrow-turn-left::before {
+  content: "\e580"; }
+
+.fa-tents::before {
+  content: "\e582"; }
+
+.fa-wand-magic::before {
+  content: "\f0d0"; }
+
+.fa-magic::before {
+  content: "\f0d0"; }
+
+.fa-dog::before {
+  content: "\f6d3"; }
+
+.fa-carrot::before {
+  content: "\f787"; }
+
+.fa-moon::before {
+  content: "\f186"; }
+
+.fa-wine-glass-empty::before {
+  content: "\f5ce"; }
+
+.fa-wine-glass-alt::before {
+  content: "\f5ce"; }
+
+.fa-cheese::before {
+  content: "\f7ef"; }
+
+.fa-yin-yang::before {
+  content: "\f6ad"; }
+
+.fa-music::before {
+  content: "\f001"; }
+
+.fa-code-commit::before {
+  content: "\f386"; }
+
+.fa-temperature-low::before {
+  content: "\f76b"; }
+
+.fa-person-biking::before {
+  content: "\f84a"; }
+
+.fa-biking::before {
+  content: "\f84a"; }
+
+.fa-broom::before {
+  content: "\f51a"; }
+
+.fa-shield-heart::before {
+  content: "\e574"; }
+
+.fa-gopuram::before {
+  content: "\f664"; }
+
+.fa-earth-oceania::before {
+  content: "\e47b"; }
+
+.fa-globe-oceania::before {
+  content: "\e47b"; }
+
+.fa-square-xmark::before {
+  content: "\f2d3"; }
+
+.fa-times-square::before {
+  content: "\f2d3"; }
+
+.fa-xmark-square::before {
+  content: "\f2d3"; }
+
+.fa-hashtag::before {
+  content: "\23"; }
+
+.fa-up-right-and-down-left-from-center::before {
+  content: "\f424"; }
+
+.fa-expand-alt::before {
+  content: "\f424"; }
+
+.fa-oil-can::before {
+  content: "\f613"; }
+
+.fa-t::before {
+  content: "\54"; }
+
+.fa-hippo::before {
+  content: "\f6ed"; }
+
+.fa-chart-column::before {
+  content: "\e0e3"; }
+
+.fa-infinity::before {
+  content: "\f534"; }
+
+.fa-vial-circle-check::before {
+  content: "\e596"; }
+
+.fa-person-arrow-down-to-line::before {
+  content: "\e538"; }
+
+.fa-voicemail::before {
+  content: "\f897"; }
+
+.fa-fan::before {
+  content: "\f863"; }
+
+.fa-person-walking-luggage::before {
+  content: "\e554"; }
+
+.fa-up-down::before {
+  content: "\f338"; }
+
+.fa-arrows-alt-v::before {
+  content: "\f338"; }
+
+.fa-cloud-moon-rain::before {
+  content: "\f73c"; }
+
+.fa-calendar::before {
+  content: "\f133"; }
+
+.fa-trailer::before {
+  content: "\e041"; }
+
+.fa-bahai::before {
+  content: "\f666"; }
+
+.fa-haykal::before {
+  content: "\f666"; }
+
+.fa-sd-card::before {
+  content: "\f7c2"; }
+
+.fa-dragon::before {
+  content: "\f6d5"; }
+
+.fa-shoe-prints::before {
+  content: "\f54b"; }
+
+.fa-circle-plus::before {
+  content: "\f055"; }
+
+.fa-plus-circle::before {
+  content: "\f055"; }
+
+.fa-face-grin-tongue-wink::before {
+  content: "\f58b"; }
+
+.fa-grin-tongue-wink::before {
+  content: "\f58b"; }
+
+.fa-hand-holding::before {
+  content: "\f4bd"; }
+
+.fa-plug-circle-exclamation::before {
+  content: "\e55d"; }
+
+.fa-link-slash::before {
+  content: "\f127"; }
+
+.fa-chain-broken::before {
+  content: "\f127"; }
+
+.fa-chain-slash::before {
+  content: "\f127"; }
+
+.fa-unlink::before {
+  content: "\f127"; }
+
+.fa-clone::before {
+  content: "\f24d"; }
+
+.fa-person-walking-arrow-loop-left::before {
+  content: "\e551"; }
+
+.fa-arrow-up-z-a::before {
+  content: "\f882"; }
+
+.fa-sort-alpha-up-alt::before {
+  content: "\f882"; }
+
+.fa-fire-flame-curved::before {
+  content: "\f7e4"; }
+
+.fa-fire-alt::before {
+  content: "\f7e4"; }
+
+.fa-tornado::before {
+  content: "\f76f"; }
+
+.fa-file-circle-plus::before {
+  content: "\e494"; }
+
+.fa-book-quran::before {
+  content: "\f687"; }
+
+.fa-quran::before {
+  content: "\f687"; }
+
+.fa-anchor::before {
+  content: "\f13d"; }
+
+.fa-border-all::before {
+  content: "\f84c"; }
+
+.fa-face-angry::before {
+  content: "\f556"; }
+
+.fa-angry::before {
+  content: "\f556"; }
+
+.fa-cookie-bite::before {
+  content: "\f564"; }
+
+.fa-arrow-trend-down::before {
+  content: "\e097"; }
+
+.fa-rss::before {
+  content: "\f09e"; }
+
+.fa-feed::before {
+  content: "\f09e"; }
+
+.fa-draw-polygon::before {
+  content: "\f5ee"; }
+
+.fa-scale-balanced::before {
+  content: "\f24e"; }
+
+.fa-balance-scale::before {
+  content: "\f24e"; }
+
+.fa-gauge-simple-high::before {
+  content: "\f62a"; }
+
+.fa-tachometer::before {
+  content: "\f62a"; }
+
+.fa-tachometer-fast::before {
+  content: "\f62a"; }
+
+.fa-shower::before {
+  content: "\f2cc"; }
+
+.fa-desktop::before {
+  content: "\f390"; }
+
+.fa-desktop-alt::before {
+  content: "\f390"; }
+
+.fa-m::before {
+  content: "\4d"; }
+
+.fa-table-list::before {
+  content: "\f00b"; }
+
+.fa-th-list::before {
+  content: "\f00b"; }
+
+.fa-comment-sms::before {
+  content: "\f7cd"; }
+
+.fa-sms::before {
+  content: "\f7cd"; }
+
+.fa-book::before {
+  content: "\f02d"; }
+
+.fa-user-plus::before {
+  content: "\f234"; }
+
+.fa-check::before {
+  content: "\f00c"; }
+
+.fa-battery-three-quarters::before {
+  content: "\f241"; }
+
+.fa-battery-4::before {
+  content: "\f241"; }
+
+.fa-house-circle-check::before {
+  content: "\e509"; }
+
+.fa-angle-left::before {
+  content: "\f104"; }
+
+.fa-diagram-successor::before {
+  content: "\e47a"; }
+
+.fa-truck-arrow-right::before {
+  content: "\e58b"; }
+
+.fa-arrows-split-up-and-left::before {
+  content: "\e4bc"; }
+
+.fa-hand-fist::before {
+  content: "\f6de"; }
+
+.fa-fist-raised::before {
+  content: "\f6de"; }
+
+.fa-cloud-moon::before {
+  content: "\f6c3"; }
+
+.fa-briefcase::before {
+  content: "\f0b1"; }
+
+.fa-person-falling::before {
+  content: "\e546"; }
+
+.fa-image-portrait::before {
+  content: "\f3e0"; }
+
+.fa-portrait::before {
+  content: "\f3e0"; }
+
+.fa-user-tag::before {
+  content: "\f507"; }
+
+.fa-rug::before {
+  content: "\e569"; }
+
+.fa-earth-europe::before {
+  content: "\f7a2"; }
+
+.fa-globe-europe::before {
+  content: "\f7a2"; }
+
+.fa-cart-flatbed-suitcase::before {
+  content: "\f59d"; }
+
+.fa-luggage-cart::before {
+  content: "\f59d"; }
+
+.fa-rectangle-xmark::before {
+  content: "\f410"; }
+
+.fa-rectangle-times::before {
+  content: "\f410"; }
+
+.fa-times-rectangle::before {
+  content: "\f410"; }
+
+.fa-window-close::before {
+  content: "\f410"; }
+
+.fa-baht-sign::before {
+  content: "\e0ac"; }
+
+.fa-book-open::before {
+  content: "\f518"; }
+
+.fa-book-journal-whills::before {
+  content: "\f66a"; }
+
+.fa-journal-whills::before {
+  content: "\f66a"; }
+
+.fa-handcuffs::before {
+  content: "\e4f8"; }
+
+.fa-triangle-exclamation::before {
+  content: "\f071"; }
+
+.fa-exclamation-triangle::before {
+  content: "\f071"; }
+
+.fa-warning::before {
+  content: "\f071"; }
+
+.fa-database::before {
+  content: "\f1c0"; }
+
+.fa-share::before {
+  content: "\f064"; }
+
+.fa-mail-forward::before {
+  content: "\f064"; }
+
+.fa-bottle-droplet::before {
+  content: "\e4c4"; }
+
+.fa-mask-face::before {
+  content: "\e1d7"; }
+
+.fa-hill-rockslide::before {
+  content: "\e508"; }
+
+.fa-right-left::before {
+  content: "\f362"; }
+
+.fa-exchange-alt::before {
+  content: "\f362"; }
+
+.fa-paper-plane::before {
+  content: "\f1d8"; }
+
+.fa-road-circle-exclamation::before {
+  content: "\e565"; }
+
+.fa-dungeon::before {
+  content: "\f6d9"; }
+
+.fa-align-right::before {
+  content: "\f038"; }
+
+.fa-money-bill-1-wave::before {
+  content: "\f53b"; }
+
+.fa-money-bill-wave-alt::before {
+  content: "\f53b"; }
+
+.fa-life-ring::before {
+  content: "\f1cd"; }
+
+.fa-hands::before {
+  content: "\f2a7"; }
+
+.fa-sign-language::before {
+  content: "\f2a7"; }
+
+.fa-signing::before {
+  content: "\f2a7"; }
+
+.fa-calendar-day::before {
+  content: "\f783"; }
+
+.fa-water-ladder::before {
+  content: "\f5c5"; }
+
+.fa-ladder-water::before {
+  content: "\f5c5"; }
+
+.fa-swimming-pool::before {
+  content: "\f5c5"; }
+
+.fa-arrows-up-down::before {
+  content: "\f07d"; }
+
+.fa-arrows-v::before {
+  content: "\f07d"; }
+
+.fa-face-grimace::before {
+  content: "\f57f"; }
+
+.fa-grimace::before {
+  content: "\f57f"; }
+
+.fa-wheelchair-move::before {
+  content: "\e2ce"; }
+
+.fa-wheelchair-alt::before {
+  content: "\e2ce"; }
+
+.fa-turn-down::before {
+  content: "\f3be"; }
+
+.fa-level-down-alt::before {
+  content: "\f3be"; }
+
+.fa-person-walking-arrow-right::before {
+  content: "\e552"; }
+
+.fa-square-envelope::before {
+  content: "\f199"; }
+
+.fa-envelope-square::before {
+  content: "\f199"; }
+
+.fa-dice::before {
+  content: "\f522"; }
+
+.fa-bowling-ball::before {
+  content: "\f436"; }
+
+.fa-brain::before {
+  content: "\f5dc"; }
+
+.fa-bandage::before {
+  content: "\f462"; }
+
+.fa-band-aid::before {
+  content: "\f462"; }
+
+.fa-calendar-minus::before {
+  content: "\f272"; }
+
+.fa-circle-xmark::before {
+  content: "\f057"; }
+
+.fa-times-circle::before {
+  content: "\f057"; }
+
+.fa-xmark-circle::before {
+  content: "\f057"; }
+
+.fa-gifts::before {
+  content: "\f79c"; }
+
+.fa-hotel::before {
+  content: "\f594"; }
+
+.fa-earth-asia::before {
+  content: "\f57e"; }
+
+.fa-globe-asia::before {
+  content: "\f57e"; }
+
+.fa-id-card-clip::before {
+  content: "\f47f"; }
+
+.fa-id-card-alt::before {
+  content: "\f47f"; }
+
+.fa-magnifying-glass-plus::before {
+  content: "\f00e"; }
+
+.fa-search-plus::before {
+  content: "\f00e"; }
+
+.fa-thumbs-up::before {
+  content: "\f164"; }
+
+.fa-user-clock::before {
+  content: "\f4fd"; }
+
+.fa-hand-dots::before {
+  content: "\f461"; }
+
+.fa-allergies::before {
+  content: "\f461"; }
+
+.fa-file-invoice::before {
+  content: "\f570"; }
+
+.fa-window-minimize::before {
+  content: "\f2d1"; }
+
+.fa-mug-saucer::before {
+  content: "\f0f4"; }
+
+.fa-coffee::before {
+  content: "\f0f4"; }
+
+.fa-brush::before {
+  content: "\f55d"; }
+
+.fa-mask::before {
+  content: "\f6fa"; }
+
+.fa-magnifying-glass-minus::before {
+  content: "\f010"; }
+
+.fa-search-minus::before {
+  content: "\f010"; }
+
+.fa-ruler-vertical::before {
+  content: "\f548"; }
+
+.fa-user-large::before {
+  content: "\f406"; }
+
+.fa-user-alt::before {
+  content: "\f406"; }
+
+.fa-train-tram::before {
+  content: "\e5b4"; }
+
+.fa-user-nurse::before {
+  content: "\f82f"; }
+
+.fa-syringe::before {
+  content: "\f48e"; }
+
+.fa-cloud-sun::before {
+  content: "\f6c4"; }
+
+.fa-stopwatch-20::before {
+  content: "\e06f"; }
+
+.fa-square-full::before {
+  content: "\f45c"; }
+
+.fa-magnet::before {
+  content: "\f076"; }
+
+.fa-jar::before {
+  content: "\e516"; }
+
+.fa-note-sticky::before {
+  content: "\f249"; }
+
+.fa-sticky-note::before {
+  content: "\f249"; }
+
+.fa-bug-slash::before {
+  content: "\e490"; }
+
+.fa-arrow-up-from-water-pump::before {
+  content: "\e4b6"; }
+
+.fa-bone::before {
+  content: "\f5d7"; }
+
+.fa-user-injured::before {
+  content: "\f728"; }
+
+.fa-face-sad-tear::before {
+  content: "\f5b4"; }
+
+.fa-sad-tear::before {
+  content: "\f5b4"; }
+
+.fa-plane::before {
+  content: "\f072"; }
+
+.fa-tent-arrows-down::before {
+  content: "\e581"; }
+
+.fa-exclamation::before {
+  content: "\21"; }
+
+.fa-arrows-spin::before {
+  content: "\e4bb"; }
+
+.fa-print::before {
+  content: "\f02f"; }
+
+.fa-turkish-lira-sign::before {
+  content: "\e2bb"; }
+
+.fa-try::before {
+  content: "\e2bb"; }
+
+.fa-turkish-lira::before {
+  content: "\e2bb"; }
+
+.fa-dollar-sign::before {
+  content: "\24"; }
+
+.fa-dollar::before {
+  content: "\24"; }
+
+.fa-usd::before {
+  content: "\24"; }
+
+.fa-x::before {
+  content: "\58"; }
+
+.fa-magnifying-glass-dollar::before {
+  content: "\f688"; }
+
+.fa-search-dollar::before {
+  content: "\f688"; }
+
+.fa-users-gear::before {
+  content: "\f509"; }
+
+.fa-users-cog::before {
+  content: "\f509"; }
+
+.fa-person-military-pointing::before {
+  content: "\e54a"; }
+
+.fa-building-columns::before {
+  content: "\f19c"; }
+
+.fa-bank::before {
+  content: "\f19c"; }
+
+.fa-institution::before {
+  content: "\f19c"; }
+
+.fa-museum::before {
+  content: "\f19c"; }
+
+.fa-university::before {
+  content: "\f19c"; }
+
+.fa-umbrella::before {
+  content: "\f0e9"; }
+
+.fa-trowel::before {
+  content: "\e589"; }
+
+.fa-d::before {
+  content: "\44"; }
+
+.fa-stapler::before {
+  content: "\e5af"; }
+
+.fa-masks-theater::before {
+  content: "\f630"; }
+
+.fa-theater-masks::before {
+  content: "\f630"; }
+
+.fa-kip-sign::before {
+  content: "\e1c4"; }
+
+.fa-hand-point-left::before {
+  content: "\f0a5"; }
+
+.fa-handshake-simple::before {
+  content: "\f4c6"; }
+
+.fa-handshake-alt::before {
+  content: "\f4c6"; }
+
+.fa-jet-fighter::before {
+  content: "\f0fb"; }
+
+.fa-fighter-jet::before {
+  content: "\f0fb"; }
+
+.fa-square-share-nodes::before {
+  content: "\f1e1"; }
+
+.fa-share-alt-square::before {
+  content: "\f1e1"; }
+
+.fa-barcode::before {
+  content: "\f02a"; }
+
+.fa-plus-minus::before {
+  content: "\e43c"; }
+
+.fa-video::before {
+  content: "\f03d"; }
+
+.fa-video-camera::before {
+  content: "\f03d"; }
+
+.fa-graduation-cap::before {
+  content: "\f19d"; }
+
+.fa-mortar-board::before {
+  content: "\f19d"; }
+
+.fa-hand-holding-medical::before {
+  content: "\e05c"; }
+
+.fa-person-circle-check::before {
+  content: "\e53e"; }
+
+.fa-turn-up::before {
+  content: "\f3bf"; }
+
+.fa-level-up-alt::before {
+  content: "\f3bf"; }
+
+.sr-only,
+.fa-sr-only {
+  position: absolute;
+  width: 1px;
+  height: 1px;
+  padding: 0;
+  margin: -1px;
+  overflow: hidden;
+  clip: rect(0, 0, 0, 0);
+  white-space: nowrap;
+  border-width: 0; }
+
+.sr-only-focusable:not(:focus),
+.fa-sr-only-focusable:not(:focus) {
+  position: absolute;
+  width: 1px;
+  height: 1px;
+  padding: 0;
+  margin: -1px;
+  overflow: hidden;
+  clip: rect(0, 0, 0, 0);
+  white-space: nowrap;
+  border-width: 0; }
+:root, :host {
+  --fa-style-family-brands: 'Font Awesome 6 Brands';
+  --fa-font-brands: normal 400 1em/1 'Font Awesome 6 Brands'; }
+
+@font-face {
+  font-family: 'Font Awesome 6 Brands';
+  font-style: normal;
+  font-weight: 400;
+  font-display: block;
+  src: url("../webfonts/fa-brands-400.woff2") format("woff2"), url("../webfonts/fa-brands-400.ttf") format("truetype"); }
+
+.fab,
+.fa-brands {
+  font-weight: 400; }
+
+.fa-monero:before {
+  content: "\f3d0"; }
+
+.fa-hooli:before {
+  content: "\f427"; }
+
+.fa-yelp:before {
+  content: "\f1e9"; }
+
+.fa-cc-visa:before {
+  content: "\f1f0"; }
+
+.fa-lastfm:before {
+  content: "\f202"; }
+
+.fa-shopware:before {
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+  content: "\e3d9"; }
+
+.fa-erlang:before {
+  content: "\f39d"; }
+
+.fa-x-twitter:before {
+  content: "\e61b"; }
+
+.fa-cotton-bureau:before {
+  content: "\f89e"; }
+
+.fa-dashcube:before {
+  content: "\f210"; }
+
+.fa-42-group:before {
+  content: "\e080"; }
+
+.fa-innosoft:before {
+  content: "\e080"; }
+
+.fa-stack-exchange:before {
+  content: "\f18d"; }
+
+.fa-elementor:before {
+  content: "\f430"; }
+
+.fa-square-pied-piper:before {
+  content: "\e01e"; }
+
+.fa-pied-piper-square:before {
+  content: "\e01e"; }
+
+.fa-creative-commons-nd:before {
+  content: "\f4eb"; }
+
+.fa-palfed:before {
+  content: "\f3d8"; }
+
+.fa-superpowers:before {
+  content: "\f2dd"; }
+
+.fa-resolving:before {
+  content: "\f3e7"; }
+
+.fa-xbox:before {
+  content: "\f412"; }
+
+.fa-square-web-awesome-stroke:before {
+  content: "\e684"; }
+
+.fa-searchengin:before {
+  content: "\f3eb"; }
+
+.fa-tiktok:before {
+  content: "\e07b"; }
+
+.fa-square-facebook:before {
+  content: "\f082"; }
+
+.fa-facebook-square:before {
+  content: "\f082"; }
+
+.fa-renren:before {
+  content: "\f18b"; }
+
+.fa-linux:before {
+  content: "\f17c"; }
+
+.fa-glide:before {
+  content: "\f2a5"; }
+
+.fa-linkedin:before {
+  content: "\f08c"; }
+
+.fa-hubspot:before {
+  content: "\f3b2"; }
+
+.fa-deploydog:before {
+  content: "\f38e"; }
+
+.fa-twitch:before {
+  content: "\f1e8"; }
+
+.fa-ravelry:before {
+  content: "\f2d9"; }
+
+.fa-mixer:before {
+  content: "\e056"; }
+
+.fa-square-lastfm:before {
+  content: "\f203"; }
+
+.fa-lastfm-square:before {
+  content: "\f203"; }
+
+.fa-vimeo:before {
+  content: "\f40a"; }
+
+.fa-mendeley:before {
+  content: "\f7b3"; }
+
+.fa-uniregistry:before {
+  content: "\f404"; }
+
+.fa-figma:before {
+  content: "\f799"; }
+
+.fa-creative-commons-remix:before {
+  content: "\f4ee"; }
+
+.fa-cc-amazon-pay:before {
+  content: "\f42d"; }
+
+.fa-dropbox:before {
+  content: "\f16b"; }
+
+.fa-instagram:before {
+  content: "\f16d"; }
+
+.fa-cmplid:before {
+  content: "\e360"; }
+
+.fa-upwork:before {
+  content: "\e641"; }
+
+.fa-facebook:before {
+  content: "\f09a"; }
+
+.fa-gripfire:before {
+  content: "\f3ac"; }
+
+.fa-jedi-order:before {
+  content: "\f50e"; }
+
+.fa-uikit:before {
+  content: "\f403"; }
+
+.fa-fort-awesome-alt:before {
+  content: "\f3a3"; }
+
+.fa-phabricator:before {
+  content: "\f3db"; }
+
+.fa-ussunnah:before {
+  content: "\f407"; }
+
+.fa-earlybirds:before {
+  content: "\f39a"; }
+
+.fa-trade-federation:before {
+  content: "\f513"; }
+
+.fa-autoprefixer:before {
+  content: "\f41c"; }
+
+.fa-whatsapp:before {
+  content: "\f232"; }
+
+.fa-square-upwork:before {
+  content: "\e67c"; }
+
+.fa-slideshare:before {
+  content: "\f1e7"; }
+
+.fa-google-play:before {
+  content: "\f3ab"; }
+
+.fa-viadeo:before {
+  content: "\f2a9"; }
+
+.fa-line:before {
+  content: "\f3c0"; }
+
+.fa-google-drive:before {
+  content: "\f3aa"; }
+
+.fa-servicestack:before {
+  content: "\f3ec"; }
+
+.fa-simplybuilt:before {
+  content: "\f215"; }
+
+.fa-bitbucket:before {
+  content: "\f171"; }
+
+.fa-imdb:before {
+  content: "\f2d8"; }
+
+.fa-deezer:before {
+  content: "\e077"; }
+
+.fa-raspberry-pi:before {
+  content: "\f7bb"; }
+
+.fa-jira:before {
+  content: "\f7b1"; }
+
+.fa-docker:before {
+  content: "\f395"; }
+
+.fa-screenpal:before {
+  content: "\e570"; }
+
+.fa-bluetooth:before {
+  content: "\f293"; }
+
+.fa-gitter:before {
+  content: "\f426"; }
+
+.fa-d-and-d:before {
+  content: "\f38d"; }
+
+.fa-microblog:before {
+  content: "\e01a"; }
+
+.fa-cc-diners-club:before {
+  content: "\f24c"; }
+
+.fa-gg-circle:before {
+  content: "\f261"; }
+
+.fa-pied-piper-hat:before {
+  content: "\f4e5"; }
+
+.fa-kickstarter-k:before {
+  content: "\f3bc"; }
+
+.fa-yandex:before {
+  content: "\f413"; }
+
+.fa-readme:before {
+  content: "\f4d5"; }
+
+.fa-html5:before {
+  content: "\f13b"; }
+
+.fa-sellsy:before {
+  content: "\f213"; }
+
+.fa-square-web-awesome:before {
+  content: "\e683"; }
+
+.fa-sass:before {
+  content: "\f41e"; }
+
+.fa-wirsindhandwerk:before {
+  content: "\e2d0"; }
+
+.fa-wsh:before {
+  content: "\e2d0"; }
+
+.fa-buromobelexperte:before {
+  content: "\f37f"; }
+
+.fa-salesforce:before {
+  content: "\f83b"; }
+
+.fa-octopus-deploy:before {
+  content: "\e082"; }
+
+.fa-medapps:before {
+  content: "\f3c6"; }
+
+.fa-ns8:before {
+  content: "\f3d5"; }
+
+.fa-pinterest-p:before {
+  content: "\f231"; }
+
+.fa-apper:before {
+  content: "\f371"; }
+
+.fa-fort-awesome:before {
+  content: "\f286"; }
+
+.fa-waze:before {
+  content: "\f83f"; }
+
+.fa-bluesky:before {
+  content: "\e671"; }
+
+.fa-cc-jcb:before {
+  content: "\f24b"; }
+
+.fa-snapchat:before {
+  content: "\f2ab"; }
+
+.fa-snapchat-ghost:before {
+  content: "\f2ab"; }
+
+.fa-fantasy-flight-games:before {
+  content: "\f6dc"; }
+
+.fa-rust:before {
+  content: "\e07a"; }
+
+.fa-wix:before {
+  content: "\f5cf"; }
+
+.fa-square-behance:before {
+  content: "\f1b5"; }
+
+.fa-behance-square:before {
+  content: "\f1b5"; }
+
+.fa-supple:before {
+  content: "\f3f9"; }
+
+.fa-webflow:before {
+  content: "\e65c"; }
+
+.fa-rebel:before {
+  content: "\f1d0"; }
+
+.fa-css3:before {
+  content: "\f13c"; }
+
+.fa-staylinked:before {
+  content: "\f3f5"; }
+
+.fa-kaggle:before {
+  content: "\f5fa"; }
+
+.fa-space-awesome:before {
+  content: "\e5ac"; }
+
+.fa-deviantart:before {
+  content: "\f1bd"; }
+
+.fa-cpanel:before {
+  content: "\f388"; }
+
+.fa-goodreads-g:before {
+  content: "\f3a9"; }
+
+.fa-square-git:before {
+  content: "\f1d2"; }
+
+.fa-git-square:before {
+  content: "\f1d2"; }
+
+.fa-square-tumblr:before {
+  content: "\f174"; }
+
+.fa-tumblr-square:before {
+  content: "\f174"; }
+
+.fa-trello:before {
+  content: "\f181"; }
+
+.fa-creative-commons-nc-jp:before {
+  content: "\f4ea"; }
+
+.fa-get-pocket:before {
+  content: "\f265"; }
+
+.fa-perbyte:before {
+  content: "\e083"; }
+
+.fa-grunt:before {
+  content: "\f3ad"; }
+
+.fa-weebly:before {
+  content: "\f5cc"; }
+
+.fa-connectdevelop:before {
+  content: "\f20e"; }
+
+.fa-leanpub:before {
+  content: "\f212"; }
+
+.fa-black-tie:before {
+  content: "\f27e"; }
+
+.fa-themeco:before {
+  content: "\f5c6"; }
+
+.fa-python:before {
+  content: "\f3e2"; }
+
+.fa-android:before {
+  content: "\f17b"; }
+
+.fa-bots:before {
+  content: "\e340"; }
+
+.fa-free-code-camp:before {
+  content: "\f2c5"; }
+
+.fa-hornbill:before {
+  content: "\f592"; }
+
+.fa-js:before {
+  content: "\f3b8"; }
+
+.fa-ideal:before {
+  content: "\e013"; }
+
+.fa-git:before {
+  content: "\f1d3"; }
+
+.fa-dev:before {
+  content: "\f6cc"; }
+
+.fa-sketch:before {
+  content: "\f7c6"; }
+
+.fa-yandex-international:before {
+  content: "\f414"; }
+
+.fa-cc-amex:before {
+  content: "\f1f3"; }
+
+.fa-uber:before {
+  content: "\f402"; }
+
+.fa-github:before {
+  content: "\f09b"; }
+
+.fa-php:before {
+  content: "\f457"; }
+
+.fa-alipay:before {
+  content: "\f642"; }
+
+.fa-youtube:before {
+  content: "\f167"; }
+
+.fa-skyatlas:before {
+  content: "\f216"; }
+
+.fa-firefox-browser:before {
+  content: "\e007"; }
+
+.fa-replyd:before {
+  content: "\f3e6"; }
+
+.fa-suse:before {
+  content: "\f7d6"; }
+
+.fa-jenkins:before {
+  content: "\f3b6"; }
+
+.fa-twitter:before {
+  content: "\f099"; }
+
+.fa-rockrms:before {
+  content: "\f3e9"; }
+
+.fa-pinterest:before {
+  content: "\f0d2"; }
+
+.fa-buffer:before {
+  content: "\f837"; }
+
+.fa-npm:before {
+  content: "\f3d4"; }
+
+.fa-yammer:before {
+  content: "\f840"; }
+
+.fa-btc:before {
+  content: "\f15a"; }
+
+.fa-dribbble:before {
+  content: "\f17d"; }
+
+.fa-stumbleupon-circle:before {
+  content: "\f1a3"; }
+
+.fa-internet-explorer:before {
+  content: "\f26b"; }
+
+.fa-stubber:before {
+  content: "\e5c7"; }
+
+.fa-telegram:before {
+  content: "\f2c6"; }
+
+.fa-telegram-plane:before {
+  content: "\f2c6"; }
+
+.fa-old-republic:before {
+  content: "\f510"; }
+
+.fa-odysee:before {
+  content: "\e5c6"; }
+
+.fa-square-whatsapp:before {
+  content: "\f40c"; }
+
+.fa-whatsapp-square:before {
+  content: "\f40c"; }
+
+.fa-node-js:before {
+  content: "\f3d3"; }
+
+.fa-edge-legacy:before {
+  content: "\e078"; }
+
+.fa-slack:before {
+  content: "\f198"; }
+
+.fa-slack-hash:before {
+  content: "\f198"; }
+
+.fa-medrt:before {
+  content: "\f3c8"; }
+
+.fa-usb:before {
+  content: "\f287"; }
+
+.fa-tumblr:before {
+  content: "\f173"; }
+
+.fa-vaadin:before {
+  content: "\f408"; }
+
+.fa-quora:before {
+  content: "\f2c4"; }
+
+.fa-square-x-twitter:before {
+  content: "\e61a"; }
+
+.fa-reacteurope:before {
+  content: "\f75d"; }
+
+.fa-medium:before {
+  content: "\f23a"; }
+
+.fa-medium-m:before {
+  content: "\f23a"; }
+
+.fa-amilia:before {
+  content: "\f36d"; }
+
+.fa-mixcloud:before {
+  content: "\f289"; }
+
+.fa-flipboard:before {
+  content: "\f44d"; }
+
+.fa-viacoin:before {
+  content: "\f237"; }
+
+.fa-critical-role:before {
+  content: "\f6c9"; }
+
+.fa-sitrox:before {
+  content: "\e44a"; }
+
+.fa-discourse:before {
+  content: "\f393"; }
+
+.fa-joomla:before {
+  content: "\f1aa"; }
+
+.fa-mastodon:before {
+  content: "\f4f6"; }
+
+.fa-airbnb:before {
+  content: "\f834"; }
+
+.fa-wolf-pack-battalion:before {
+  content: "\f514"; }
+
+.fa-buy-n-large:before {
+  content: "\f8a6"; }
+
+.fa-gulp:before {
+  content: "\f3ae"; }
+
+.fa-creative-commons-sampling-plus:before {
+  content: "\f4f1"; }
+
+.fa-strava:before {
+  content: "\f428"; }
+
+.fa-ember:before {
+  content: "\f423"; }
+
+.fa-canadian-maple-leaf:before {
+  content: "\f785"; }
+
+.fa-teamspeak:before {
+  content: "\f4f9"; }
+
+.fa-pushed:before {
+  content: "\f3e1"; }
+
+.fa-wordpress-simple:before {
+  content: "\f411"; }
+
+.fa-nutritionix:before {
+  content: "\f3d6"; }
+
+.fa-wodu:before {
+  content: "\e088"; }
+
+.fa-google-pay:before {
+  content: "\e079"; }
+
+.fa-intercom:before {
+  content: "\f7af"; }
+
+.fa-zhihu:before {
+  content: "\f63f"; }
+
+.fa-korvue:before {
+  content: "\f42f"; }
+
+.fa-pix:before {
+  content: "\e43a"; }
+
+.fa-steam-symbol:before {
+  content: "\f3f6"; }
+:root, :host {
+  --fa-style-family-classic: 'Font Awesome 6 Free';
+  --fa-font-regular: normal 400 1em/1 'Font Awesome 6 Free'; }
+
+@font-face {
+  font-family: 'Font Awesome 6 Free';
+  font-style: normal;
+  font-weight: 400;
+  font-display: block;
+  src: url("../webfonts/fa-regular-400.woff2") format("woff2"), url("../webfonts/fa-regular-400.ttf") format("truetype"); }
+
+.far,
+.fa-regular {
+  font-weight: 400; }
+:root, :host {
+  --fa-style-family-classic: 'Font Awesome 6 Free';
+  --fa-font-solid: normal 900 1em/1 'Font Awesome 6 Free'; }
+
+@font-face {
+  font-family: 'Font Awesome 6 Free';
+  font-style: normal;
+  font-weight: 900;
+  font-display: block;
+  src: url("../webfonts/fa-solid-900.woff2") format("woff2"), url("../webfonts/fa-solid-900.ttf") format("truetype"); }
+
+.fas,
+.fa-solid {
+  font-weight: 900; }
+@font-face {
+  font-family: 'Font Awesome 5 Brands';
+  font-display: block;
+  font-weight: 400;
+  src: url("../webfonts/fa-brands-400.woff2") format("woff2"), url("../webfonts/fa-brands-400.ttf") format("truetype"); }
+
+@font-face {
+  font-family: 'Font Awesome 5 Free';
+  font-display: block;
+  font-weight: 900;
+  src: url("../webfonts/fa-solid-900.woff2") format("woff2"), url("../webfonts/fa-solid-900.ttf") format("truetype"); }
+
+@font-face {
+  font-family: 'Font Awesome 5 Free';
+  font-display: block;
+  font-weight: 400;
+  src: url("../webfonts/fa-regular-400.woff2") format("woff2"), url("../webfonts/fa-regular-400.ttf") format("truetype"); }
+@font-face {
+  font-family: 'FontAwesome';
+  font-display: block;
+  src: url("../webfonts/fa-solid-900.woff2") format("woff2"), url("../webfonts/fa-solid-900.ttf") format("truetype"); }
+
+@font-face {
+  font-family: 'FontAwesome';
+  font-display: block;
+  src: url("../webfonts/fa-brands-400.woff2") format("woff2"), url("../webfonts/fa-brands-400.ttf") format("truetype"); }
+
+@font-face {
+  font-family: 'FontAwesome';
+  font-display: block;
+  src: url("../webfonts/fa-regular-400.woff2") format("woff2"), url("../webfonts/fa-regular-400.ttf") format("truetype"); }
+
+@font-face {
+  font-family: 'FontAwesome';
+  font-display: block;
+  src: url("../webfonts/fa-v4compatibility.woff2") format("woff2"), url("../webfonts/fa-v4compatibility.ttf") format("truetype"); }
diff --git a/docs/deps/font-awesome-6.5.2/css/all.min.css b/docs/deps/font-awesome-6.5.2/css/all.min.css
new file mode 100644
index 0000000..269bcee
--- /dev/null
+++ b/docs/deps/font-awesome-6.5.2/css/all.min.css
@@ -0,0 +1,9 @@
+/*!
+ * Font Awesome Free 6.5.2 by @fontawesome - https://fontawesome.com
+ * License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License)
+ * Copyright 2024 Fonticons, Inc.
+ */
+.fa{font-family:var(--fa-style-family,"Font Awesome 6 Free");font-weight:var(--fa-style,900)}.fa,.fa-brands,.fa-classic,.fa-regular,.fa-sharp,.fa-solid,.fab,.far,.fas{-moz-osx-font-smoothing:grayscale;-webkit-font-smoothing:antialiased;display:var(--fa-display,inline-block);font-style:normal;font-variant:normal;line-height:1;text-rendering:auto}.fa-classic,.fa-regular,.fa-solid,.far,.fas{font-family:"Font Awesome 6 Free"}.fa-brands,.fab{font-family:"Font Awesome 6 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diff --git a/docs/deps/font-awesome-6.5.2/css/v4-shims.css b/docs/deps/font-awesome-6.5.2/css/v4-shims.css
new file mode 100644
index 0000000..ea60ea4
--- /dev/null
+++ b/docs/deps/font-awesome-6.5.2/css/v4-shims.css
@@ -0,0 +1,2194 @@
+/*!
+ * Font Awesome Free 6.5.2 by @fontawesome - https://fontawesome.com
+ * License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License)
+ * Copyright 2024 Fonticons, Inc.
+ */
+.fa.fa-glass:before {
+  content: "\f000"; }
+
+.fa.fa-envelope-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-envelope-o:before {
+  content: "\f0e0"; }
+
+.fa.fa-star-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-star-o:before {
+  content: "\f005"; }
+
+.fa.fa-remove:before {
+  content: "\f00d"; }
+
+.fa.fa-close:before {
+  content: "\f00d"; }
+
+.fa.fa-gear:before {
+  content: "\f013"; }
+
+.fa.fa-trash-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-trash-o:before {
+  content: "\f2ed"; }
+
+.fa.fa-home:before {
+  content: "\f015"; }
+
+.fa.fa-file-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-file-o:before {
+  content: "\f15b"; }
+
+.fa.fa-clock-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-clock-o:before {
+  content: "\f017"; }
+
+.fa.fa-arrow-circle-o-down {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-arrow-circle-o-down:before {
+  content: "\f358"; }
+
+.fa.fa-arrow-circle-o-up {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-arrow-circle-o-up:before {
+  content: "\f35b"; }
+
+.fa.fa-play-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-play-circle-o:before {
+  content: "\f144"; }
+
+.fa.fa-repeat:before {
+  content: "\f01e"; }
+
+.fa.fa-rotate-right:before {
+  content: "\f01e"; }
+
+.fa.fa-refresh:before {
+  content: "\f021"; }
+
+.fa.fa-list-alt {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-list-alt:before {
+  content: "\f022"; }
+
+.fa.fa-dedent:before {
+  content: "\f03b"; }
+
+.fa.fa-video-camera:before {
+  content: "\f03d"; }
+
+.fa.fa-picture-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-picture-o:before {
+  content: "\f03e"; }
+
+.fa.fa-photo {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-photo:before {
+  content: "\f03e"; }
+
+.fa.fa-image {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-image:before {
+  content: "\f03e"; }
+
+.fa.fa-map-marker:before {
+  content: "\f3c5"; }
+
+.fa.fa-pencil-square-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-pencil-square-o:before {
+  content: "\f044"; }
+
+.fa.fa-edit {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-edit:before {
+  content: "\f044"; }
+
+.fa.fa-share-square-o:before {
+  content: "\f14d"; }
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+.fa.fa-check-square-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-check-square-o:before {
+  content: "\f14a"; }
+
+.fa.fa-arrows:before {
+  content: "\f0b2"; }
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+.fa.fa-times-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
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+.fa.fa-times-circle-o:before {
+  content: "\f057"; }
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+.fa.fa-check-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
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+.fa.fa-check-circle-o:before {
+  content: "\f058"; }
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+.fa.fa-mail-forward:before {
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+  font-weight: 400; }
+
+.fa.fa-modx {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-fort-awesome {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-usb {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-product-hunt {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-mixcloud {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-scribd {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-pause-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-pause-circle-o:before {
+  content: "\f28b"; }
+
+.fa.fa-stop-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-stop-circle-o:before {
+  content: "\f28d"; }
+
+.fa.fa-bluetooth {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-bluetooth-b {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-gitlab {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-wpbeginner {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-wpforms {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-envira {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-wheelchair-alt {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-wheelchair-alt:before {
+  content: "\f368"; }
+
+.fa.fa-question-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-question-circle-o:before {
+  content: "\f059"; }
+
+.fa.fa-volume-control-phone:before {
+  content: "\f2a0"; }
+
+.fa.fa-asl-interpreting:before {
+  content: "\f2a3"; }
+
+.fa.fa-deafness:before {
+  content: "\f2a4"; }
+
+.fa.fa-hard-of-hearing:before {
+  content: "\f2a4"; }
+
+.fa.fa-glide {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-glide-g {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-signing:before {
+  content: "\f2a7"; }
+
+.fa.fa-viadeo {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-viadeo-square {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-viadeo-square:before {
+  content: "\f2aa"; }
+
+.fa.fa-snapchat {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-snapchat-ghost {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-snapchat-ghost:before {
+  content: "\f2ab"; }
+
+.fa.fa-snapchat-square {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-snapchat-square:before {
+  content: "\f2ad"; }
+
+.fa.fa-pied-piper {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-first-order {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-yoast {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-themeisle {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-google-plus-official {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-google-plus-official:before {
+  content: "\f2b3"; }
+
+.fa.fa-google-plus-circle {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-google-plus-circle:before {
+  content: "\f2b3"; }
+
+.fa.fa-font-awesome {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-fa {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-fa:before {
+  content: "\f2b4"; }
+
+.fa.fa-handshake-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-handshake-o:before {
+  content: "\f2b5"; }
+
+.fa.fa-envelope-open-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-envelope-open-o:before {
+  content: "\f2b6"; }
+
+.fa.fa-linode {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-address-book-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-address-book-o:before {
+  content: "\f2b9"; }
+
+.fa.fa-vcard:before {
+  content: "\f2bb"; }
+
+.fa.fa-address-card-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-address-card-o:before {
+  content: "\f2bb"; }
+
+.fa.fa-vcard-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-vcard-o:before {
+  content: "\f2bb"; }
+
+.fa.fa-user-circle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-user-circle-o:before {
+  content: "\f2bd"; }
+
+.fa.fa-user-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-user-o:before {
+  content: "\f007"; }
+
+.fa.fa-id-badge {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-drivers-license:before {
+  content: "\f2c2"; }
+
+.fa.fa-id-card-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-id-card-o:before {
+  content: "\f2c2"; }
+
+.fa.fa-drivers-license-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-drivers-license-o:before {
+  content: "\f2c2"; }
+
+.fa.fa-quora {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-free-code-camp {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-telegram {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-thermometer-4:before {
+  content: "\f2c7"; }
+
+.fa.fa-thermometer:before {
+  content: "\f2c7"; }
+
+.fa.fa-thermometer-3:before {
+  content: "\f2c8"; }
+
+.fa.fa-thermometer-2:before {
+  content: "\f2c9"; }
+
+.fa.fa-thermometer-1:before {
+  content: "\f2ca"; }
+
+.fa.fa-thermometer-0:before {
+  content: "\f2cb"; }
+
+.fa.fa-bathtub:before {
+  content: "\f2cd"; }
+
+.fa.fa-s15:before {
+  content: "\f2cd"; }
+
+.fa.fa-window-maximize {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-window-restore {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-times-rectangle:before {
+  content: "\f410"; }
+
+.fa.fa-window-close-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-window-close-o:before {
+  content: "\f410"; }
+
+.fa.fa-times-rectangle-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-times-rectangle-o:before {
+  content: "\f410"; }
+
+.fa.fa-bandcamp {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-grav {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-etsy {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-imdb {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-ravelry {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-eercast {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-eercast:before {
+  content: "\f2da"; }
+
+.fa.fa-snowflake-o {
+  font-family: 'Font Awesome 6 Free';
+  font-weight: 400; }
+
+.fa.fa-snowflake-o:before {
+  content: "\f2dc"; }
+
+.fa.fa-superpowers {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-wpexplorer {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
+
+.fa.fa-meetup {
+  font-family: 'Font Awesome 6 Brands';
+  font-weight: 400; }
diff --git a/docs/deps/font-awesome-6.5.2/css/v4-shims.min.css b/docs/deps/font-awesome-6.5.2/css/v4-shims.min.css
new file mode 100644
index 0000000..09baf5f
--- /dev/null
+++ b/docs/deps/font-awesome-6.5.2/css/v4-shims.min.css
@@ -0,0 +1,6 @@
+/*!
+ * Font Awesome Free 6.5.2 by @fontawesome - https://fontawesome.com
+ * License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License)
+ * Copyright 2024 Fonticons, Inc.
+ */
+.fa.fa-glass:before{content:"\f000"}.fa.fa-envelope-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-envelope-o:before{content:"\f0e0"}.fa.fa-star-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-star-o:before{content:"\f005"}.fa.fa-close:before,.fa.fa-remove:before{content:"\f00d"}.fa.fa-gear:before{content:"\f013"}.fa.fa-trash-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-trash-o:before{content:"\f2ed"}.fa.fa-home:before{content:"\f015"}.fa.fa-file-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-file-o:before{content:"\f15b"}.fa.fa-clock-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-clock-o:before{content:"\f017"}.fa.fa-arrow-circle-o-down{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-arrow-circle-o-down:before{content:"\f358"}.fa.fa-arrow-circle-o-up{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-arrow-circle-o-up:before{content:"\f35b"}.fa.fa-play-circle-o{font-family:"Font Awesome 6 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Awesome 6 Free";font-weight:400}.fa.fa-check-square-o:before{content:"\f14a"}.fa.fa-arrows:before{content:"\f0b2"}.fa.fa-times-circle-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-times-circle-o:before{content:"\f057"}.fa.fa-check-circle-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-check-circle-o:before{content:"\f058"}.fa.fa-mail-forward:before{content:"\f064"}.fa.fa-expand:before{content:"\f424"}.fa.fa-compress:before{content:"\f422"}.fa.fa-eye,.fa.fa-eye-slash{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-warning:before{content:"\f071"}.fa.fa-calendar:before{content:"\f073"}.fa.fa-arrows-v:before{content:"\f338"}.fa.fa-arrows-h:before{content:"\f337"}.fa.fa-bar-chart-o:before,.fa.fa-bar-chart:before{content:"\e0e3"}.fa.fa-twitter-square{font-family:"Font Awesome 6 Brands";font-weight:400}.fa.fa-twitter-square:before{content:"\f081"}.fa.fa-facebook-square{font-family:"Font Awesome 6 Brands";font-weight:400}.fa.fa-facebook-square:before{content:"\f082"}.fa.fa-gears:before{content:"\f085"}.fa.fa-thumbs-o-up{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-thumbs-o-up:before{content:"\f164"}.fa.fa-thumbs-o-down{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-thumbs-o-down:before{content:"\f165"}.fa.fa-heart-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-heart-o:before{content:"\f004"}.fa.fa-sign-out:before{content:"\f2f5"}.fa.fa-linkedin-square{font-family:"Font Awesome 6 Brands";font-weight:400}.fa.fa-linkedin-square:before{content:"\f08c"}.fa.fa-thumb-tack:before{content:"\f08d"}.fa.fa-external-link:before{content:"\f35d"}.fa.fa-sign-in:before{content:"\f2f6"}.fa.fa-github-square{font-family:"Font Awesome 6 Brands";font-weight:400}.fa.fa-github-square:before{content:"\f092"}.fa.fa-lemon-o{font-family:"Font Awesome 6 Free";font-weight:400}.fa.fa-lemon-o:before{content:"\f094"}.fa.fa-square-o{font-family:"Font Awesome 6 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index 0000000..433069f
--- /dev/null
+++ b/docs/deps/headroom-0.11.0/headroom.min.js
@@ -0,0 +1,7 @@
+/*!
+ * headroom.js v0.11.0 - Give your page some headroom. Hide your header until you need it
+ * Copyright (c) 2020 Nick Williams - http://wicky.nillia.ms/headroom.js
+ * License: MIT
+ */
+
+!function(t,n){"object"==typeof exports&&"undefined"!=typeof module?module.exports=n():"function"==typeof define&&define.amd?define(n):(t=t||self).Headroom=n()}(this,function(){"use strict";function t(){return"undefined"!=typeof window}function d(t){return function(t){return t&&t.document&&function(t){return 9===t.nodeType}(t.document)}(t)?function(t){var n=t.document,o=n.body,s=n.documentElement;return{scrollHeight:function(){return Math.max(o.scrollHeight,s.scrollHeight,o.offsetHeight,s.offsetHeight,o.clientHeight,s.clientHeight)},height:function(){return t.innerHeight||s.clientHeight||o.clientHeight},scrollY:function(){return void 0!==t.pageYOffset?t.pageYOffset:(s||o.parentNode||o).scrollTop}}}(t):function(t){return{scrollHeight:function(){return Math.max(t.scrollHeight,t.offsetHeight,t.clientHeight)},height:function(){return Math.max(t.offsetHeight,t.clientHeight)},scrollY:function(){return t.scrollTop}}}(t)}function n(t,s,e){var n,o=function(){var n=!1;try{var t={get passive(){n=!0}};window.addEventListener("test",t,t),window.removeEventListener("test",t,t)}catch(t){n=!1}return n}(),i=!1,r=d(t),l=r.scrollY(),a={};function c(){var t=Math.round(r.scrollY()),n=r.height(),o=r.scrollHeight();a.scrollY=t,a.lastScrollY=l,a.direction=ls.tolerance[a.direction],e(a),l=t,i=!1}function h(){i||(i=!0,n=requestAnimationFrame(c))}var u=!!o&&{passive:!0,capture:!1};return t.addEventListener("scroll",h,u),c(),{destroy:function(){cancelAnimationFrame(n),t.removeEventListener("scroll",h,u)}}}function o(t,n){n=n||{},Object.assign(this,o.options,n),this.classes=Object.assign({},o.options.classes,n.classes),this.elem=t,this.tolerance=function(t){return t===Object(t)?t:{down:t,up:t}}(this.tolerance),this.initialised=!1,this.frozen=!1}return o.prototype={constructor:o,init:function(){return o.cutsTheMustard&&!this.initialised&&(this.addClass("initial"),this.initialised=!0,setTimeout(function(t){t.scrollTracker=n(t.scroller,{offset:t.offset,tolerance:t.tolerance},t.update.bind(t))},100,this)),this},destroy:function(){this.initialised=!1,Object.keys(this.classes).forEach(this.removeClass,this),this.scrollTracker.destroy()},unpin:function(){!this.hasClass("pinned")&&this.hasClass("unpinned")||(this.addClass("unpinned"),this.removeClass("pinned"),this.onUnpin&&this.onUnpin.call(this))},pin:function(){this.hasClass("unpinned")&&(this.addClass("pinned"),this.removeClass("unpinned"),this.onPin&&this.onPin.call(this))},freeze:function(){this.frozen=!0,this.addClass("frozen")},unfreeze:function(){this.frozen=!1,this.removeClass("frozen")},top:function(){this.hasClass("top")||(this.addClass("top"),this.removeClass("notTop"),this.onTop&&this.onTop.call(this))},notTop:function(){this.hasClass("notTop")||(this.addClass("notTop"),this.removeClass("top"),this.onNotTop&&this.onNotTop.call(this))},bottom:function(){this.hasClass("bottom")||(this.addClass("bottom"),this.removeClass("notBottom"),this.onBottom&&this.onBottom.call(this))},notBottom:function(){this.hasClass("notBottom")||(this.addClass("notBottom"),this.removeClass("bottom"),this.onNotBottom&&this.onNotBottom.call(this))},shouldUnpin:function(t){return"down"===t.direction&&!t.top&&t.toleranceExceeded},shouldPin:function(t){return"up"===t.direction&&t.toleranceExceeded||t.top},addClass:function(t){this.elem.classList.add.apply(this.elem.classList,this.classes[t].split(" "))},removeClass:function(t){this.elem.classList.remove.apply(this.elem.classList,this.classes[t].split(" "))},hasClass:function(t){return this.classes[t].split(" ").every(function(t){return this.classList.contains(t)},this.elem)},update:function(t){t.isOutOfBounds||!0!==this.frozen&&(t.top?this.top():this.notTop(),t.bottom?this.bottom():this.notBottom(),this.shouldUnpin(t)?this.unpin():this.shouldPin(t)&&this.pin())}},o.options={tolerance:{up:0,down:0},offset:0,scroller:t()?window:null,classes:{frozen:"headroom--frozen",pinned:"headroom--pinned",unpinned:"headroom--unpinned",top:"headroom--top",notTop:"headroom--not-top",bottom:"headroom--bottom",notBottom:"headroom--not-bottom",initial:"headroom"}},o.cutsTheMustard=!!(t()&&function(){}.bind&&"classList"in document.documentElement&&Object.assign&&Object.keys&&requestAnimationFrame),o});
\ No newline at end of file
diff --git a/docs/deps/headroom-0.11.0/jQuery.headroom.min.js b/docs/deps/headroom-0.11.0/jQuery.headroom.min.js
new file mode 100644
index 0000000..17f70c9
--- /dev/null
+++ b/docs/deps/headroom-0.11.0/jQuery.headroom.min.js
@@ -0,0 +1,7 @@
+/*!
+ * headroom.js v0.9.4 - Give your page some headroom. Hide your header until you need it
+ * Copyright (c) 2017 Nick Williams - http://wicky.nillia.ms/headroom.js
+ * License: MIT
+ */
+
+!function(a){a&&(a.fn.headroom=function(b){return this.each(function(){var c=a(this),d=c.data("headroom"),e="object"==typeof b&&b;e=a.extend(!0,{},Headroom.options,e),d||(d=new Headroom(this,e),d.init(),c.data("headroom",d)),"string"==typeof b&&(d[b](),"destroy"===b&&c.removeData("headroom"))})},a("[data-headroom]").each(function(){var b=a(this);b.headroom(b.data())}))}(window.Zepto||window.jQuery);
\ No newline at end of file
diff --git a/docs/deps/jquery-3.6.0/jquery-3.6.0.js b/docs/deps/jquery-3.6.0/jquery-3.6.0.js
new file mode 100644
index 0000000..fc6c299
--- /dev/null
+++ b/docs/deps/jquery-3.6.0/jquery-3.6.0.js
@@ -0,0 +1,10881 @@
+/*!
+ * jQuery JavaScript Library v3.6.0
+ * https://jquery.com/
+ *
+ * Includes Sizzle.js
+ * https://sizzlejs.com/
+ *
+ * Copyright OpenJS Foundation and other contributors
+ * Released under the MIT license
+ * https://jquery.org/license
+ *
+ * Date: 2021-03-02T17:08Z
+ */
+( function( global, factory ) {
+
+	"use strict";
+
+	if ( typeof module === "object" && typeof module.exports === "object" ) {
+
+		// For CommonJS and CommonJS-like environments where a proper `window`
+		// is present, execute the factory and get jQuery.
+		// For environments that do not have a `window` with a `document`
+		// (such as Node.js), expose a factory as module.exports.
+		// This accentuates the need for the creation of a real `window`.
+		// e.g. var jQuery = require("jquery")(window);
+		// See ticket #14549 for more info.
+		module.exports = global.document ?
+			factory( global, true ) :
+			function( w ) {
+				if ( !w.document ) {
+					throw new Error( "jQuery requires a window with a document" );
+				}
+				return factory( w );
+			};
+	} else {
+		factory( global );
+	}
+
+// Pass this if window is not defined yet
+} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) {
+
+// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1
+// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode
+// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common
+// enough that all such attempts are guarded in a try block.
+"use strict";
+
+var arr = [];
+
+var getProto = Object.getPrototypeOf;
+
+var slice = arr.slice;
+
+var flat = arr.flat ? function( array ) {
+	return arr.flat.call( array );
+} : function( array ) {
+	return arr.concat.apply( [], array );
+};
+
+
+var push = arr.push;
+
+var indexOf = arr.indexOf;
+
+var class2type = {};
+
+var toString = class2type.toString;
+
+var hasOwn = class2type.hasOwnProperty;
+
+var fnToString = hasOwn.toString;
+
+var ObjectFunctionString = fnToString.call( Object );
+
+var support = {};
+
+var isFunction = function isFunction( obj ) {
+
+		// Support: Chrome <=57, Firefox <=52
+		// In some browsers, typeof returns "function" for HTML  elements
+		// (i.e., `typeof document.createElement( "object" ) === "function"`).
+		// We don't want to classify *any* DOM node as a function.
+		// Support: QtWeb <=3.8.5, WebKit <=534.34, wkhtmltopdf tool <=0.12.5
+		// Plus for old WebKit, typeof returns "function" for HTML collections
+		// (e.g., `typeof document.getElementsByTagName("div") === "function"`). (gh-4756)
+		return typeof obj === "function" && typeof obj.nodeType !== "number" &&
+			typeof obj.item !== "function";
+	};
+
+
+var isWindow = function isWindow( obj ) {
+		return obj != null && obj === obj.window;
+	};
+
+
+var document = window.document;
+
+
+
+	var preservedScriptAttributes = {
+		type: true,
+		src: true,
+		nonce: true,
+		noModule: true
+	};
+
+	function DOMEval( code, node, doc ) {
+		doc = doc || document;
+
+		var i, val,
+			script = doc.createElement( "script" );
+
+		script.text = code;
+		if ( node ) {
+			for ( i in preservedScriptAttributes ) {
+
+				// Support: Firefox 64+, Edge 18+
+				// Some browsers don't support the "nonce" property on scripts.
+				// On the other hand, just using `getAttribute` is not enough as
+				// the `nonce` attribute is reset to an empty string whenever it
+				// becomes browsing-context connected.
+				// See https://github.com/whatwg/html/issues/2369
+				// See https://html.spec.whatwg.org/#nonce-attributes
+				// The `node.getAttribute` check was added for the sake of
+				// `jQuery.globalEval` so that it can fake a nonce-containing node
+				// via an object.
+				val = node[ i ] || node.getAttribute && node.getAttribute( i );
+				if ( val ) {
+					script.setAttribute( i, val );
+				}
+			}
+		}
+		doc.head.appendChild( script ).parentNode.removeChild( script );
+	}
+
+
+function toType( obj ) {
+	if ( obj == null ) {
+		return obj + "";
+	}
+
+	// Support: Android <=2.3 only (functionish RegExp)
+	return typeof obj === "object" || typeof obj === "function" ?
+		class2type[ toString.call( obj ) ] || "object" :
+		typeof obj;
+}
+/* global Symbol */
+// Defining this global in .eslintrc.json would create a danger of using the global
+// unguarded in another place, it seems safer to define global only for this module
+
+
+
+var
+	version = "3.6.0",
+
+	// Define a local copy of jQuery
+	jQuery = function( selector, context ) {
+
+		// The jQuery object is actually just the init constructor 'enhanced'
+		// Need init if jQuery is called (just allow error to be thrown if not included)
+		return new jQuery.fn.init( selector, context );
+	};
+
+jQuery.fn = jQuery.prototype = {
+
+	// The current version of jQuery being used
+	jquery: version,
+
+	constructor: jQuery,
+
+	// The default length of a jQuery object is 0
+	length: 0,
+
+	toArray: function() {
+		return slice.call( this );
+	},
+
+	// Get the Nth element in the matched element set OR
+	// Get the whole matched element set as a clean array
+	get: function( num ) {
+
+		// Return all the elements in a clean array
+		if ( num == null ) {
+			return slice.call( this );
+		}
+
+		// Return just the one element from the set
+		return num < 0 ? this[ num + this.length ] : this[ num ];
+	},
+
+	// Take an array of elements and push it onto the stack
+	// (returning the new matched element set)
+	pushStack: function( elems ) {
+
+		// Build a new jQuery matched element set
+		var ret = jQuery.merge( this.constructor(), elems );
+
+		// Add the old object onto the stack (as a reference)
+		ret.prevObject = this;
+
+		// Return the newly-formed element set
+		return ret;
+	},
+
+	// Execute a callback for every element in the matched set.
+	each: function( callback ) {
+		return jQuery.each( this, callback );
+	},
+
+	map: function( callback ) {
+		return this.pushStack( jQuery.map( this, function( elem, i ) {
+			return callback.call( elem, i, elem );
+		} ) );
+	},
+
+	slice: function() {
+		return this.pushStack( slice.apply( this, arguments ) );
+	},
+
+	first: function() {
+		return this.eq( 0 );
+	},
+
+	last: function() {
+		return this.eq( -1 );
+	},
+
+	even: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return ( i + 1 ) % 2;
+		} ) );
+	},
+
+	odd: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return i % 2;
+		} ) );
+	},
+
+	eq: function( i ) {
+		var len = this.length,
+			j = +i + ( i < 0 ? len : 0 );
+		return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] );
+	},
+
+	end: function() {
+		return this.prevObject || this.constructor();
+	},
+
+	// For internal use only.
+	// Behaves like an Array's method, not like a jQuery method.
+	push: push,
+	sort: arr.sort,
+	splice: arr.splice
+};
+
+jQuery.extend = jQuery.fn.extend = function() {
+	var options, name, src, copy, copyIsArray, clone,
+		target = arguments[ 0 ] || {},
+		i = 1,
+		length = arguments.length,
+		deep = false;
+
+	// Handle a deep copy situation
+	if ( typeof target === "boolean" ) {
+		deep = target;
+
+		// Skip the boolean and the target
+		target = arguments[ i ] || {};
+		i++;
+	}
+
+	// Handle case when target is a string or something (possible in deep copy)
+	if ( typeof target !== "object" && !isFunction( target ) ) {
+		target = {};
+	}
+
+	// Extend jQuery itself if only one argument is passed
+	if ( i === length ) {
+		target = this;
+		i--;
+	}
+
+	for ( ; i < length; i++ ) {
+
+		// Only deal with non-null/undefined values
+		if ( ( options = arguments[ i ] ) != null ) {
+
+			// Extend the base object
+			for ( name in options ) {
+				copy = options[ name ];
+
+				// Prevent Object.prototype pollution
+				// Prevent never-ending loop
+				if ( name === "__proto__" || target === copy ) {
+					continue;
+				}
+
+				// Recurse if we're merging plain objects or arrays
+				if ( deep && copy && ( jQuery.isPlainObject( copy ) ||
+					( copyIsArray = Array.isArray( copy ) ) ) ) {
+					src = target[ name ];
+
+					// Ensure proper type for the source value
+					if ( copyIsArray && !Array.isArray( src ) ) {
+						clone = [];
+					} else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) {
+						clone = {};
+					} else {
+						clone = src;
+					}
+					copyIsArray = false;
+
+					// Never move original objects, clone them
+					target[ name ] = jQuery.extend( deep, clone, copy );
+
+				// Don't bring in undefined values
+				} else if ( copy !== undefined ) {
+					target[ name ] = copy;
+				}
+			}
+		}
+	}
+
+	// Return the modified object
+	return target;
+};
+
+jQuery.extend( {
+
+	// Unique for each copy of jQuery on the page
+	expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ),
+
+	// Assume jQuery is ready without the ready module
+	isReady: true,
+
+	error: function( msg ) {
+		throw new Error( msg );
+	},
+
+	noop: function() {},
+
+	isPlainObject: function( obj ) {
+		var proto, Ctor;
+
+		// Detect obvious negatives
+		// Use toString instead of jQuery.type to catch host objects
+		if ( !obj || toString.call( obj ) !== "[object Object]" ) {
+			return false;
+		}
+
+		proto = getProto( obj );
+
+		// Objects with no prototype (e.g., `Object.create( null )`) are plain
+		if ( !proto ) {
+			return true;
+		}
+
+		// Objects with prototype are plain iff they were constructed by a global Object function
+		Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor;
+		return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString;
+	},
+
+	isEmptyObject: function( obj ) {
+		var name;
+
+		for ( name in obj ) {
+			return false;
+		}
+		return true;
+	},
+
+	// Evaluates a script in a provided context; falls back to the global one
+	// if not specified.
+	globalEval: function( code, options, doc ) {
+		DOMEval( code, { nonce: options && options.nonce }, doc );
+	},
+
+	each: function( obj, callback ) {
+		var length, i = 0;
+
+		if ( isArrayLike( obj ) ) {
+			length = obj.length;
+			for ( ; i < length; i++ ) {
+				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+					break;
+				}
+			}
+		} else {
+			for ( i in obj ) {
+				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+					break;
+				}
+			}
+		}
+
+		return obj;
+	},
+
+	// results is for internal usage only
+	makeArray: function( arr, results ) {
+		var ret = results || [];
+
+		if ( arr != null ) {
+			if ( isArrayLike( Object( arr ) ) ) {
+				jQuery.merge( ret,
+					typeof arr === "string" ?
+						[ arr ] : arr
+				);
+			} else {
+				push.call( ret, arr );
+			}
+		}
+
+		return ret;
+	},
+
+	inArray: function( elem, arr, i ) {
+		return arr == null ? -1 : indexOf.call( arr, elem, i );
+	},
+
+	// Support: Android <=4.0 only, PhantomJS 1 only
+	// push.apply(_, arraylike) throws on ancient WebKit
+	merge: function( first, second ) {
+		var len = +second.length,
+			j = 0,
+			i = first.length;
+
+		for ( ; j < len; j++ ) {
+			first[ i++ ] = second[ j ];
+		}
+
+		first.length = i;
+
+		return first;
+	},
+
+	grep: function( elems, callback, invert ) {
+		var callbackInverse,
+			matches = [],
+			i = 0,
+			length = elems.length,
+			callbackExpect = !invert;
+
+		// Go through the array, only saving the items
+		// that pass the validator function
+		for ( ; i < length; i++ ) {
+			callbackInverse = !callback( elems[ i ], i );
+			if ( callbackInverse !== callbackExpect ) {
+				matches.push( elems[ i ] );
+			}
+		}
+
+		return matches;
+	},
+
+	// arg is for internal usage only
+	map: function( elems, callback, arg ) {
+		var length, value,
+			i = 0,
+			ret = [];
+
+		// Go through the array, translating each of the items to their new values
+		if ( isArrayLike( elems ) ) {
+			length = elems.length;
+			for ( ; i < length; i++ ) {
+				value = callback( elems[ i ], i, arg );
+
+				if ( value != null ) {
+					ret.push( value );
+				}
+			}
+
+		// Go through every key on the object,
+		} else {
+			for ( i in elems ) {
+				value = callback( elems[ i ], i, arg );
+
+				if ( value != null ) {
+					ret.push( value );
+				}
+			}
+		}
+
+		// Flatten any nested arrays
+		return flat( ret );
+	},
+
+	// A global GUID counter for objects
+	guid: 1,
+
+	// jQuery.support is not used in Core but other projects attach their
+	// properties to it so it needs to exist.
+	support: support
+} );
+
+if ( typeof Symbol === "function" ) {
+	jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ];
+}
+
+// Populate the class2type map
+jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ),
+	function( _i, name ) {
+		class2type[ "[object " + name + "]" ] = name.toLowerCase();
+	} );
+
+function isArrayLike( obj ) {
+
+	// Support: real iOS 8.2 only (not reproducible in simulator)
+	// `in` check used to prevent JIT error (gh-2145)
+	// hasOwn isn't used here due to false negatives
+	// regarding Nodelist length in IE
+	var length = !!obj && "length" in obj && obj.length,
+		type = toType( obj );
+
+	if ( isFunction( obj ) || isWindow( obj ) ) {
+		return false;
+	}
+
+	return type === "array" || length === 0 ||
+		typeof length === "number" && length > 0 && ( length - 1 ) in obj;
+}
+var Sizzle =
+/*!
+ * Sizzle CSS Selector Engine v2.3.6
+ * https://sizzlejs.com/
+ *
+ * Copyright JS Foundation and other contributors
+ * Released under the MIT license
+ * https://js.foundation/
+ *
+ * Date: 2021-02-16
+ */
+( function( window ) {
+var i,
+	support,
+	Expr,
+	getText,
+	isXML,
+	tokenize,
+	compile,
+	select,
+	outermostContext,
+	sortInput,
+	hasDuplicate,
+
+	// Local document vars
+	setDocument,
+	document,
+	docElem,
+	documentIsHTML,
+	rbuggyQSA,
+	rbuggyMatches,
+	matches,
+	contains,
+
+	// Instance-specific data
+	expando = "sizzle" + 1 * new Date(),
+	preferredDoc = window.document,
+	dirruns = 0,
+	done = 0,
+	classCache = createCache(),
+	tokenCache = createCache(),
+	compilerCache = createCache(),
+	nonnativeSelectorCache = createCache(),
+	sortOrder = function( a, b ) {
+		if ( a === b ) {
+			hasDuplicate = true;
+		}
+		return 0;
+	},
+
+	// Instance methods
+	hasOwn = ( {} ).hasOwnProperty,
+	arr = [],
+	pop = arr.pop,
+	pushNative = arr.push,
+	push = arr.push,
+	slice = arr.slice,
+
+	// Use a stripped-down indexOf as it's faster than native
+	// https://jsperf.com/thor-indexof-vs-for/5
+	indexOf = function( list, elem ) {
+		var i = 0,
+			len = list.length;
+		for ( ; i < len; i++ ) {
+			if ( list[ i ] === elem ) {
+				return i;
+			}
+		}
+		return -1;
+	},
+
+	booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" +
+		"ismap|loop|multiple|open|readonly|required|scoped",
+
+	// Regular expressions
+
+	// http://www.w3.org/TR/css3-selectors/#whitespace
+	whitespace = "[\\x20\\t\\r\\n\\f]",
+
+	// https://www.w3.org/TR/css-syntax-3/#ident-token-diagram
+	identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace +
+		"?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+",
+
+	// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
+	attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
+
+		// Operator (capture 2)
+		"*([*^$|!~]?=)" + whitespace +
+
+		// "Attribute values must be CSS identifiers [capture 5]
+		// or strings [capture 3 or capture 4]"
+		"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" +
+		whitespace + "*\\]",
+
+	pseudos = ":(" + identifier + ")(?:\\((" +
+
+		// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
+		// 1. quoted (capture 3; capture 4 or capture 5)
+		"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
+
+		// 2. simple (capture 6)
+		"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
+
+		// 3. anything else (capture 2)
+		".*" +
+		")\\)|)",
+
+	// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
+	rwhitespace = new RegExp( whitespace + "+", "g" ),
+	rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" +
+		whitespace + "+$", "g" ),
+
+	rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
+	rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace +
+		"*" ),
+	rdescend = new RegExp( whitespace + "|>" ),
+
+	rpseudo = new RegExp( pseudos ),
+	ridentifier = new RegExp( "^" + identifier + "$" ),
+
+	matchExpr = {
+		"ID": new RegExp( "^#(" + identifier + ")" ),
+		"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
+		"TAG": new RegExp( "^(" + identifier + "|[*])" ),
+		"ATTR": new RegExp( "^" + attributes ),
+		"PSEUDO": new RegExp( "^" + pseudos ),
+		"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" +
+			whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" +
+			whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
+		"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
+
+		// For use in libraries implementing .is()
+		// We use this for POS matching in `select`
+		"needsContext": new RegExp( "^" + whitespace +
+			"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace +
+			"*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
+	},
+
+	rhtml = /HTML$/i,
+	rinputs = /^(?:input|select|textarea|button)$/i,
+	rheader = /^h\d$/i,
+
+	rnative = /^[^{]+\{\s*\[native \w/,
+
+	// Easily-parseable/retrievable ID or TAG or CLASS selectors
+	rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
+
+	rsibling = /[+~]/,
+
+	// CSS escapes
+	// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
+	runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ),
+	funescape = function( escape, nonHex ) {
+		var high = "0x" + escape.slice( 1 ) - 0x10000;
+
+		return nonHex ?
+
+			// Strip the backslash prefix from a non-hex escape sequence
+			nonHex :
+
+			// Replace a hexadecimal escape sequence with the encoded Unicode code point
+			// Support: IE <=11+
+			// For values outside the Basic Multilingual Plane (BMP), manually construct a
+			// surrogate pair
+			high < 0 ?
+				String.fromCharCode( high + 0x10000 ) :
+				String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
+	},
+
+	// CSS string/identifier serialization
+	// https://drafts.csswg.org/cssom/#common-serializing-idioms
+	rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
+	fcssescape = function( ch, asCodePoint ) {
+		if ( asCodePoint ) {
+
+			// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
+			if ( ch === "\0" ) {
+				return "\uFFFD";
+			}
+
+			// Control characters and (dependent upon position) numbers get escaped as code points
+			return ch.slice( 0, -1 ) + "\\" +
+				ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
+		}
+
+		// Other potentially-special ASCII characters get backslash-escaped
+		return "\\" + ch;
+	},
+
+	// Used for iframes
+	// See setDocument()
+	// Removing the function wrapper causes a "Permission Denied"
+	// error in IE
+	unloadHandler = function() {
+		setDocument();
+	},
+
+	inDisabledFieldset = addCombinator(
+		function( elem ) {
+			return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
+		},
+		{ dir: "parentNode", next: "legend" }
+	);
+
+// Optimize for push.apply( _, NodeList )
+try {
+	push.apply(
+		( arr = slice.call( preferredDoc.childNodes ) ),
+		preferredDoc.childNodes
+	);
+
+	// Support: Android<4.0
+	// Detect silently failing push.apply
+	// eslint-disable-next-line no-unused-expressions
+	arr[ preferredDoc.childNodes.length ].nodeType;
+} catch ( e ) {
+	push = { apply: arr.length ?
+
+		// Leverage slice if possible
+		function( target, els ) {
+			pushNative.apply( target, slice.call( els ) );
+		} :
+
+		// Support: IE<9
+		// Otherwise append directly
+		function( target, els ) {
+			var j = target.length,
+				i = 0;
+
+			// Can't trust NodeList.length
+			while ( ( target[ j++ ] = els[ i++ ] ) ) {}
+			target.length = j - 1;
+		}
+	};
+}
+
+function Sizzle( selector, context, results, seed ) {
+	var m, i, elem, nid, match, groups, newSelector,
+		newContext = context && context.ownerDocument,
+
+		// nodeType defaults to 9, since context defaults to document
+		nodeType = context ? context.nodeType : 9;
+
+	results = results || [];
+
+	// Return early from calls with invalid selector or context
+	if ( typeof selector !== "string" || !selector ||
+		nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
+
+		return results;
+	}
+
+	// Try to shortcut find operations (as opposed to filters) in HTML documents
+	if ( !seed ) {
+		setDocument( context );
+		context = context || document;
+
+		if ( documentIsHTML ) {
+
+			// If the selector is sufficiently simple, try using a "get*By*" DOM method
+			// (excepting DocumentFragment context, where the methods don't exist)
+			if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) {
+
+				// ID selector
+				if ( ( m = match[ 1 ] ) ) {
+
+					// Document context
+					if ( nodeType === 9 ) {
+						if ( ( elem = context.getElementById( m ) ) ) {
+
+							// Support: IE, Opera, Webkit
+							// TODO: identify versions
+							// getElementById can match elements by name instead of ID
+							if ( elem.id === m ) {
+								results.push( elem );
+								return results;
+							}
+						} else {
+							return results;
+						}
+
+					// Element context
+					} else {
+
+						// Support: IE, Opera, Webkit
+						// TODO: identify versions
+						// getElementById can match elements by name instead of ID
+						if ( newContext && ( elem = newContext.getElementById( m ) ) &&
+							contains( context, elem ) &&
+							elem.id === m ) {
+
+							results.push( elem );
+							return results;
+						}
+					}
+
+				// Type selector
+				} else if ( match[ 2 ] ) {
+					push.apply( results, context.getElementsByTagName( selector ) );
+					return results;
+
+				// Class selector
+				} else if ( ( m = match[ 3 ] ) && support.getElementsByClassName &&
+					context.getElementsByClassName ) {
+
+					push.apply( results, context.getElementsByClassName( m ) );
+					return results;
+				}
+			}
+
+			// Take advantage of querySelectorAll
+			if ( support.qsa &&
+				!nonnativeSelectorCache[ selector + " " ] &&
+				( !rbuggyQSA || !rbuggyQSA.test( selector ) ) &&
+
+				// Support: IE 8 only
+				// Exclude object elements
+				( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) {
+
+				newSelector = selector;
+				newContext = context;
+
+				// qSA considers elements outside a scoping root when evaluating child or
+				// descendant combinators, which is not what we want.
+				// In such cases, we work around the behavior by prefixing every selector in the
+				// list with an ID selector referencing the scope context.
+				// The technique has to be used as well when a leading combinator is used
+				// as such selectors are not recognized by querySelectorAll.
+				// Thanks to Andrew Dupont for this technique.
+				if ( nodeType === 1 &&
+					( rdescend.test( selector ) || rcombinators.test( selector ) ) ) {
+
+					// Expand context for sibling selectors
+					newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
+						context;
+
+					// We can use :scope instead of the ID hack if the browser
+					// supports it & if we're not changing the context.
+					if ( newContext !== context || !support.scope ) {
+
+						// Capture the context ID, setting it first if necessary
+						if ( ( nid = context.getAttribute( "id" ) ) ) {
+							nid = nid.replace( rcssescape, fcssescape );
+						} else {
+							context.setAttribute( "id", ( nid = expando ) );
+						}
+					}
+
+					// Prefix every selector in the list
+					groups = tokenize( selector );
+					i = groups.length;
+					while ( i-- ) {
+						groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " +
+							toSelector( groups[ i ] );
+					}
+					newSelector = groups.join( "," );
+				}
+
+				try {
+					push.apply( results,
+						newContext.querySelectorAll( newSelector )
+					);
+					return results;
+				} catch ( qsaError ) {
+					nonnativeSelectorCache( selector, true );
+				} finally {
+					if ( nid === expando ) {
+						context.removeAttribute( "id" );
+					}
+				}
+			}
+		}
+	}
+
+	// All others
+	return select( selector.replace( rtrim, "$1" ), context, results, seed );
+}
+
+/**
+ * Create key-value caches of limited size
+ * @returns {function(string, object)} Returns the Object data after storing it on itself with
+ *	property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
+ *	deleting the oldest entry
+ */
+function createCache() {
+	var keys = [];
+
+	function cache( key, value ) {
+
+		// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
+		if ( keys.push( key + " " ) > Expr.cacheLength ) {
+
+			// Only keep the most recent entries
+			delete cache[ keys.shift() ];
+		}
+		return ( cache[ key + " " ] = value );
+	}
+	return cache;
+}
+
+/**
+ * Mark a function for special use by Sizzle
+ * @param {Function} fn The function to mark
+ */
+function markFunction( fn ) {
+	fn[ expando ] = true;
+	return fn;
+}
+
+/**
+ * Support testing using an element
+ * @param {Function} fn Passed the created element and returns a boolean result
+ */
+function assert( fn ) {
+	var el = document.createElement( "fieldset" );
+
+	try {
+		return !!fn( el );
+	} catch ( e ) {
+		return false;
+	} finally {
+
+		// Remove from its parent by default
+		if ( el.parentNode ) {
+			el.parentNode.removeChild( el );
+		}
+
+		// release memory in IE
+		el = null;
+	}
+}
+
+/**
+ * Adds the same handler for all of the specified attrs
+ * @param {String} attrs Pipe-separated list of attributes
+ * @param {Function} handler The method that will be applied
+ */
+function addHandle( attrs, handler ) {
+	var arr = attrs.split( "|" ),
+		i = arr.length;
+
+	while ( i-- ) {
+		Expr.attrHandle[ arr[ i ] ] = handler;
+	}
+}
+
+/**
+ * Checks document order of two siblings
+ * @param {Element} a
+ * @param {Element} b
+ * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
+ */
+function siblingCheck( a, b ) {
+	var cur = b && a,
+		diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
+			a.sourceIndex - b.sourceIndex;
+
+	// Use IE sourceIndex if available on both nodes
+	if ( diff ) {
+		return diff;
+	}
+
+	// Check if b follows a
+	if ( cur ) {
+		while ( ( cur = cur.nextSibling ) ) {
+			if ( cur === b ) {
+				return -1;
+			}
+		}
+	}
+
+	return a ? 1 : -1;
+}
+
+/**
+ * Returns a function to use in pseudos for input types
+ * @param {String} type
+ */
+function createInputPseudo( type ) {
+	return function( elem ) {
+		var name = elem.nodeName.toLowerCase();
+		return name === "input" && elem.type === type;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for buttons
+ * @param {String} type
+ */
+function createButtonPseudo( type ) {
+	return function( elem ) {
+		var name = elem.nodeName.toLowerCase();
+		return ( name === "input" || name === "button" ) && elem.type === type;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for :enabled/:disabled
+ * @param {Boolean} disabled true for :disabled; false for :enabled
+ */
+function createDisabledPseudo( disabled ) {
+
+	// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
+	return function( elem ) {
+
+		// Only certain elements can match :enabled or :disabled
+		// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
+		// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
+		if ( "form" in elem ) {
+
+			// Check for inherited disabledness on relevant non-disabled elements:
+			// * listed form-associated elements in a disabled fieldset
+			//   https://html.spec.whatwg.org/multipage/forms.html#category-listed
+			//   https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
+			// * option elements in a disabled optgroup
+			//   https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
+			// All such elements have a "form" property.
+			if ( elem.parentNode && elem.disabled === false ) {
+
+				// Option elements defer to a parent optgroup if present
+				if ( "label" in elem ) {
+					if ( "label" in elem.parentNode ) {
+						return elem.parentNode.disabled === disabled;
+					} else {
+						return elem.disabled === disabled;
+					}
+				}
+
+				// Support: IE 6 - 11
+				// Use the isDisabled shortcut property to check for disabled fieldset ancestors
+				return elem.isDisabled === disabled ||
+
+					// Where there is no isDisabled, check manually
+					/* jshint -W018 */
+					elem.isDisabled !== !disabled &&
+					inDisabledFieldset( elem ) === disabled;
+			}
+
+			return elem.disabled === disabled;
+
+		// Try to winnow out elements that can't be disabled before trusting the disabled property.
+		// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
+		// even exist on them, let alone have a boolean value.
+		} else if ( "label" in elem ) {
+			return elem.disabled === disabled;
+		}
+
+		// Remaining elements are neither :enabled nor :disabled
+		return false;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for positionals
+ * @param {Function} fn
+ */
+function createPositionalPseudo( fn ) {
+	return markFunction( function( argument ) {
+		argument = +argument;
+		return markFunction( function( seed, matches ) {
+			var j,
+				matchIndexes = fn( [], seed.length, argument ),
+				i = matchIndexes.length;
+
+			// Match elements found at the specified indexes
+			while ( i-- ) {
+				if ( seed[ ( j = matchIndexes[ i ] ) ] ) {
+					seed[ j ] = !( matches[ j ] = seed[ j ] );
+				}
+			}
+		} );
+	} );
+}
+
+/**
+ * Checks a node for validity as a Sizzle context
+ * @param {Element|Object=} context
+ * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
+ */
+function testContext( context ) {
+	return context && typeof context.getElementsByTagName !== "undefined" && context;
+}
+
+// Expose support vars for convenience
+support = Sizzle.support = {};
+
+/**
+ * Detects XML nodes
+ * @param {Element|Object} elem An element or a document
+ * @returns {Boolean} True iff elem is a non-HTML XML node
+ */
+isXML = Sizzle.isXML = function( elem ) {
+	var namespace = elem && elem.namespaceURI,
+		docElem = elem && ( elem.ownerDocument || elem ).documentElement;
+
+	// Support: IE <=8
+	// Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
+	// https://bugs.jquery.com/ticket/4833
+	return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
+};
+
+/**
+ * Sets document-related variables once based on the current document
+ * @param {Element|Object} [doc] An element or document object to use to set the document
+ * @returns {Object} Returns the current document
+ */
+setDocument = Sizzle.setDocument = function( node ) {
+	var hasCompare, subWindow,
+		doc = node ? node.ownerDocument || node : preferredDoc;
+
+	// Return early if doc is invalid or already selected
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) {
+		return document;
+	}
+
+	// Update global variables
+	document = doc;
+	docElem = document.documentElement;
+	documentIsHTML = !isXML( document );
+
+	// Support: IE 9 - 11+, Edge 12 - 18+
+	// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( preferredDoc != document &&
+		( subWindow = document.defaultView ) && subWindow.top !== subWindow ) {
+
+		// Support: IE 11, Edge
+		if ( subWindow.addEventListener ) {
+			subWindow.addEventListener( "unload", unloadHandler, false );
+
+		// Support: IE 9 - 10 only
+		} else if ( subWindow.attachEvent ) {
+			subWindow.attachEvent( "onunload", unloadHandler );
+		}
+	}
+
+	// Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only,
+	// Safari 4 - 5 only, Opera <=11.6 - 12.x only
+	// IE/Edge & older browsers don't support the :scope pseudo-class.
+	// Support: Safari 6.0 only
+	// Safari 6.0 supports :scope but it's an alias of :root there.
+	support.scope = assert( function( el ) {
+		docElem.appendChild( el ).appendChild( document.createElement( "div" ) );
+		return typeof el.querySelectorAll !== "undefined" &&
+			!el.querySelectorAll( ":scope fieldset div" ).length;
+	} );
+
+	/* Attributes
+	---------------------------------------------------------------------- */
+
+	// Support: IE<8
+	// Verify that getAttribute really returns attributes and not properties
+	// (excepting IE8 booleans)
+	support.attributes = assert( function( el ) {
+		el.className = "i";
+		return !el.getAttribute( "className" );
+	} );
+
+	/* getElement(s)By*
+	---------------------------------------------------------------------- */
+
+	// Check if getElementsByTagName("*") returns only elements
+	support.getElementsByTagName = assert( function( el ) {
+		el.appendChild( document.createComment( "" ) );
+		return !el.getElementsByTagName( "*" ).length;
+	} );
+
+	// Support: IE<9
+	support.getElementsByClassName = rnative.test( document.getElementsByClassName );
+
+	// Support: IE<10
+	// Check if getElementById returns elements by name
+	// The broken getElementById methods don't pick up programmatically-set names,
+	// so use a roundabout getElementsByName test
+	support.getById = assert( function( el ) {
+		docElem.appendChild( el ).id = expando;
+		return !document.getElementsByName || !document.getElementsByName( expando ).length;
+	} );
+
+	// ID filter and find
+	if ( support.getById ) {
+		Expr.filter[ "ID" ] = function( id ) {
+			var attrId = id.replace( runescape, funescape );
+			return function( elem ) {
+				return elem.getAttribute( "id" ) === attrId;
+			};
+		};
+		Expr.find[ "ID" ] = function( id, context ) {
+			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+				var elem = context.getElementById( id );
+				return elem ? [ elem ] : [];
+			}
+		};
+	} else {
+		Expr.filter[ "ID" ] =  function( id ) {
+			var attrId = id.replace( runescape, funescape );
+			return function( elem ) {
+				var node = typeof elem.getAttributeNode !== "undefined" &&
+					elem.getAttributeNode( "id" );
+				return node && node.value === attrId;
+			};
+		};
+
+		// Support: IE 6 - 7 only
+		// getElementById is not reliable as a find shortcut
+		Expr.find[ "ID" ] = function( id, context ) {
+			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+				var node, i, elems,
+					elem = context.getElementById( id );
+
+				if ( elem ) {
+
+					// Verify the id attribute
+					node = elem.getAttributeNode( "id" );
+					if ( node && node.value === id ) {
+						return [ elem ];
+					}
+
+					// Fall back on getElementsByName
+					elems = context.getElementsByName( id );
+					i = 0;
+					while ( ( elem = elems[ i++ ] ) ) {
+						node = elem.getAttributeNode( "id" );
+						if ( node && node.value === id ) {
+							return [ elem ];
+						}
+					}
+				}
+
+				return [];
+			}
+		};
+	}
+
+	// Tag
+	Expr.find[ "TAG" ] = support.getElementsByTagName ?
+		function( tag, context ) {
+			if ( typeof context.getElementsByTagName !== "undefined" ) {
+				return context.getElementsByTagName( tag );
+
+			// DocumentFragment nodes don't have gEBTN
+			} else if ( support.qsa ) {
+				return context.querySelectorAll( tag );
+			}
+		} :
+
+		function( tag, context ) {
+			var elem,
+				tmp = [],
+				i = 0,
+
+				// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
+				results = context.getElementsByTagName( tag );
+
+			// Filter out possible comments
+			if ( tag === "*" ) {
+				while ( ( elem = results[ i++ ] ) ) {
+					if ( elem.nodeType === 1 ) {
+						tmp.push( elem );
+					}
+				}
+
+				return tmp;
+			}
+			return results;
+		};
+
+	// Class
+	Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) {
+		if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
+			return context.getElementsByClassName( className );
+		}
+	};
+
+	/* QSA/matchesSelector
+	---------------------------------------------------------------------- */
+
+	// QSA and matchesSelector support
+
+	// matchesSelector(:active) reports false when true (IE9/Opera 11.5)
+	rbuggyMatches = [];
+
+	// qSa(:focus) reports false when true (Chrome 21)
+	// We allow this because of a bug in IE8/9 that throws an error
+	// whenever `document.activeElement` is accessed on an iframe
+	// So, we allow :focus to pass through QSA all the time to avoid the IE error
+	// See https://bugs.jquery.com/ticket/13378
+	rbuggyQSA = [];
+
+	if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) {
+
+		// Build QSA regex
+		// Regex strategy adopted from Diego Perini
+		assert( function( el ) {
+
+			var input;
+
+			// Select is set to empty string on purpose
+			// This is to test IE's treatment of not explicitly
+			// setting a boolean content attribute,
+			// since its presence should be enough
+			// https://bugs.jquery.com/ticket/12359
+			docElem.appendChild( el ).innerHTML = "" +
+				"";
+
+			// Support: IE8, Opera 11-12.16
+			// Nothing should be selected when empty strings follow ^= or $= or *=
+			// The test attribute must be unknown in Opera but "safe" for WinRT
+			// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
+			if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) {
+				rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
+			}
+
+			// Support: IE8
+			// Boolean attributes and "value" are not treated correctly
+			if ( !el.querySelectorAll( "[selected]" ).length ) {
+				rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
+			}
+
+			// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
+			if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
+				rbuggyQSA.push( "~=" );
+			}
+
+			// Support: IE 11+, Edge 15 - 18+
+			// IE 11/Edge don't find elements on a `[name='']` query in some cases.
+			// Adding a temporary attribute to the document before the selection works
+			// around the issue.
+			// Interestingly, IE 10 & older don't seem to have the issue.
+			input = document.createElement( "input" );
+			input.setAttribute( "name", "" );
+			el.appendChild( input );
+			if ( !el.querySelectorAll( "[name='']" ).length ) {
+				rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" +
+					whitespace + "*(?:''|\"\")" );
+			}
+
+			// Webkit/Opera - :checked should return selected option elements
+			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+			// IE8 throws error here and will not see later tests
+			if ( !el.querySelectorAll( ":checked" ).length ) {
+				rbuggyQSA.push( ":checked" );
+			}
+
+			// Support: Safari 8+, iOS 8+
+			// https://bugs.webkit.org/show_bug.cgi?id=136851
+			// In-page `selector#id sibling-combinator selector` fails
+			if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
+				rbuggyQSA.push( ".#.+[+~]" );
+			}
+
+			// Support: Firefox <=3.6 - 5 only
+			// Old Firefox doesn't throw on a badly-escaped identifier.
+			el.querySelectorAll( "\\\f" );
+			rbuggyQSA.push( "[\\r\\n\\f]" );
+		} );
+
+		assert( function( el ) {
+			el.innerHTML = "" +
+				"";
+
+			// Support: Windows 8 Native Apps
+			// The type and name attributes are restricted during .innerHTML assignment
+			var input = document.createElement( "input" );
+			input.setAttribute( "type", "hidden" );
+			el.appendChild( input ).setAttribute( "name", "D" );
+
+			// Support: IE8
+			// Enforce case-sensitivity of name attribute
+			if ( el.querySelectorAll( "[name=d]" ).length ) {
+				rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
+			}
+
+			// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
+			// IE8 throws error here and will not see later tests
+			if ( el.querySelectorAll( ":enabled" ).length !== 2 ) {
+				rbuggyQSA.push( ":enabled", ":disabled" );
+			}
+
+			// Support: IE9-11+
+			// IE's :disabled selector does not pick up the children of disabled fieldsets
+			docElem.appendChild( el ).disabled = true;
+			if ( el.querySelectorAll( ":disabled" ).length !== 2 ) {
+				rbuggyQSA.push( ":enabled", ":disabled" );
+			}
+
+			// Support: Opera 10 - 11 only
+			// Opera 10-11 does not throw on post-comma invalid pseudos
+			el.querySelectorAll( "*,:x" );
+			rbuggyQSA.push( ",.*:" );
+		} );
+	}
+
+	if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches ||
+		docElem.webkitMatchesSelector ||
+		docElem.mozMatchesSelector ||
+		docElem.oMatchesSelector ||
+		docElem.msMatchesSelector ) ) ) ) {
+
+		assert( function( el ) {
+
+			// Check to see if it's possible to do matchesSelector
+			// on a disconnected node (IE 9)
+			support.disconnectedMatch = matches.call( el, "*" );
+
+			// This should fail with an exception
+			// Gecko does not error, returns false instead
+			matches.call( el, "[s!='']:x" );
+			rbuggyMatches.push( "!=", pseudos );
+		} );
+	}
+
+	rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) );
+	rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) );
+
+	/* Contains
+	---------------------------------------------------------------------- */
+	hasCompare = rnative.test( docElem.compareDocumentPosition );
+
+	// Element contains another
+	// Purposefully self-exclusive
+	// As in, an element does not contain itself
+	contains = hasCompare || rnative.test( docElem.contains ) ?
+		function( a, b ) {
+			var adown = a.nodeType === 9 ? a.documentElement : a,
+				bup = b && b.parentNode;
+			return a === bup || !!( bup && bup.nodeType === 1 && (
+				adown.contains ?
+					adown.contains( bup ) :
+					a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
+			) );
+		} :
+		function( a, b ) {
+			if ( b ) {
+				while ( ( b = b.parentNode ) ) {
+					if ( b === a ) {
+						return true;
+					}
+				}
+			}
+			return false;
+		};
+
+	/* Sorting
+	---------------------------------------------------------------------- */
+
+	// Document order sorting
+	sortOrder = hasCompare ?
+	function( a, b ) {
+
+		// Flag for duplicate removal
+		if ( a === b ) {
+			hasDuplicate = true;
+			return 0;
+		}
+
+		// Sort on method existence if only one input has compareDocumentPosition
+		var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
+		if ( compare ) {
+			return compare;
+		}
+
+		// Calculate position if both inputs belong to the same document
+		// Support: IE 11+, Edge 17 - 18+
+		// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+		// two documents; shallow comparisons work.
+		// eslint-disable-next-line eqeqeq
+		compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ?
+			a.compareDocumentPosition( b ) :
+
+			// Otherwise we know they are disconnected
+			1;
+
+		// Disconnected nodes
+		if ( compare & 1 ||
+			( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) {
+
+			// Choose the first element that is related to our preferred document
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( a == document || a.ownerDocument == preferredDoc &&
+				contains( preferredDoc, a ) ) {
+				return -1;
+			}
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( b == document || b.ownerDocument == preferredDoc &&
+				contains( preferredDoc, b ) ) {
+				return 1;
+			}
+
+			// Maintain original order
+			return sortInput ?
+				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+				0;
+		}
+
+		return compare & 4 ? -1 : 1;
+	} :
+	function( a, b ) {
+
+		// Exit early if the nodes are identical
+		if ( a === b ) {
+			hasDuplicate = true;
+			return 0;
+		}
+
+		var cur,
+			i = 0,
+			aup = a.parentNode,
+			bup = b.parentNode,
+			ap = [ a ],
+			bp = [ b ];
+
+		// Parentless nodes are either documents or disconnected
+		if ( !aup || !bup ) {
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			return a == document ? -1 :
+				b == document ? 1 :
+				/* eslint-enable eqeqeq */
+				aup ? -1 :
+				bup ? 1 :
+				sortInput ?
+				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+				0;
+
+		// If the nodes are siblings, we can do a quick check
+		} else if ( aup === bup ) {
+			return siblingCheck( a, b );
+		}
+
+		// Otherwise we need full lists of their ancestors for comparison
+		cur = a;
+		while ( ( cur = cur.parentNode ) ) {
+			ap.unshift( cur );
+		}
+		cur = b;
+		while ( ( cur = cur.parentNode ) ) {
+			bp.unshift( cur );
+		}
+
+		// Walk down the tree looking for a discrepancy
+		while ( ap[ i ] === bp[ i ] ) {
+			i++;
+		}
+
+		return i ?
+
+			// Do a sibling check if the nodes have a common ancestor
+			siblingCheck( ap[ i ], bp[ i ] ) :
+
+			// Otherwise nodes in our document sort first
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			ap[ i ] == preferredDoc ? -1 :
+			bp[ i ] == preferredDoc ? 1 :
+			/* eslint-enable eqeqeq */
+			0;
+	};
+
+	return document;
+};
+
+Sizzle.matches = function( expr, elements ) {
+	return Sizzle( expr, null, null, elements );
+};
+
+Sizzle.matchesSelector = function( elem, expr ) {
+	setDocument( elem );
+
+	if ( support.matchesSelector && documentIsHTML &&
+		!nonnativeSelectorCache[ expr + " " ] &&
+		( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
+		( !rbuggyQSA     || !rbuggyQSA.test( expr ) ) ) {
+
+		try {
+			var ret = matches.call( elem, expr );
+
+			// IE 9's matchesSelector returns false on disconnected nodes
+			if ( ret || support.disconnectedMatch ||
+
+				// As well, disconnected nodes are said to be in a document
+				// fragment in IE 9
+				elem.document && elem.document.nodeType !== 11 ) {
+				return ret;
+			}
+		} catch ( e ) {
+			nonnativeSelectorCache( expr, true );
+		}
+	}
+
+	return Sizzle( expr, document, null, [ elem ] ).length > 0;
+};
+
+Sizzle.contains = function( context, elem ) {
+
+	// Set document vars if needed
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( context.ownerDocument || context ) != document ) {
+		setDocument( context );
+	}
+	return contains( context, elem );
+};
+
+Sizzle.attr = function( elem, name ) {
+
+	// Set document vars if needed
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( elem.ownerDocument || elem ) != document ) {
+		setDocument( elem );
+	}
+
+	var fn = Expr.attrHandle[ name.toLowerCase() ],
+
+		// Don't get fooled by Object.prototype properties (jQuery #13807)
+		val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
+			fn( elem, name, !documentIsHTML ) :
+			undefined;
+
+	return val !== undefined ?
+		val :
+		support.attributes || !documentIsHTML ?
+			elem.getAttribute( name ) :
+			( val = elem.getAttributeNode( name ) ) && val.specified ?
+				val.value :
+				null;
+};
+
+Sizzle.escape = function( sel ) {
+	return ( sel + "" ).replace( rcssescape, fcssescape );
+};
+
+Sizzle.error = function( msg ) {
+	throw new Error( "Syntax error, unrecognized expression: " + msg );
+};
+
+/**
+ * Document sorting and removing duplicates
+ * @param {ArrayLike} results
+ */
+Sizzle.uniqueSort = function( results ) {
+	var elem,
+		duplicates = [],
+		j = 0,
+		i = 0;
+
+	// Unless we *know* we can detect duplicates, assume their presence
+	hasDuplicate = !support.detectDuplicates;
+	sortInput = !support.sortStable && results.slice( 0 );
+	results.sort( sortOrder );
+
+	if ( hasDuplicate ) {
+		while ( ( elem = results[ i++ ] ) ) {
+			if ( elem === results[ i ] ) {
+				j = duplicates.push( i );
+			}
+		}
+		while ( j-- ) {
+			results.splice( duplicates[ j ], 1 );
+		}
+	}
+
+	// Clear input after sorting to release objects
+	// See https://github.com/jquery/sizzle/pull/225
+	sortInput = null;
+
+	return results;
+};
+
+/**
+ * Utility function for retrieving the text value of an array of DOM nodes
+ * @param {Array|Element} elem
+ */
+getText = Sizzle.getText = function( elem ) {
+	var node,
+		ret = "",
+		i = 0,
+		nodeType = elem.nodeType;
+
+	if ( !nodeType ) {
+
+		// If no nodeType, this is expected to be an array
+		while ( ( node = elem[ i++ ] ) ) {
+
+			// Do not traverse comment nodes
+			ret += getText( node );
+		}
+	} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
+
+		// Use textContent for elements
+		// innerText usage removed for consistency of new lines (jQuery #11153)
+		if ( typeof elem.textContent === "string" ) {
+			return elem.textContent;
+		} else {
+
+			// Traverse its children
+			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+				ret += getText( elem );
+			}
+		}
+	} else if ( nodeType === 3 || nodeType === 4 ) {
+		return elem.nodeValue;
+	}
+
+	// Do not include comment or processing instruction nodes
+
+	return ret;
+};
+
+Expr = Sizzle.selectors = {
+
+	// Can be adjusted by the user
+	cacheLength: 50,
+
+	createPseudo: markFunction,
+
+	match: matchExpr,
+
+	attrHandle: {},
+
+	find: {},
+
+	relative: {
+		">": { dir: "parentNode", first: true },
+		" ": { dir: "parentNode" },
+		"+": { dir: "previousSibling", first: true },
+		"~": { dir: "previousSibling" }
+	},
+
+	preFilter: {
+		"ATTR": function( match ) {
+			match[ 1 ] = match[ 1 ].replace( runescape, funescape );
+
+			// Move the given value to match[3] whether quoted or unquoted
+			match[ 3 ] = ( match[ 3 ] || match[ 4 ] ||
+				match[ 5 ] || "" ).replace( runescape, funescape );
+
+			if ( match[ 2 ] === "~=" ) {
+				match[ 3 ] = " " + match[ 3 ] + " ";
+			}
+
+			return match.slice( 0, 4 );
+		},
+
+		"CHILD": function( match ) {
+
+			/* matches from matchExpr["CHILD"]
+				1 type (only|nth|...)
+				2 what (child|of-type)
+				3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
+				4 xn-component of xn+y argument ([+-]?\d*n|)
+				5 sign of xn-component
+				6 x of xn-component
+				7 sign of y-component
+				8 y of y-component
+			*/
+			match[ 1 ] = match[ 1 ].toLowerCase();
+
+			if ( match[ 1 ].slice( 0, 3 ) === "nth" ) {
+
+				// nth-* requires argument
+				if ( !match[ 3 ] ) {
+					Sizzle.error( match[ 0 ] );
+				}
+
+				// numeric x and y parameters for Expr.filter.CHILD
+				// remember that false/true cast respectively to 0/1
+				match[ 4 ] = +( match[ 4 ] ?
+					match[ 5 ] + ( match[ 6 ] || 1 ) :
+					2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) );
+				match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" );
+
+				// other types prohibit arguments
+			} else if ( match[ 3 ] ) {
+				Sizzle.error( match[ 0 ] );
+			}
+
+			return match;
+		},
+
+		"PSEUDO": function( match ) {
+			var excess,
+				unquoted = !match[ 6 ] && match[ 2 ];
+
+			if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) {
+				return null;
+			}
+
+			// Accept quoted arguments as-is
+			if ( match[ 3 ] ) {
+				match[ 2 ] = match[ 4 ] || match[ 5 ] || "";
+
+			// Strip excess characters from unquoted arguments
+			} else if ( unquoted && rpseudo.test( unquoted ) &&
+
+				// Get excess from tokenize (recursively)
+				( excess = tokenize( unquoted, true ) ) &&
+
+				// advance to the next closing parenthesis
+				( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) {
+
+				// excess is a negative index
+				match[ 0 ] = match[ 0 ].slice( 0, excess );
+				match[ 2 ] = unquoted.slice( 0, excess );
+			}
+
+			// Return only captures needed by the pseudo filter method (type and argument)
+			return match.slice( 0, 3 );
+		}
+	},
+
+	filter: {
+
+		"TAG": function( nodeNameSelector ) {
+			var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
+			return nodeNameSelector === "*" ?
+				function() {
+					return true;
+				} :
+				function( elem ) {
+					return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
+				};
+		},
+
+		"CLASS": function( className ) {
+			var pattern = classCache[ className + " " ];
+
+			return pattern ||
+				( pattern = new RegExp( "(^|" + whitespace +
+					")" + className + "(" + whitespace + "|$)" ) ) && classCache(
+						className, function( elem ) {
+							return pattern.test(
+								typeof elem.className === "string" && elem.className ||
+								typeof elem.getAttribute !== "undefined" &&
+									elem.getAttribute( "class" ) ||
+								""
+							);
+				} );
+		},
+
+		"ATTR": function( name, operator, check ) {
+			return function( elem ) {
+				var result = Sizzle.attr( elem, name );
+
+				if ( result == null ) {
+					return operator === "!=";
+				}
+				if ( !operator ) {
+					return true;
+				}
+
+				result += "";
+
+				/* eslint-disable max-len */
+
+				return operator === "=" ? result === check :
+					operator === "!=" ? result !== check :
+					operator === "^=" ? check && result.indexOf( check ) === 0 :
+					operator === "*=" ? check && result.indexOf( check ) > -1 :
+					operator === "$=" ? check && result.slice( -check.length ) === check :
+					operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
+					operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
+					false;
+				/* eslint-enable max-len */
+
+			};
+		},
+
+		"CHILD": function( type, what, _argument, first, last ) {
+			var simple = type.slice( 0, 3 ) !== "nth",
+				forward = type.slice( -4 ) !== "last",
+				ofType = what === "of-type";
+
+			return first === 1 && last === 0 ?
+
+				// Shortcut for :nth-*(n)
+				function( elem ) {
+					return !!elem.parentNode;
+				} :
+
+				function( elem, _context, xml ) {
+					var cache, uniqueCache, outerCache, node, nodeIndex, start,
+						dir = simple !== forward ? "nextSibling" : "previousSibling",
+						parent = elem.parentNode,
+						name = ofType && elem.nodeName.toLowerCase(),
+						useCache = !xml && !ofType,
+						diff = false;
+
+					if ( parent ) {
+
+						// :(first|last|only)-(child|of-type)
+						if ( simple ) {
+							while ( dir ) {
+								node = elem;
+								while ( ( node = node[ dir ] ) ) {
+									if ( ofType ?
+										node.nodeName.toLowerCase() === name :
+										node.nodeType === 1 ) {
+
+										return false;
+									}
+								}
+
+								// Reverse direction for :only-* (if we haven't yet done so)
+								start = dir = type === "only" && !start && "nextSibling";
+							}
+							return true;
+						}
+
+						start = [ forward ? parent.firstChild : parent.lastChild ];
+
+						// non-xml :nth-child(...) stores cache data on `parent`
+						if ( forward && useCache ) {
+
+							// Seek `elem` from a previously-cached index
+
+							// ...in a gzip-friendly way
+							node = parent;
+							outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+							// Support: IE <9 only
+							// Defend against cloned attroperties (jQuery gh-1709)
+							uniqueCache = outerCache[ node.uniqueID ] ||
+								( outerCache[ node.uniqueID ] = {} );
+
+							cache = uniqueCache[ type ] || [];
+							nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+							diff = nodeIndex && cache[ 2 ];
+							node = nodeIndex && parent.childNodes[ nodeIndex ];
+
+							while ( ( node = ++nodeIndex && node && node[ dir ] ||
+
+								// Fallback to seeking `elem` from the start
+								( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+								// When found, cache indexes on `parent` and break
+								if ( node.nodeType === 1 && ++diff && node === elem ) {
+									uniqueCache[ type ] = [ dirruns, nodeIndex, diff ];
+									break;
+								}
+							}
+
+						} else {
+
+							// Use previously-cached element index if available
+							if ( useCache ) {
+
+								// ...in a gzip-friendly way
+								node = elem;
+								outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+								// Support: IE <9 only
+								// Defend against cloned attroperties (jQuery gh-1709)
+								uniqueCache = outerCache[ node.uniqueID ] ||
+									( outerCache[ node.uniqueID ] = {} );
+
+								cache = uniqueCache[ type ] || [];
+								nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+								diff = nodeIndex;
+							}
+
+							// xml :nth-child(...)
+							// or :nth-last-child(...) or :nth(-last)?-of-type(...)
+							if ( diff === false ) {
+
+								// Use the same loop as above to seek `elem` from the start
+								while ( ( node = ++nodeIndex && node && node[ dir ] ||
+									( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+									if ( ( ofType ?
+										node.nodeName.toLowerCase() === name :
+										node.nodeType === 1 ) &&
+										++diff ) {
+
+										// Cache the index of each encountered element
+										if ( useCache ) {
+											outerCache = node[ expando ] ||
+												( node[ expando ] = {} );
+
+											// Support: IE <9 only
+											// Defend against cloned attroperties (jQuery gh-1709)
+											uniqueCache = outerCache[ node.uniqueID ] ||
+												( outerCache[ node.uniqueID ] = {} );
+
+											uniqueCache[ type ] = [ dirruns, diff ];
+										}
+
+										if ( node === elem ) {
+											break;
+										}
+									}
+								}
+							}
+						}
+
+						// Incorporate the offset, then check against cycle size
+						diff -= last;
+						return diff === first || ( diff % first === 0 && diff / first >= 0 );
+					}
+				};
+		},
+
+		"PSEUDO": function( pseudo, argument ) {
+
+			// pseudo-class names are case-insensitive
+			// http://www.w3.org/TR/selectors/#pseudo-classes
+			// Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
+			// Remember that setFilters inherits from pseudos
+			var args,
+				fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] ||
+					Sizzle.error( "unsupported pseudo: " + pseudo );
+
+			// The user may use createPseudo to indicate that
+			// arguments are needed to create the filter function
+			// just as Sizzle does
+			if ( fn[ expando ] ) {
+				return fn( argument );
+			}
+
+			// But maintain support for old signatures
+			if ( fn.length > 1 ) {
+				args = [ pseudo, pseudo, "", argument ];
+				return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
+					markFunction( function( seed, matches ) {
+						var idx,
+							matched = fn( seed, argument ),
+							i = matched.length;
+						while ( i-- ) {
+							idx = indexOf( seed, matched[ i ] );
+							seed[ idx ] = !( matches[ idx ] = matched[ i ] );
+						}
+					} ) :
+					function( elem ) {
+						return fn( elem, 0, args );
+					};
+			}
+
+			return fn;
+		}
+	},
+
+	pseudos: {
+
+		// Potentially complex pseudos
+		"not": markFunction( function( selector ) {
+
+			// Trim the selector passed to compile
+			// to avoid treating leading and trailing
+			// spaces as combinators
+			var input = [],
+				results = [],
+				matcher = compile( selector.replace( rtrim, "$1" ) );
+
+			return matcher[ expando ] ?
+				markFunction( function( seed, matches, _context, xml ) {
+					var elem,
+						unmatched = matcher( seed, null, xml, [] ),
+						i = seed.length;
+
+					// Match elements unmatched by `matcher`
+					while ( i-- ) {
+						if ( ( elem = unmatched[ i ] ) ) {
+							seed[ i ] = !( matches[ i ] = elem );
+						}
+					}
+				} ) :
+				function( elem, _context, xml ) {
+					input[ 0 ] = elem;
+					matcher( input, null, xml, results );
+
+					// Don't keep the element (issue #299)
+					input[ 0 ] = null;
+					return !results.pop();
+				};
+		} ),
+
+		"has": markFunction( function( selector ) {
+			return function( elem ) {
+				return Sizzle( selector, elem ).length > 0;
+			};
+		} ),
+
+		"contains": markFunction( function( text ) {
+			text = text.replace( runescape, funescape );
+			return function( elem ) {
+				return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1;
+			};
+		} ),
+
+		// "Whether an element is represented by a :lang() selector
+		// is based solely on the element's language value
+		// being equal to the identifier C,
+		// or beginning with the identifier C immediately followed by "-".
+		// The matching of C against the element's language value is performed case-insensitively.
+		// The identifier C does not have to be a valid language name."
+		// http://www.w3.org/TR/selectors/#lang-pseudo
+		"lang": markFunction( function( lang ) {
+
+			// lang value must be a valid identifier
+			if ( !ridentifier.test( lang || "" ) ) {
+				Sizzle.error( "unsupported lang: " + lang );
+			}
+			lang = lang.replace( runescape, funescape ).toLowerCase();
+			return function( elem ) {
+				var elemLang;
+				do {
+					if ( ( elemLang = documentIsHTML ?
+						elem.lang :
+						elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) {
+
+						elemLang = elemLang.toLowerCase();
+						return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
+					}
+				} while ( ( elem = elem.parentNode ) && elem.nodeType === 1 );
+				return false;
+			};
+		} ),
+
+		// Miscellaneous
+		"target": function( elem ) {
+			var hash = window.location && window.location.hash;
+			return hash && hash.slice( 1 ) === elem.id;
+		},
+
+		"root": function( elem ) {
+			return elem === docElem;
+		},
+
+		"focus": function( elem ) {
+			return elem === document.activeElement &&
+				( !document.hasFocus || document.hasFocus() ) &&
+				!!( elem.type || elem.href || ~elem.tabIndex );
+		},
+
+		// Boolean properties
+		"enabled": createDisabledPseudo( false ),
+		"disabled": createDisabledPseudo( true ),
+
+		"checked": function( elem ) {
+
+			// In CSS3, :checked should return both checked and selected elements
+			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+			var nodeName = elem.nodeName.toLowerCase();
+			return ( nodeName === "input" && !!elem.checked ) ||
+				( nodeName === "option" && !!elem.selected );
+		},
+
+		"selected": function( elem ) {
+
+			// Accessing this property makes selected-by-default
+			// options in Safari work properly
+			if ( elem.parentNode ) {
+				// eslint-disable-next-line no-unused-expressions
+				elem.parentNode.selectedIndex;
+			}
+
+			return elem.selected === true;
+		},
+
+		// Contents
+		"empty": function( elem ) {
+
+			// http://www.w3.org/TR/selectors/#empty-pseudo
+			// :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
+			//   but not by others (comment: 8; processing instruction: 7; etc.)
+			// nodeType < 6 works because attributes (2) do not appear as children
+			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+				if ( elem.nodeType < 6 ) {
+					return false;
+				}
+			}
+			return true;
+		},
+
+		"parent": function( elem ) {
+			return !Expr.pseudos[ "empty" ]( elem );
+		},
+
+		// Element/input types
+		"header": function( elem ) {
+			return rheader.test( elem.nodeName );
+		},
+
+		"input": function( elem ) {
+			return rinputs.test( elem.nodeName );
+		},
+
+		"button": function( elem ) {
+			var name = elem.nodeName.toLowerCase();
+			return name === "input" && elem.type === "button" || name === "button";
+		},
+
+		"text": function( elem ) {
+			var attr;
+			return elem.nodeName.toLowerCase() === "input" &&
+				elem.type === "text" &&
+
+				// Support: IE<8
+				// New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
+				( ( attr = elem.getAttribute( "type" ) ) == null ||
+					attr.toLowerCase() === "text" );
+		},
+
+		// Position-in-collection
+		"first": createPositionalPseudo( function() {
+			return [ 0 ];
+		} ),
+
+		"last": createPositionalPseudo( function( _matchIndexes, length ) {
+			return [ length - 1 ];
+		} ),
+
+		"eq": createPositionalPseudo( function( _matchIndexes, length, argument ) {
+			return [ argument < 0 ? argument + length : argument ];
+		} ),
+
+		"even": createPositionalPseudo( function( matchIndexes, length ) {
+			var i = 0;
+			for ( ; i < length; i += 2 ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"odd": createPositionalPseudo( function( matchIndexes, length ) {
+			var i = 1;
+			for ( ; i < length; i += 2 ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"lt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+			var i = argument < 0 ?
+				argument + length :
+				argument > length ?
+					length :
+					argument;
+			for ( ; --i >= 0; ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"gt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+			var i = argument < 0 ? argument + length : argument;
+			for ( ; ++i < length; ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} )
+	}
+};
+
+Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ];
+
+// Add button/input type pseudos
+for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
+	Expr.pseudos[ i ] = createInputPseudo( i );
+}
+for ( i in { submit: true, reset: true } ) {
+	Expr.pseudos[ i ] = createButtonPseudo( i );
+}
+
+// Easy API for creating new setFilters
+function setFilters() {}
+setFilters.prototype = Expr.filters = Expr.pseudos;
+Expr.setFilters = new setFilters();
+
+tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
+	var matched, match, tokens, type,
+		soFar, groups, preFilters,
+		cached = tokenCache[ selector + " " ];
+
+	if ( cached ) {
+		return parseOnly ? 0 : cached.slice( 0 );
+	}
+
+	soFar = selector;
+	groups = [];
+	preFilters = Expr.preFilter;
+
+	while ( soFar ) {
+
+		// Comma and first run
+		if ( !matched || ( match = rcomma.exec( soFar ) ) ) {
+			if ( match ) {
+
+				// Don't consume trailing commas as valid
+				soFar = soFar.slice( match[ 0 ].length ) || soFar;
+			}
+			groups.push( ( tokens = [] ) );
+		}
+
+		matched = false;
+
+		// Combinators
+		if ( ( match = rcombinators.exec( soFar ) ) ) {
+			matched = match.shift();
+			tokens.push( {
+				value: matched,
+
+				// Cast descendant combinators to space
+				type: match[ 0 ].replace( rtrim, " " )
+			} );
+			soFar = soFar.slice( matched.length );
+		}
+
+		// Filters
+		for ( type in Expr.filter ) {
+			if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] ||
+				( match = preFilters[ type ]( match ) ) ) ) {
+				matched = match.shift();
+				tokens.push( {
+					value: matched,
+					type: type,
+					matches: match
+				} );
+				soFar = soFar.slice( matched.length );
+			}
+		}
+
+		if ( !matched ) {
+			break;
+		}
+	}
+
+	// Return the length of the invalid excess
+	// if we're just parsing
+	// Otherwise, throw an error or return tokens
+	return parseOnly ?
+		soFar.length :
+		soFar ?
+			Sizzle.error( selector ) :
+
+			// Cache the tokens
+			tokenCache( selector, groups ).slice( 0 );
+};
+
+function toSelector( tokens ) {
+	var i = 0,
+		len = tokens.length,
+		selector = "";
+	for ( ; i < len; i++ ) {
+		selector += tokens[ i ].value;
+	}
+	return selector;
+}
+
+function addCombinator( matcher, combinator, base ) {
+	var dir = combinator.dir,
+		skip = combinator.next,
+		key = skip || dir,
+		checkNonElements = base && key === "parentNode",
+		doneName = done++;
+
+	return combinator.first ?
+
+		// Check against closest ancestor/preceding element
+		function( elem, context, xml ) {
+			while ( ( elem = elem[ dir ] ) ) {
+				if ( elem.nodeType === 1 || checkNonElements ) {
+					return matcher( elem, context, xml );
+				}
+			}
+			return false;
+		} :
+
+		// Check against all ancestor/preceding elements
+		function( elem, context, xml ) {
+			var oldCache, uniqueCache, outerCache,
+				newCache = [ dirruns, doneName ];
+
+			// We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
+			if ( xml ) {
+				while ( ( elem = elem[ dir ] ) ) {
+					if ( elem.nodeType === 1 || checkNonElements ) {
+						if ( matcher( elem, context, xml ) ) {
+							return true;
+						}
+					}
+				}
+			} else {
+				while ( ( elem = elem[ dir ] ) ) {
+					if ( elem.nodeType === 1 || checkNonElements ) {
+						outerCache = elem[ expando ] || ( elem[ expando ] = {} );
+
+						// Support: IE <9 only
+						// Defend against cloned attroperties (jQuery gh-1709)
+						uniqueCache = outerCache[ elem.uniqueID ] ||
+							( outerCache[ elem.uniqueID ] = {} );
+
+						if ( skip && skip === elem.nodeName.toLowerCase() ) {
+							elem = elem[ dir ] || elem;
+						} else if ( ( oldCache = uniqueCache[ key ] ) &&
+							oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
+
+							// Assign to newCache so results back-propagate to previous elements
+							return ( newCache[ 2 ] = oldCache[ 2 ] );
+						} else {
+
+							// Reuse newcache so results back-propagate to previous elements
+							uniqueCache[ key ] = newCache;
+
+							// A match means we're done; a fail means we have to keep checking
+							if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) {
+								return true;
+							}
+						}
+					}
+				}
+			}
+			return false;
+		};
+}
+
+function elementMatcher( matchers ) {
+	return matchers.length > 1 ?
+		function( elem, context, xml ) {
+			var i = matchers.length;
+			while ( i-- ) {
+				if ( !matchers[ i ]( elem, context, xml ) ) {
+					return false;
+				}
+			}
+			return true;
+		} :
+		matchers[ 0 ];
+}
+
+function multipleContexts( selector, contexts, results ) {
+	var i = 0,
+		len = contexts.length;
+	for ( ; i < len; i++ ) {
+		Sizzle( selector, contexts[ i ], results );
+	}
+	return results;
+}
+
+function condense( unmatched, map, filter, context, xml ) {
+	var elem,
+		newUnmatched = [],
+		i = 0,
+		len = unmatched.length,
+		mapped = map != null;
+
+	for ( ; i < len; i++ ) {
+		if ( ( elem = unmatched[ i ] ) ) {
+			if ( !filter || filter( elem, context, xml ) ) {
+				newUnmatched.push( elem );
+				if ( mapped ) {
+					map.push( i );
+				}
+			}
+		}
+	}
+
+	return newUnmatched;
+}
+
+function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) {
+	if ( postFilter && !postFilter[ expando ] ) {
+		postFilter = setMatcher( postFilter );
+	}
+	if ( postFinder && !postFinder[ expando ] ) {
+		postFinder = setMatcher( postFinder, postSelector );
+	}
+	return markFunction( function( seed, results, context, xml ) {
+		var temp, i, elem,
+			preMap = [],
+			postMap = [],
+			preexisting = results.length,
+
+			// Get initial elements from seed or context
+			elems = seed || multipleContexts(
+				selector || "*",
+				context.nodeType ? [ context ] : context,
+				[]
+			),
+
+			// Prefilter to get matcher input, preserving a map for seed-results synchronization
+			matcherIn = preFilter && ( seed || !selector ) ?
+				condense( elems, preMap, preFilter, context, xml ) :
+				elems,
+
+			matcherOut = matcher ?
+
+				// If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
+				postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
+
+					// ...intermediate processing is necessary
+					[] :
+
+					// ...otherwise use results directly
+					results :
+				matcherIn;
+
+		// Find primary matches
+		if ( matcher ) {
+			matcher( matcherIn, matcherOut, context, xml );
+		}
+
+		// Apply postFilter
+		if ( postFilter ) {
+			temp = condense( matcherOut, postMap );
+			postFilter( temp, [], context, xml );
+
+			// Un-match failing elements by moving them back to matcherIn
+			i = temp.length;
+			while ( i-- ) {
+				if ( ( elem = temp[ i ] ) ) {
+					matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem );
+				}
+			}
+		}
+
+		if ( seed ) {
+			if ( postFinder || preFilter ) {
+				if ( postFinder ) {
+
+					// Get the final matcherOut by condensing this intermediate into postFinder contexts
+					temp = [];
+					i = matcherOut.length;
+					while ( i-- ) {
+						if ( ( elem = matcherOut[ i ] ) ) {
+
+							// Restore matcherIn since elem is not yet a final match
+							temp.push( ( matcherIn[ i ] = elem ) );
+						}
+					}
+					postFinder( null, ( matcherOut = [] ), temp, xml );
+				}
+
+				// Move matched elements from seed to results to keep them synchronized
+				i = matcherOut.length;
+				while ( i-- ) {
+					if ( ( elem = matcherOut[ i ] ) &&
+						( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) {
+
+						seed[ temp ] = !( results[ temp ] = elem );
+					}
+				}
+			}
+
+		// Add elements to results, through postFinder if defined
+		} else {
+			matcherOut = condense(
+				matcherOut === results ?
+					matcherOut.splice( preexisting, matcherOut.length ) :
+					matcherOut
+			);
+			if ( postFinder ) {
+				postFinder( null, results, matcherOut, xml );
+			} else {
+				push.apply( results, matcherOut );
+			}
+		}
+	} );
+}
+
+function matcherFromTokens( tokens ) {
+	var checkContext, matcher, j,
+		len = tokens.length,
+		leadingRelative = Expr.relative[ tokens[ 0 ].type ],
+		implicitRelative = leadingRelative || Expr.relative[ " " ],
+		i = leadingRelative ? 1 : 0,
+
+		// The foundational matcher ensures that elements are reachable from top-level context(s)
+		matchContext = addCombinator( function( elem ) {
+			return elem === checkContext;
+		}, implicitRelative, true ),
+		matchAnyContext = addCombinator( function( elem ) {
+			return indexOf( checkContext, elem ) > -1;
+		}, implicitRelative, true ),
+		matchers = [ function( elem, context, xml ) {
+			var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
+				( checkContext = context ).nodeType ?
+					matchContext( elem, context, xml ) :
+					matchAnyContext( elem, context, xml ) );
+
+			// Avoid hanging onto element (issue #299)
+			checkContext = null;
+			return ret;
+		} ];
+
+	for ( ; i < len; i++ ) {
+		if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) {
+			matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ];
+		} else {
+			matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches );
+
+			// Return special upon seeing a positional matcher
+			if ( matcher[ expando ] ) {
+
+				// Find the next relative operator (if any) for proper handling
+				j = ++i;
+				for ( ; j < len; j++ ) {
+					if ( Expr.relative[ tokens[ j ].type ] ) {
+						break;
+					}
+				}
+				return setMatcher(
+					i > 1 && elementMatcher( matchers ),
+					i > 1 && toSelector(
+
+					// If the preceding token was a descendant combinator, insert an implicit any-element `*`
+					tokens
+						.slice( 0, i - 1 )
+						.concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } )
+					).replace( rtrim, "$1" ),
+					matcher,
+					i < j && matcherFromTokens( tokens.slice( i, j ) ),
+					j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ),
+					j < len && toSelector( tokens )
+				);
+			}
+			matchers.push( matcher );
+		}
+	}
+
+	return elementMatcher( matchers );
+}
+
+function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
+	var bySet = setMatchers.length > 0,
+		byElement = elementMatchers.length > 0,
+		superMatcher = function( seed, context, xml, results, outermost ) {
+			var elem, j, matcher,
+				matchedCount = 0,
+				i = "0",
+				unmatched = seed && [],
+				setMatched = [],
+				contextBackup = outermostContext,
+
+				// We must always have either seed elements or outermost context
+				elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ),
+
+				// Use integer dirruns iff this is the outermost matcher
+				dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ),
+				len = elems.length;
+
+			if ( outermost ) {
+
+				// Support: IE 11+, Edge 17 - 18+
+				// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+				// two documents; shallow comparisons work.
+				// eslint-disable-next-line eqeqeq
+				outermostContext = context == document || context || outermost;
+			}
+
+			// Add elements passing elementMatchers directly to results
+			// Support: IE<9, Safari
+			// Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id
+			for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) {
+				if ( byElement && elem ) {
+					j = 0;
+
+					// Support: IE 11+, Edge 17 - 18+
+					// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+					// two documents; shallow comparisons work.
+					// eslint-disable-next-line eqeqeq
+					if ( !context && elem.ownerDocument != document ) {
+						setDocument( elem );
+						xml = !documentIsHTML;
+					}
+					while ( ( matcher = elementMatchers[ j++ ] ) ) {
+						if ( matcher( elem, context || document, xml ) ) {
+							results.push( elem );
+							break;
+						}
+					}
+					if ( outermost ) {
+						dirruns = dirrunsUnique;
+					}
+				}
+
+				// Track unmatched elements for set filters
+				if ( bySet ) {
+
+					// They will have gone through all possible matchers
+					if ( ( elem = !matcher && elem ) ) {
+						matchedCount--;
+					}
+
+					// Lengthen the array for every element, matched or not
+					if ( seed ) {
+						unmatched.push( elem );
+					}
+				}
+			}
+
+			// `i` is now the count of elements visited above, and adding it to `matchedCount`
+			// makes the latter nonnegative.
+			matchedCount += i;
+
+			// Apply set filters to unmatched elements
+			// NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount`
+			// equals `i`), unless we didn't visit _any_ elements in the above loop because we have
+			// no element matchers and no seed.
+			// Incrementing an initially-string "0" `i` allows `i` to remain a string only in that
+			// case, which will result in a "00" `matchedCount` that differs from `i` but is also
+			// numerically zero.
+			if ( bySet && i !== matchedCount ) {
+				j = 0;
+				while ( ( matcher = setMatchers[ j++ ] ) ) {
+					matcher( unmatched, setMatched, context, xml );
+				}
+
+				if ( seed ) {
+
+					// Reintegrate element matches to eliminate the need for sorting
+					if ( matchedCount > 0 ) {
+						while ( i-- ) {
+							if ( !( unmatched[ i ] || setMatched[ i ] ) ) {
+								setMatched[ i ] = pop.call( results );
+							}
+						}
+					}
+
+					// Discard index placeholder values to get only actual matches
+					setMatched = condense( setMatched );
+				}
+
+				// Add matches to results
+				push.apply( results, setMatched );
+
+				// Seedless set matches succeeding multiple successful matchers stipulate sorting
+				if ( outermost && !seed && setMatched.length > 0 &&
+					( matchedCount + setMatchers.length ) > 1 ) {
+
+					Sizzle.uniqueSort( results );
+				}
+			}
+
+			// Override manipulation of globals by nested matchers
+			if ( outermost ) {
+				dirruns = dirrunsUnique;
+				outermostContext = contextBackup;
+			}
+
+			return unmatched;
+		};
+
+	return bySet ?
+		markFunction( superMatcher ) :
+		superMatcher;
+}
+
+compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
+	var i,
+		setMatchers = [],
+		elementMatchers = [],
+		cached = compilerCache[ selector + " " ];
+
+	if ( !cached ) {
+
+		// Generate a function of recursive functions that can be used to check each element
+		if ( !match ) {
+			match = tokenize( selector );
+		}
+		i = match.length;
+		while ( i-- ) {
+			cached = matcherFromTokens( match[ i ] );
+			if ( cached[ expando ] ) {
+				setMatchers.push( cached );
+			} else {
+				elementMatchers.push( cached );
+			}
+		}
+
+		// Cache the compiled function
+		cached = compilerCache(
+			selector,
+			matcherFromGroupMatchers( elementMatchers, setMatchers )
+		);
+
+		// Save selector and tokenization
+		cached.selector = selector;
+	}
+	return cached;
+};
+
+/**
+ * A low-level selection function that works with Sizzle's compiled
+ *  selector functions
+ * @param {String|Function} selector A selector or a pre-compiled
+ *  selector function built with Sizzle.compile
+ * @param {Element} context
+ * @param {Array} [results]
+ * @param {Array} [seed] A set of elements to match against
+ */
+select = Sizzle.select = function( selector, context, results, seed ) {
+	var i, tokens, token, type, find,
+		compiled = typeof selector === "function" && selector,
+		match = !seed && tokenize( ( selector = compiled.selector || selector ) );
+
+	results = results || [];
+
+	// Try to minimize operations if there is only one selector in the list and no seed
+	// (the latter of which guarantees us context)
+	if ( match.length === 1 ) {
+
+		// Reduce context if the leading compound selector is an ID
+		tokens = match[ 0 ] = match[ 0 ].slice( 0 );
+		if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" &&
+			context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) {
+
+			context = ( Expr.find[ "ID" ]( token.matches[ 0 ]
+				.replace( runescape, funescape ), context ) || [] )[ 0 ];
+			if ( !context ) {
+				return results;
+
+			// Precompiled matchers will still verify ancestry, so step up a level
+			} else if ( compiled ) {
+				context = context.parentNode;
+			}
+
+			selector = selector.slice( tokens.shift().value.length );
+		}
+
+		// Fetch a seed set for right-to-left matching
+		i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length;
+		while ( i-- ) {
+			token = tokens[ i ];
+
+			// Abort if we hit a combinator
+			if ( Expr.relative[ ( type = token.type ) ] ) {
+				break;
+			}
+			if ( ( find = Expr.find[ type ] ) ) {
+
+				// Search, expanding context for leading sibling combinators
+				if ( ( seed = find(
+					token.matches[ 0 ].replace( runescape, funescape ),
+					rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) ||
+						context
+				) ) ) {
+
+					// If seed is empty or no tokens remain, we can return early
+					tokens.splice( i, 1 );
+					selector = seed.length && toSelector( tokens );
+					if ( !selector ) {
+						push.apply( results, seed );
+						return results;
+					}
+
+					break;
+				}
+			}
+		}
+	}
+
+	// Compile and execute a filtering function if one is not provided
+	// Provide `match` to avoid retokenization if we modified the selector above
+	( compiled || compile( selector, match ) )(
+		seed,
+		context,
+		!documentIsHTML,
+		results,
+		!context || rsibling.test( selector ) && testContext( context.parentNode ) || context
+	);
+	return results;
+};
+
+// One-time assignments
+
+// Sort stability
+support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando;
+
+// Support: Chrome 14-35+
+// Always assume duplicates if they aren't passed to the comparison function
+support.detectDuplicates = !!hasDuplicate;
+
+// Initialize against the default document
+setDocument();
+
+// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27)
+// Detached nodes confoundingly follow *each other*
+support.sortDetached = assert( function( el ) {
+
+	// Should return 1, but returns 4 (following)
+	return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1;
+} );
+
+// Support: IE<8
+// Prevent attribute/property "interpolation"
+// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx
+if ( !assert( function( el ) {
+	el.innerHTML = "";
+	return el.firstChild.getAttribute( "href" ) === "#";
+} ) ) {
+	addHandle( "type|href|height|width", function( elem, name, isXML ) {
+		if ( !isXML ) {
+			return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 );
+		}
+	} );
+}
+
+// Support: IE<9
+// Use defaultValue in place of getAttribute("value")
+if ( !support.attributes || !assert( function( el ) {
+	el.innerHTML = "";
+	el.firstChild.setAttribute( "value", "" );
+	return el.firstChild.getAttribute( "value" ) === "";
+} ) ) {
+	addHandle( "value", function( elem, _name, isXML ) {
+		if ( !isXML && elem.nodeName.toLowerCase() === "input" ) {
+			return elem.defaultValue;
+		}
+	} );
+}
+
+// Support: IE<9
+// Use getAttributeNode to fetch booleans when getAttribute lies
+if ( !assert( function( el ) {
+	return el.getAttribute( "disabled" ) == null;
+} ) ) {
+	addHandle( booleans, function( elem, name, isXML ) {
+		var val;
+		if ( !isXML ) {
+			return elem[ name ] === true ? name.toLowerCase() :
+				( val = elem.getAttributeNode( name ) ) && val.specified ?
+					val.value :
+					null;
+		}
+	} );
+}
+
+return Sizzle;
+
+} )( window );
+
+
+
+jQuery.find = Sizzle;
+jQuery.expr = Sizzle.selectors;
+
+// Deprecated
+jQuery.expr[ ":" ] = jQuery.expr.pseudos;
+jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort;
+jQuery.text = Sizzle.getText;
+jQuery.isXMLDoc = Sizzle.isXML;
+jQuery.contains = Sizzle.contains;
+jQuery.escapeSelector = Sizzle.escape;
+
+
+
+
+var dir = function( elem, dir, until ) {
+	var matched = [],
+		truncate = until !== undefined;
+
+	while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) {
+		if ( elem.nodeType === 1 ) {
+			if ( truncate && jQuery( elem ).is( until ) ) {
+				break;
+			}
+			matched.push( elem );
+		}
+	}
+	return matched;
+};
+
+
+var siblings = function( n, elem ) {
+	var matched = [];
+
+	for ( ; n; n = n.nextSibling ) {
+		if ( n.nodeType === 1 && n !== elem ) {
+			matched.push( n );
+		}
+	}
+
+	return matched;
+};
+
+
+var rneedsContext = jQuery.expr.match.needsContext;
+
+
+
+function nodeName( elem, name ) {
+
+	return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase();
+
+}
+var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i );
+
+
+
+// Implement the identical functionality for filter and not
+function winnow( elements, qualifier, not ) {
+	if ( isFunction( qualifier ) ) {
+		return jQuery.grep( elements, function( elem, i ) {
+			return !!qualifier.call( elem, i, elem ) !== not;
+		} );
+	}
+
+	// Single element
+	if ( qualifier.nodeType ) {
+		return jQuery.grep( elements, function( elem ) {
+			return ( elem === qualifier ) !== not;
+		} );
+	}
+
+	// Arraylike of elements (jQuery, arguments, Array)
+	if ( typeof qualifier !== "string" ) {
+		return jQuery.grep( elements, function( elem ) {
+			return ( indexOf.call( qualifier, elem ) > -1 ) !== not;
+		} );
+	}
+
+	// Filtered directly for both simple and complex selectors
+	return jQuery.filter( qualifier, elements, not );
+}
+
+jQuery.filter = function( expr, elems, not ) {
+	var elem = elems[ 0 ];
+
+	if ( not ) {
+		expr = ":not(" + expr + ")";
+	}
+
+	if ( elems.length === 1 && elem.nodeType === 1 ) {
+		return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : [];
+	}
+
+	return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) {
+		return elem.nodeType === 1;
+	} ) );
+};
+
+jQuery.fn.extend( {
+	find: function( selector ) {
+		var i, ret,
+			len = this.length,
+			self = this;
+
+		if ( typeof selector !== "string" ) {
+			return this.pushStack( jQuery( selector ).filter( function() {
+				for ( i = 0; i < len; i++ ) {
+					if ( jQuery.contains( self[ i ], this ) ) {
+						return true;
+					}
+				}
+			} ) );
+		}
+
+		ret = this.pushStack( [] );
+
+		for ( i = 0; i < len; i++ ) {
+			jQuery.find( selector, self[ i ], ret );
+		}
+
+		return len > 1 ? jQuery.uniqueSort( ret ) : ret;
+	},
+	filter: function( selector ) {
+		return this.pushStack( winnow( this, selector || [], false ) );
+	},
+	not: function( selector ) {
+		return this.pushStack( winnow( this, selector || [], true ) );
+	},
+	is: function( selector ) {
+		return !!winnow(
+			this,
+
+			// If this is a positional/relative selector, check membership in the returned set
+			// so $("p:first").is("p:last") won't return true for a doc with two "p".
+			typeof selector === "string" && rneedsContext.test( selector ) ?
+				jQuery( selector ) :
+				selector || [],
+			false
+		).length;
+	}
+} );
+
+
+// Initialize a jQuery object
+
+
+// A central reference to the root jQuery(document)
+var rootjQuery,
+
+	// A simple way to check for HTML strings
+	// Prioritize #id over  to avoid XSS via location.hash (#9521)
+	// Strict HTML recognition (#11290: must start with <)
+	// Shortcut simple #id case for speed
+	rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/,
+
+	init = jQuery.fn.init = function( selector, context, root ) {
+		var match, elem;
+
+		// HANDLE: $(""), $(null), $(undefined), $(false)
+		if ( !selector ) {
+			return this;
+		}
+
+		// Method init() accepts an alternate rootjQuery
+		// so migrate can support jQuery.sub (gh-2101)
+		root = root || rootjQuery;
+
+		// Handle HTML strings
+		if ( typeof selector === "string" ) {
+			if ( selector[ 0 ] === "<" &&
+				selector[ selector.length - 1 ] === ">" &&
+				selector.length >= 3 ) {
+
+				// Assume that strings that start and end with <> are HTML and skip the regex check
+				match = [ null, selector, null ];
+
+			} else {
+				match = rquickExpr.exec( selector );
+			}
+
+			// Match html or make sure no context is specified for #id
+			if ( match && ( match[ 1 ] || !context ) ) {
+
+				// HANDLE: $(html) -> $(array)
+				if ( match[ 1 ] ) {
+					context = context instanceof jQuery ? context[ 0 ] : context;
+
+					// Option to run scripts is true for back-compat
+					// Intentionally let the error be thrown if parseHTML is not present
+					jQuery.merge( this, jQuery.parseHTML(
+						match[ 1 ],
+						context && context.nodeType ? context.ownerDocument || context : document,
+						true
+					) );
+
+					// HANDLE: $(html, props)
+					if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) {
+						for ( match in context ) {
+
+							// Properties of context are called as methods if possible
+							if ( isFunction( this[ match ] ) ) {
+								this[ match ]( context[ match ] );
+
+							// ...and otherwise set as attributes
+							} else {
+								this.attr( match, context[ match ] );
+							}
+						}
+					}
+
+					return this;
+
+				// HANDLE: $(#id)
+				} else {
+					elem = document.getElementById( match[ 2 ] );
+
+					if ( elem ) {
+
+						// Inject the element directly into the jQuery object
+						this[ 0 ] = elem;
+						this.length = 1;
+					}
+					return this;
+				}
+
+			// HANDLE: $(expr, $(...))
+			} else if ( !context || context.jquery ) {
+				return ( context || root ).find( selector );
+
+			// HANDLE: $(expr, context)
+			// (which is just equivalent to: $(context).find(expr)
+			} else {
+				return this.constructor( context ).find( selector );
+			}
+
+		// HANDLE: $(DOMElement)
+		} else if ( selector.nodeType ) {
+			this[ 0 ] = selector;
+			this.length = 1;
+			return this;
+
+		// HANDLE: $(function)
+		// Shortcut for document ready
+		} else if ( isFunction( selector ) ) {
+			return root.ready !== undefined ?
+				root.ready( selector ) :
+
+				// Execute immediately if ready is not present
+				selector( jQuery );
+		}
+
+		return jQuery.makeArray( selector, this );
+	};
+
+// Give the init function the jQuery prototype for later instantiation
+init.prototype = jQuery.fn;
+
+// Initialize central reference
+rootjQuery = jQuery( document );
+
+
+var rparentsprev = /^(?:parents|prev(?:Until|All))/,
+
+	// Methods guaranteed to produce a unique set when starting from a unique set
+	guaranteedUnique = {
+		children: true,
+		contents: true,
+		next: true,
+		prev: true
+	};
+
+jQuery.fn.extend( {
+	has: function( target ) {
+		var targets = jQuery( target, this ),
+			l = targets.length;
+
+		return this.filter( function() {
+			var i = 0;
+			for ( ; i < l; i++ ) {
+				if ( jQuery.contains( this, targets[ i ] ) ) {
+					return true;
+				}
+			}
+		} );
+	},
+
+	closest: function( selectors, context ) {
+		var cur,
+			i = 0,
+			l = this.length,
+			matched = [],
+			targets = typeof selectors !== "string" && jQuery( selectors );
+
+		// Positional selectors never match, since there's no _selection_ context
+		if ( !rneedsContext.test( selectors ) ) {
+			for ( ; i < l; i++ ) {
+				for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) {
+
+					// Always skip document fragments
+					if ( cur.nodeType < 11 && ( targets ?
+						targets.index( cur ) > -1 :
+
+						// Don't pass non-elements to Sizzle
+						cur.nodeType === 1 &&
+							jQuery.find.matchesSelector( cur, selectors ) ) ) {
+
+						matched.push( cur );
+						break;
+					}
+				}
+			}
+		}
+
+		return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched );
+	},
+
+	// Determine the position of an element within the set
+	index: function( elem ) {
+
+		// No argument, return index in parent
+		if ( !elem ) {
+			return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1;
+		}
+
+		// Index in selector
+		if ( typeof elem === "string" ) {
+			return indexOf.call( jQuery( elem ), this[ 0 ] );
+		}
+
+		// Locate the position of the desired element
+		return indexOf.call( this,
+
+			// If it receives a jQuery object, the first element is used
+			elem.jquery ? elem[ 0 ] : elem
+		);
+	},
+
+	add: function( selector, context ) {
+		return this.pushStack(
+			jQuery.uniqueSort(
+				jQuery.merge( this.get(), jQuery( selector, context ) )
+			)
+		);
+	},
+
+	addBack: function( selector ) {
+		return this.add( selector == null ?
+			this.prevObject : this.prevObject.filter( selector )
+		);
+	}
+} );
+
+function sibling( cur, dir ) {
+	while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {}
+	return cur;
+}
+
+jQuery.each( {
+	parent: function( elem ) {
+		var parent = elem.parentNode;
+		return parent && parent.nodeType !== 11 ? parent : null;
+	},
+	parents: function( elem ) {
+		return dir( elem, "parentNode" );
+	},
+	parentsUntil: function( elem, _i, until ) {
+		return dir( elem, "parentNode", until );
+	},
+	next: function( elem ) {
+		return sibling( elem, "nextSibling" );
+	},
+	prev: function( elem ) {
+		return sibling( elem, "previousSibling" );
+	},
+	nextAll: function( elem ) {
+		return dir( elem, "nextSibling" );
+	},
+	prevAll: function( elem ) {
+		return dir( elem, "previousSibling" );
+	},
+	nextUntil: function( elem, _i, until ) {
+		return dir( elem, "nextSibling", until );
+	},
+	prevUntil: function( elem, _i, until ) {
+		return dir( elem, "previousSibling", until );
+	},
+	siblings: function( elem ) {
+		return siblings( ( elem.parentNode || {} ).firstChild, elem );
+	},
+	children: function( elem ) {
+		return siblings( elem.firstChild );
+	},
+	contents: function( elem ) {
+		if ( elem.contentDocument != null &&
+
+			// Support: IE 11+
+			//  elements with no `data` attribute has an object
+			// `contentDocument` with a `null` prototype.
+			getProto( elem.contentDocument ) ) {
+
+			return elem.contentDocument;
+		}
+
+		// Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only
+		// Treat the template element as a regular one in browsers that
+		// don't support it.
+		if ( nodeName( elem, "template" ) ) {
+			elem = elem.content || elem;
+		}
+
+		return jQuery.merge( [], elem.childNodes );
+	}
+}, function( name, fn ) {
+	jQuery.fn[ name ] = function( until, selector ) {
+		var matched = jQuery.map( this, fn, until );
+
+		if ( name.slice( -5 ) !== "Until" ) {
+			selector = until;
+		}
+
+		if ( selector && typeof selector === "string" ) {
+			matched = jQuery.filter( selector, matched );
+		}
+
+		if ( this.length > 1 ) {
+
+			// Remove duplicates
+			if ( !guaranteedUnique[ name ] ) {
+				jQuery.uniqueSort( matched );
+			}
+
+			// Reverse order for parents* and prev-derivatives
+			if ( rparentsprev.test( name ) ) {
+				matched.reverse();
+			}
+		}
+
+		return this.pushStack( matched );
+	};
+} );
+var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g );
+
+
+
+// Convert String-formatted options into Object-formatted ones
+function createOptions( options ) {
+	var object = {};
+	jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) {
+		object[ flag ] = true;
+	} );
+	return object;
+}
+
+/*
+ * Create a callback list using the following parameters:
+ *
+ *	options: an optional list of space-separated options that will change how
+ *			the callback list behaves or a more traditional option object
+ *
+ * By default a callback list will act like an event callback list and can be
+ * "fired" multiple times.
+ *
+ * Possible options:
+ *
+ *	once:			will ensure the callback list can only be fired once (like a Deferred)
+ *
+ *	memory:			will keep track of previous values and will call any callback added
+ *					after the list has been fired right away with the latest "memorized"
+ *					values (like a Deferred)
+ *
+ *	unique:			will ensure a callback can only be added once (no duplicate in the list)
+ *
+ *	stopOnFalse:	interrupt callings when a callback returns false
+ *
+ */
+jQuery.Callbacks = function( options ) {
+
+	// Convert options from String-formatted to Object-formatted if needed
+	// (we check in cache first)
+	options = typeof options === "string" ?
+		createOptions( options ) :
+		jQuery.extend( {}, options );
+
+	var // Flag to know if list is currently firing
+		firing,
+
+		// Last fire value for non-forgettable lists
+		memory,
+
+		// Flag to know if list was already fired
+		fired,
+
+		// Flag to prevent firing
+		locked,
+
+		// Actual callback list
+		list = [],
+
+		// Queue of execution data for repeatable lists
+		queue = [],
+
+		// Index of currently firing callback (modified by add/remove as needed)
+		firingIndex = -1,
+
+		// Fire callbacks
+		fire = function() {
+
+			// Enforce single-firing
+			locked = locked || options.once;
+
+			// Execute callbacks for all pending executions,
+			// respecting firingIndex overrides and runtime changes
+			fired = firing = true;
+			for ( ; queue.length; firingIndex = -1 ) {
+				memory = queue.shift();
+				while ( ++firingIndex < list.length ) {
+
+					// Run callback and check for early termination
+					if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false &&
+						options.stopOnFalse ) {
+
+						// Jump to end and forget the data so .add doesn't re-fire
+						firingIndex = list.length;
+						memory = false;
+					}
+				}
+			}
+
+			// Forget the data if we're done with it
+			if ( !options.memory ) {
+				memory = false;
+			}
+
+			firing = false;
+
+			// Clean up if we're done firing for good
+			if ( locked ) {
+
+				// Keep an empty list if we have data for future add calls
+				if ( memory ) {
+					list = [];
+
+				// Otherwise, this object is spent
+				} else {
+					list = "";
+				}
+			}
+		},
+
+		// Actual Callbacks object
+		self = {
+
+			// Add a callback or a collection of callbacks to the list
+			add: function() {
+				if ( list ) {
+
+					// If we have memory from a past run, we should fire after adding
+					if ( memory && !firing ) {
+						firingIndex = list.length - 1;
+						queue.push( memory );
+					}
+
+					( function add( args ) {
+						jQuery.each( args, function( _, arg ) {
+							if ( isFunction( arg ) ) {
+								if ( !options.unique || !self.has( arg ) ) {
+									list.push( arg );
+								}
+							} else if ( arg && arg.length && toType( arg ) !== "string" ) {
+
+								// Inspect recursively
+								add( arg );
+							}
+						} );
+					} )( arguments );
+
+					if ( memory && !firing ) {
+						fire();
+					}
+				}
+				return this;
+			},
+
+			// Remove a callback from the list
+			remove: function() {
+				jQuery.each( arguments, function( _, arg ) {
+					var index;
+					while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) {
+						list.splice( index, 1 );
+
+						// Handle firing indexes
+						if ( index <= firingIndex ) {
+							firingIndex--;
+						}
+					}
+				} );
+				return this;
+			},
+
+			// Check if a given callback is in the list.
+			// If no argument is given, return whether or not list has callbacks attached.
+			has: function( fn ) {
+				return fn ?
+					jQuery.inArray( fn, list ) > -1 :
+					list.length > 0;
+			},
+
+			// Remove all callbacks from the list
+			empty: function() {
+				if ( list ) {
+					list = [];
+				}
+				return this;
+			},
+
+			// Disable .fire and .add
+			// Abort any current/pending executions
+			// Clear all callbacks and values
+			disable: function() {
+				locked = queue = [];
+				list = memory = "";
+				return this;
+			},
+			disabled: function() {
+				return !list;
+			},
+
+			// Disable .fire
+			// Also disable .add unless we have memory (since it would have no effect)
+			// Abort any pending executions
+			lock: function() {
+				locked = queue = [];
+				if ( !memory && !firing ) {
+					list = memory = "";
+				}
+				return this;
+			},
+			locked: function() {
+				return !!locked;
+			},
+
+			// Call all callbacks with the given context and arguments
+			fireWith: function( context, args ) {
+				if ( !locked ) {
+					args = args || [];
+					args = [ context, args.slice ? args.slice() : args ];
+					queue.push( args );
+					if ( !firing ) {
+						fire();
+					}
+				}
+				return this;
+			},
+
+			// Call all the callbacks with the given arguments
+			fire: function() {
+				self.fireWith( this, arguments );
+				return this;
+			},
+
+			// To know if the callbacks have already been called at least once
+			fired: function() {
+				return !!fired;
+			}
+		};
+
+	return self;
+};
+
+
+function Identity( v ) {
+	return v;
+}
+function Thrower( ex ) {
+	throw ex;
+}
+
+function adoptValue( value, resolve, reject, noValue ) {
+	var method;
+
+	try {
+
+		// Check for promise aspect first to privilege synchronous behavior
+		if ( value && isFunction( ( method = value.promise ) ) ) {
+			method.call( value ).done( resolve ).fail( reject );
+
+		// Other thenables
+		} else if ( value && isFunction( ( method = value.then ) ) ) {
+			method.call( value, resolve, reject );
+
+		// Other non-thenables
+		} else {
+
+			// Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer:
+			// * false: [ value ].slice( 0 ) => resolve( value )
+			// * true: [ value ].slice( 1 ) => resolve()
+			resolve.apply( undefined, [ value ].slice( noValue ) );
+		}
+
+	// For Promises/A+, convert exceptions into rejections
+	// Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in
+	// Deferred#then to conditionally suppress rejection.
+	} catch ( value ) {
+
+		// Support: Android 4.0 only
+		// Strict mode functions invoked without .call/.apply get global-object context
+		reject.apply( undefined, [ value ] );
+	}
+}
+
+jQuery.extend( {
+
+	Deferred: function( func ) {
+		var tuples = [
+
+				// action, add listener, callbacks,
+				// ... .then handlers, argument index, [final state]
+				[ "notify", "progress", jQuery.Callbacks( "memory" ),
+					jQuery.Callbacks( "memory" ), 2 ],
+				[ "resolve", "done", jQuery.Callbacks( "once memory" ),
+					jQuery.Callbacks( "once memory" ), 0, "resolved" ],
+				[ "reject", "fail", jQuery.Callbacks( "once memory" ),
+					jQuery.Callbacks( "once memory" ), 1, "rejected" ]
+			],
+			state = "pending",
+			promise = {
+				state: function() {
+					return state;
+				},
+				always: function() {
+					deferred.done( arguments ).fail( arguments );
+					return this;
+				},
+				"catch": function( fn ) {
+					return promise.then( null, fn );
+				},
+
+				// Keep pipe for back-compat
+				pipe: function( /* fnDone, fnFail, fnProgress */ ) {
+					var fns = arguments;
+
+					return jQuery.Deferred( function( newDefer ) {
+						jQuery.each( tuples, function( _i, tuple ) {
+
+							// Map tuples (progress, done, fail) to arguments (done, fail, progress)
+							var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ];
+
+							// deferred.progress(function() { bind to newDefer or newDefer.notify })
+							// deferred.done(function() { bind to newDefer or newDefer.resolve })
+							// deferred.fail(function() { bind to newDefer or newDefer.reject })
+							deferred[ tuple[ 1 ] ]( function() {
+								var returned = fn && fn.apply( this, arguments );
+								if ( returned && isFunction( returned.promise ) ) {
+									returned.promise()
+										.progress( newDefer.notify )
+										.done( newDefer.resolve )
+										.fail( newDefer.reject );
+								} else {
+									newDefer[ tuple[ 0 ] + "With" ](
+										this,
+										fn ? [ returned ] : arguments
+									);
+								}
+							} );
+						} );
+						fns = null;
+					} ).promise();
+				},
+				then: function( onFulfilled, onRejected, onProgress ) {
+					var maxDepth = 0;
+					function resolve( depth, deferred, handler, special ) {
+						return function() {
+							var that = this,
+								args = arguments,
+								mightThrow = function() {
+									var returned, then;
+
+									// Support: Promises/A+ section 2.3.3.3.3
+									// https://promisesaplus.com/#point-59
+									// Ignore double-resolution attempts
+									if ( depth < maxDepth ) {
+										return;
+									}
+
+									returned = handler.apply( that, args );
+
+									// Support: Promises/A+ section 2.3.1
+									// https://promisesaplus.com/#point-48
+									if ( returned === deferred.promise() ) {
+										throw new TypeError( "Thenable self-resolution" );
+									}
+
+									// Support: Promises/A+ sections 2.3.3.1, 3.5
+									// https://promisesaplus.com/#point-54
+									// https://promisesaplus.com/#point-75
+									// Retrieve `then` only once
+									then = returned &&
+
+										// Support: Promises/A+ section 2.3.4
+										// https://promisesaplus.com/#point-64
+										// Only check objects and functions for thenability
+										( typeof returned === "object" ||
+											typeof returned === "function" ) &&
+										returned.then;
+
+									// Handle a returned thenable
+									if ( isFunction( then ) ) {
+
+										// Special processors (notify) just wait for resolution
+										if ( special ) {
+											then.call(
+												returned,
+												resolve( maxDepth, deferred, Identity, special ),
+												resolve( maxDepth, deferred, Thrower, special )
+											);
+
+										// Normal processors (resolve) also hook into progress
+										} else {
+
+											// ...and disregard older resolution values
+											maxDepth++;
+
+											then.call(
+												returned,
+												resolve( maxDepth, deferred, Identity, special ),
+												resolve( maxDepth, deferred, Thrower, special ),
+												resolve( maxDepth, deferred, Identity,
+													deferred.notifyWith )
+											);
+										}
+
+									// Handle all other returned values
+									} else {
+
+										// Only substitute handlers pass on context
+										// and multiple values (non-spec behavior)
+										if ( handler !== Identity ) {
+											that = undefined;
+											args = [ returned ];
+										}
+
+										// Process the value(s)
+										// Default process is resolve
+										( special || deferred.resolveWith )( that, args );
+									}
+								},
+
+								// Only normal processors (resolve) catch and reject exceptions
+								process = special ?
+									mightThrow :
+									function() {
+										try {
+											mightThrow();
+										} catch ( e ) {
+
+											if ( jQuery.Deferred.exceptionHook ) {
+												jQuery.Deferred.exceptionHook( e,
+													process.stackTrace );
+											}
+
+											// Support: Promises/A+ section 2.3.3.3.4.1
+											// https://promisesaplus.com/#point-61
+											// Ignore post-resolution exceptions
+											if ( depth + 1 >= maxDepth ) {
+
+												// Only substitute handlers pass on context
+												// and multiple values (non-spec behavior)
+												if ( handler !== Thrower ) {
+													that = undefined;
+													args = [ e ];
+												}
+
+												deferred.rejectWith( that, args );
+											}
+										}
+									};
+
+							// Support: Promises/A+ section 2.3.3.3.1
+							// https://promisesaplus.com/#point-57
+							// Re-resolve promises immediately to dodge false rejection from
+							// subsequent errors
+							if ( depth ) {
+								process();
+							} else {
+
+								// Call an optional hook to record the stack, in case of exception
+								// since it's otherwise lost when execution goes async
+								if ( jQuery.Deferred.getStackHook ) {
+									process.stackTrace = jQuery.Deferred.getStackHook();
+								}
+								window.setTimeout( process );
+							}
+						};
+					}
+
+					return jQuery.Deferred( function( newDefer ) {
+
+						// progress_handlers.add( ... )
+						tuples[ 0 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onProgress ) ?
+									onProgress :
+									Identity,
+								newDefer.notifyWith
+							)
+						);
+
+						// fulfilled_handlers.add( ... )
+						tuples[ 1 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onFulfilled ) ?
+									onFulfilled :
+									Identity
+							)
+						);
+
+						// rejected_handlers.add( ... )
+						tuples[ 2 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onRejected ) ?
+									onRejected :
+									Thrower
+							)
+						);
+					} ).promise();
+				},
+
+				// Get a promise for this deferred
+				// If obj is provided, the promise aspect is added to the object
+				promise: function( obj ) {
+					return obj != null ? jQuery.extend( obj, promise ) : promise;
+				}
+			},
+			deferred = {};
+
+		// Add list-specific methods
+		jQuery.each( tuples, function( i, tuple ) {
+			var list = tuple[ 2 ],
+				stateString = tuple[ 5 ];
+
+			// promise.progress = list.add
+			// promise.done = list.add
+			// promise.fail = list.add
+			promise[ tuple[ 1 ] ] = list.add;
+
+			// Handle state
+			if ( stateString ) {
+				list.add(
+					function() {
+
+						// state = "resolved" (i.e., fulfilled)
+						// state = "rejected"
+						state = stateString;
+					},
+
+					// rejected_callbacks.disable
+					// fulfilled_callbacks.disable
+					tuples[ 3 - i ][ 2 ].disable,
+
+					// rejected_handlers.disable
+					// fulfilled_handlers.disable
+					tuples[ 3 - i ][ 3 ].disable,
+
+					// progress_callbacks.lock
+					tuples[ 0 ][ 2 ].lock,
+
+					// progress_handlers.lock
+					tuples[ 0 ][ 3 ].lock
+				);
+			}
+
+			// progress_handlers.fire
+			// fulfilled_handlers.fire
+			// rejected_handlers.fire
+			list.add( tuple[ 3 ].fire );
+
+			// deferred.notify = function() { deferred.notifyWith(...) }
+			// deferred.resolve = function() { deferred.resolveWith(...) }
+			// deferred.reject = function() { deferred.rejectWith(...) }
+			deferred[ tuple[ 0 ] ] = function() {
+				deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments );
+				return this;
+			};
+
+			// deferred.notifyWith = list.fireWith
+			// deferred.resolveWith = list.fireWith
+			// deferred.rejectWith = list.fireWith
+			deferred[ tuple[ 0 ] + "With" ] = list.fireWith;
+		} );
+
+		// Make the deferred a promise
+		promise.promise( deferred );
+
+		// Call given func if any
+		if ( func ) {
+			func.call( deferred, deferred );
+		}
+
+		// All done!
+		return deferred;
+	},
+
+	// Deferred helper
+	when: function( singleValue ) {
+		var
+
+			// count of uncompleted subordinates
+			remaining = arguments.length,
+
+			// count of unprocessed arguments
+			i = remaining,
+
+			// subordinate fulfillment data
+			resolveContexts = Array( i ),
+			resolveValues = slice.call( arguments ),
+
+			// the primary Deferred
+			primary = jQuery.Deferred(),
+
+			// subordinate callback factory
+			updateFunc = function( i ) {
+				return function( value ) {
+					resolveContexts[ i ] = this;
+					resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value;
+					if ( !( --remaining ) ) {
+						primary.resolveWith( resolveContexts, resolveValues );
+					}
+				};
+			};
+
+		// Single- and empty arguments are adopted like Promise.resolve
+		if ( remaining <= 1 ) {
+			adoptValue( singleValue, primary.done( updateFunc( i ) ).resolve, primary.reject,
+				!remaining );
+
+			// Use .then() to unwrap secondary thenables (cf. gh-3000)
+			if ( primary.state() === "pending" ||
+				isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) {
+
+				return primary.then();
+			}
+		}
+
+		// Multiple arguments are aggregated like Promise.all array elements
+		while ( i-- ) {
+			adoptValue( resolveValues[ i ], updateFunc( i ), primary.reject );
+		}
+
+		return primary.promise();
+	}
+} );
+
+
+// These usually indicate a programmer mistake during development,
+// warn about them ASAP rather than swallowing them by default.
+var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/;
+
+jQuery.Deferred.exceptionHook = function( error, stack ) {
+
+	// Support: IE 8 - 9 only
+	// Console exists when dev tools are open, which can happen at any time
+	if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) {
+		window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack );
+	}
+};
+
+
+
+
+jQuery.readyException = function( error ) {
+	window.setTimeout( function() {
+		throw error;
+	} );
+};
+
+
+
+
+// The deferred used on DOM ready
+var readyList = jQuery.Deferred();
+
+jQuery.fn.ready = function( fn ) {
+
+	readyList
+		.then( fn )
+
+		// Wrap jQuery.readyException in a function so that the lookup
+		// happens at the time of error handling instead of callback
+		// registration.
+		.catch( function( error ) {
+			jQuery.readyException( error );
+		} );
+
+	return this;
+};
+
+jQuery.extend( {
+
+	// Is the DOM ready to be used? Set to true once it occurs.
+	isReady: false,
+
+	// A counter to track how many items to wait for before
+	// the ready event fires. See #6781
+	readyWait: 1,
+
+	// Handle when the DOM is ready
+	ready: function( wait ) {
+
+		// Abort if there are pending holds or we're already ready
+		if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) {
+			return;
+		}
+
+		// Remember that the DOM is ready
+		jQuery.isReady = true;
+
+		// If a normal DOM Ready event fired, decrement, and wait if need be
+		if ( wait !== true && --jQuery.readyWait > 0 ) {
+			return;
+		}
+
+		// If there are functions bound, to execute
+		readyList.resolveWith( document, [ jQuery ] );
+	}
+} );
+
+jQuery.ready.then = readyList.then;
+
+// The ready event handler and self cleanup method
+function completed() {
+	document.removeEventListener( "DOMContentLoaded", completed );
+	window.removeEventListener( "load", completed );
+	jQuery.ready();
+}
+
+// Catch cases where $(document).ready() is called
+// after the browser event has already occurred.
+// Support: IE <=9 - 10 only
+// Older IE sometimes signals "interactive" too soon
+if ( document.readyState === "complete" ||
+	( document.readyState !== "loading" && !document.documentElement.doScroll ) ) {
+
+	// Handle it asynchronously to allow scripts the opportunity to delay ready
+	window.setTimeout( jQuery.ready );
+
+} else {
+
+	// Use the handy event callback
+	document.addEventListener( "DOMContentLoaded", completed );
+
+	// A fallback to window.onload, that will always work
+	window.addEventListener( "load", completed );
+}
+
+
+
+
+// Multifunctional method to get and set values of a collection
+// The value/s can optionally be executed if it's a function
+var access = function( elems, fn, key, value, chainable, emptyGet, raw ) {
+	var i = 0,
+		len = elems.length,
+		bulk = key == null;
+
+	// Sets many values
+	if ( toType( key ) === "object" ) {
+		chainable = true;
+		for ( i in key ) {
+			access( elems, fn, i, key[ i ], true, emptyGet, raw );
+		}
+
+	// Sets one value
+	} else if ( value !== undefined ) {
+		chainable = true;
+
+		if ( !isFunction( value ) ) {
+			raw = true;
+		}
+
+		if ( bulk ) {
+
+			// Bulk operations run against the entire set
+			if ( raw ) {
+				fn.call( elems, value );
+				fn = null;
+
+			// ...except when executing function values
+			} else {
+				bulk = fn;
+				fn = function( elem, _key, value ) {
+					return bulk.call( jQuery( elem ), value );
+				};
+			}
+		}
+
+		if ( fn ) {
+			for ( ; i < len; i++ ) {
+				fn(
+					elems[ i ], key, raw ?
+						value :
+						value.call( elems[ i ], i, fn( elems[ i ], key ) )
+				);
+			}
+		}
+	}
+
+	if ( chainable ) {
+		return elems;
+	}
+
+	// Gets
+	if ( bulk ) {
+		return fn.call( elems );
+	}
+
+	return len ? fn( elems[ 0 ], key ) : emptyGet;
+};
+
+
+// Matches dashed string for camelizing
+var rmsPrefix = /^-ms-/,
+	rdashAlpha = /-([a-z])/g;
+
+// Used by camelCase as callback to replace()
+function fcamelCase( _all, letter ) {
+	return letter.toUpperCase();
+}
+
+// Convert dashed to camelCase; used by the css and data modules
+// Support: IE <=9 - 11, Edge 12 - 15
+// Microsoft forgot to hump their vendor prefix (#9572)
+function camelCase( string ) {
+	return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase );
+}
+var acceptData = function( owner ) {
+
+	// Accepts only:
+	//  - Node
+	//    - Node.ELEMENT_NODE
+	//    - Node.DOCUMENT_NODE
+	//  - Object
+	//    - Any
+	return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType );
+};
+
+
+
+
+function Data() {
+	this.expando = jQuery.expando + Data.uid++;
+}
+
+Data.uid = 1;
+
+Data.prototype = {
+
+	cache: function( owner ) {
+
+		// Check if the owner object already has a cache
+		var value = owner[ this.expando ];
+
+		// If not, create one
+		if ( !value ) {
+			value = {};
+
+			// We can accept data for non-element nodes in modern browsers,
+			// but we should not, see #8335.
+			// Always return an empty object.
+			if ( acceptData( owner ) ) {
+
+				// If it is a node unlikely to be stringify-ed or looped over
+				// use plain assignment
+				if ( owner.nodeType ) {
+					owner[ this.expando ] = value;
+
+				// Otherwise secure it in a non-enumerable property
+				// configurable must be true to allow the property to be
+				// deleted when data is removed
+				} else {
+					Object.defineProperty( owner, this.expando, {
+						value: value,
+						configurable: true
+					} );
+				}
+			}
+		}
+
+		return value;
+	},
+	set: function( owner, data, value ) {
+		var prop,
+			cache = this.cache( owner );
+
+		// Handle: [ owner, key, value ] args
+		// Always use camelCase key (gh-2257)
+		if ( typeof data === "string" ) {
+			cache[ camelCase( data ) ] = value;
+
+		// Handle: [ owner, { properties } ] args
+		} else {
+
+			// Copy the properties one-by-one to the cache object
+			for ( prop in data ) {
+				cache[ camelCase( prop ) ] = data[ prop ];
+			}
+		}
+		return cache;
+	},
+	get: function( owner, key ) {
+		return key === undefined ?
+			this.cache( owner ) :
+
+			// Always use camelCase key (gh-2257)
+			owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ];
+	},
+	access: function( owner, key, value ) {
+
+		// In cases where either:
+		//
+		//   1. No key was specified
+		//   2. A string key was specified, but no value provided
+		//
+		// Take the "read" path and allow the get method to determine
+		// which value to return, respectively either:
+		//
+		//   1. The entire cache object
+		//   2. The data stored at the key
+		//
+		if ( key === undefined ||
+				( ( key && typeof key === "string" ) && value === undefined ) ) {
+
+			return this.get( owner, key );
+		}
+
+		// When the key is not a string, or both a key and value
+		// are specified, set or extend (existing objects) with either:
+		//
+		//   1. An object of properties
+		//   2. A key and value
+		//
+		this.set( owner, key, value );
+
+		// Since the "set" path can have two possible entry points
+		// return the expected data based on which path was taken[*]
+		return value !== undefined ? value : key;
+	},
+	remove: function( owner, key ) {
+		var i,
+			cache = owner[ this.expando ];
+
+		if ( cache === undefined ) {
+			return;
+		}
+
+		if ( key !== undefined ) {
+
+			// Support array or space separated string of keys
+			if ( Array.isArray( key ) ) {
+
+				// If key is an array of keys...
+				// We always set camelCase keys, so remove that.
+				key = key.map( camelCase );
+			} else {
+				key = camelCase( key );
+
+				// If a key with the spaces exists, use it.
+				// Otherwise, create an array by matching non-whitespace
+				key = key in cache ?
+					[ key ] :
+					( key.match( rnothtmlwhite ) || [] );
+			}
+
+			i = key.length;
+
+			while ( i-- ) {
+				delete cache[ key[ i ] ];
+			}
+		}
+
+		// Remove the expando if there's no more data
+		if ( key === undefined || jQuery.isEmptyObject( cache ) ) {
+
+			// Support: Chrome <=35 - 45
+			// Webkit & Blink performance suffers when deleting properties
+			// from DOM nodes, so set to undefined instead
+			// https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted)
+			if ( owner.nodeType ) {
+				owner[ this.expando ] = undefined;
+			} else {
+				delete owner[ this.expando ];
+			}
+		}
+	},
+	hasData: function( owner ) {
+		var cache = owner[ this.expando ];
+		return cache !== undefined && !jQuery.isEmptyObject( cache );
+	}
+};
+var dataPriv = new Data();
+
+var dataUser = new Data();
+
+
+
+//	Implementation Summary
+//
+//	1. Enforce API surface and semantic compatibility with 1.9.x branch
+//	2. Improve the module's maintainability by reducing the storage
+//		paths to a single mechanism.
+//	3. Use the same single mechanism to support "private" and "user" data.
+//	4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData)
+//	5. Avoid exposing implementation details on user objects (eg. expando properties)
+//	6. Provide a clear path for implementation upgrade to WeakMap in 2014
+
+var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/,
+	rmultiDash = /[A-Z]/g;
+
+function getData( data ) {
+	if ( data === "true" ) {
+		return true;
+	}
+
+	if ( data === "false" ) {
+		return false;
+	}
+
+	if ( data === "null" ) {
+		return null;
+	}
+
+	// Only convert to a number if it doesn't change the string
+	if ( data === +data + "" ) {
+		return +data;
+	}
+
+	if ( rbrace.test( data ) ) {
+		return JSON.parse( data );
+	}
+
+	return data;
+}
+
+function dataAttr( elem, key, data ) {
+	var name;
+
+	// If nothing was found internally, try to fetch any
+	// data from the HTML5 data-* attribute
+	if ( data === undefined && elem.nodeType === 1 ) {
+		name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase();
+		data = elem.getAttribute( name );
+
+		if ( typeof data === "string" ) {
+			try {
+				data = getData( data );
+			} catch ( e ) {}
+
+			// Make sure we set the data so it isn't changed later
+			dataUser.set( elem, key, data );
+		} else {
+			data = undefined;
+		}
+	}
+	return data;
+}
+
+jQuery.extend( {
+	hasData: function( elem ) {
+		return dataUser.hasData( elem ) || dataPriv.hasData( elem );
+	},
+
+	data: function( elem, name, data ) {
+		return dataUser.access( elem, name, data );
+	},
+
+	removeData: function( elem, name ) {
+		dataUser.remove( elem, name );
+	},
+
+	// TODO: Now that all calls to _data and _removeData have been replaced
+	// with direct calls to dataPriv methods, these can be deprecated.
+	_data: function( elem, name, data ) {
+		return dataPriv.access( elem, name, data );
+	},
+
+	_removeData: function( elem, name ) {
+		dataPriv.remove( elem, name );
+	}
+} );
+
+jQuery.fn.extend( {
+	data: function( key, value ) {
+		var i, name, data,
+			elem = this[ 0 ],
+			attrs = elem && elem.attributes;
+
+		// Gets all values
+		if ( key === undefined ) {
+			if ( this.length ) {
+				data = dataUser.get( elem );
+
+				if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) {
+					i = attrs.length;
+					while ( i-- ) {
+
+						// Support: IE 11 only
+						// The attrs elements can be null (#14894)
+						if ( attrs[ i ] ) {
+							name = attrs[ i ].name;
+							if ( name.indexOf( "data-" ) === 0 ) {
+								name = camelCase( name.slice( 5 ) );
+								dataAttr( elem, name, data[ name ] );
+							}
+						}
+					}
+					dataPriv.set( elem, "hasDataAttrs", true );
+				}
+			}
+
+			return data;
+		}
+
+		// Sets multiple values
+		if ( typeof key === "object" ) {
+			return this.each( function() {
+				dataUser.set( this, key );
+			} );
+		}
+
+		return access( this, function( value ) {
+			var data;
+
+			// The calling jQuery object (element matches) is not empty
+			// (and therefore has an element appears at this[ 0 ]) and the
+			// `value` parameter was not undefined. An empty jQuery object
+			// will result in `undefined` for elem = this[ 0 ] which will
+			// throw an exception if an attempt to read a data cache is made.
+			if ( elem && value === undefined ) {
+
+				// Attempt to get data from the cache
+				// The key will always be camelCased in Data
+				data = dataUser.get( elem, key );
+				if ( data !== undefined ) {
+					return data;
+				}
+
+				// Attempt to "discover" the data in
+				// HTML5 custom data-* attrs
+				data = dataAttr( elem, key );
+				if ( data !== undefined ) {
+					return data;
+				}
+
+				// We tried really hard, but the data doesn't exist.
+				return;
+			}
+
+			// Set the data...
+			this.each( function() {
+
+				// We always store the camelCased key
+				dataUser.set( this, key, value );
+			} );
+		}, null, value, arguments.length > 1, null, true );
+	},
+
+	removeData: function( key ) {
+		return this.each( function() {
+			dataUser.remove( this, key );
+		} );
+	}
+} );
+
+
+jQuery.extend( {
+	queue: function( elem, type, data ) {
+		var queue;
+
+		if ( elem ) {
+			type = ( type || "fx" ) + "queue";
+			queue = dataPriv.get( elem, type );
+
+			// Speed up dequeue by getting out quickly if this is just a lookup
+			if ( data ) {
+				if ( !queue || Array.isArray( data ) ) {
+					queue = dataPriv.access( elem, type, jQuery.makeArray( data ) );
+				} else {
+					queue.push( data );
+				}
+			}
+			return queue || [];
+		}
+	},
+
+	dequeue: function( elem, type ) {
+		type = type || "fx";
+
+		var queue = jQuery.queue( elem, type ),
+			startLength = queue.length,
+			fn = queue.shift(),
+			hooks = jQuery._queueHooks( elem, type ),
+			next = function() {
+				jQuery.dequeue( elem, type );
+			};
+
+		// If the fx queue is dequeued, always remove the progress sentinel
+		if ( fn === "inprogress" ) {
+			fn = queue.shift();
+			startLength--;
+		}
+
+		if ( fn ) {
+
+			// Add a progress sentinel to prevent the fx queue from being
+			// automatically dequeued
+			if ( type === "fx" ) {
+				queue.unshift( "inprogress" );
+			}
+
+			// Clear up the last queue stop function
+			delete hooks.stop;
+			fn.call( elem, next, hooks );
+		}
+
+		if ( !startLength && hooks ) {
+			hooks.empty.fire();
+		}
+	},
+
+	// Not public - generate a queueHooks object, or return the current one
+	_queueHooks: function( elem, type ) {
+		var key = type + "queueHooks";
+		return dataPriv.get( elem, key ) || dataPriv.access( elem, key, {
+			empty: jQuery.Callbacks( "once memory" ).add( function() {
+				dataPriv.remove( elem, [ type + "queue", key ] );
+			} )
+		} );
+	}
+} );
+
+jQuery.fn.extend( {
+	queue: function( type, data ) {
+		var setter = 2;
+
+		if ( typeof type !== "string" ) {
+			data = type;
+			type = "fx";
+			setter--;
+		}
+
+		if ( arguments.length < setter ) {
+			return jQuery.queue( this[ 0 ], type );
+		}
+
+		return data === undefined ?
+			this :
+			this.each( function() {
+				var queue = jQuery.queue( this, type, data );
+
+				// Ensure a hooks for this queue
+				jQuery._queueHooks( this, type );
+
+				if ( type === "fx" && queue[ 0 ] !== "inprogress" ) {
+					jQuery.dequeue( this, type );
+				}
+			} );
+	},
+	dequeue: function( type ) {
+		return this.each( function() {
+			jQuery.dequeue( this, type );
+		} );
+	},
+	clearQueue: function( type ) {
+		return this.queue( type || "fx", [] );
+	},
+
+	// Get a promise resolved when queues of a certain type
+	// are emptied (fx is the type by default)
+	promise: function( type, obj ) {
+		var tmp,
+			count = 1,
+			defer = jQuery.Deferred(),
+			elements = this,
+			i = this.length,
+			resolve = function() {
+				if ( !( --count ) ) {
+					defer.resolveWith( elements, [ elements ] );
+				}
+			};
+
+		if ( typeof type !== "string" ) {
+			obj = type;
+			type = undefined;
+		}
+		type = type || "fx";
+
+		while ( i-- ) {
+			tmp = dataPriv.get( elements[ i ], type + "queueHooks" );
+			if ( tmp && tmp.empty ) {
+				count++;
+				tmp.empty.add( resolve );
+			}
+		}
+		resolve();
+		return defer.promise( obj );
+	}
+} );
+var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source;
+
+var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" );
+
+
+var cssExpand = [ "Top", "Right", "Bottom", "Left" ];
+
+var documentElement = document.documentElement;
+
+
+
+	var isAttached = function( elem ) {
+			return jQuery.contains( elem.ownerDocument, elem );
+		},
+		composed = { composed: true };
+
+	// Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only
+	// Check attachment across shadow DOM boundaries when possible (gh-3504)
+	// Support: iOS 10.0-10.2 only
+	// Early iOS 10 versions support `attachShadow` but not `getRootNode`,
+	// leading to errors. We need to check for `getRootNode`.
+	if ( documentElement.getRootNode ) {
+		isAttached = function( elem ) {
+			return jQuery.contains( elem.ownerDocument, elem ) ||
+				elem.getRootNode( composed ) === elem.ownerDocument;
+		};
+	}
+var isHiddenWithinTree = function( elem, el ) {
+
+		// isHiddenWithinTree might be called from jQuery#filter function;
+		// in that case, element will be second argument
+		elem = el || elem;
+
+		// Inline style trumps all
+		return elem.style.display === "none" ||
+			elem.style.display === "" &&
+
+			// Otherwise, check computed style
+			// Support: Firefox <=43 - 45
+			// Disconnected elements can have computed display: none, so first confirm that elem is
+			// in the document.
+			isAttached( elem ) &&
+
+			jQuery.css( elem, "display" ) === "none";
+	};
+
+
+
+function adjustCSS( elem, prop, valueParts, tween ) {
+	var adjusted, scale,
+		maxIterations = 20,
+		currentValue = tween ?
+			function() {
+				return tween.cur();
+			} :
+			function() {
+				return jQuery.css( elem, prop, "" );
+			},
+		initial = currentValue(),
+		unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ),
+
+		// Starting value computation is required for potential unit mismatches
+		initialInUnit = elem.nodeType &&
+			( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) &&
+			rcssNum.exec( jQuery.css( elem, prop ) );
+
+	if ( initialInUnit && initialInUnit[ 3 ] !== unit ) {
+
+		// Support: Firefox <=54
+		// Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144)
+		initial = initial / 2;
+
+		// Trust units reported by jQuery.css
+		unit = unit || initialInUnit[ 3 ];
+
+		// Iteratively approximate from a nonzero starting point
+		initialInUnit = +initial || 1;
+
+		while ( maxIterations-- ) {
+
+			// Evaluate and update our best guess (doubling guesses that zero out).
+			// Finish if the scale equals or crosses 1 (making the old*new product non-positive).
+			jQuery.style( elem, prop, initialInUnit + unit );
+			if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) {
+				maxIterations = 0;
+			}
+			initialInUnit = initialInUnit / scale;
+
+		}
+
+		initialInUnit = initialInUnit * 2;
+		jQuery.style( elem, prop, initialInUnit + unit );
+
+		// Make sure we update the tween properties later on
+		valueParts = valueParts || [];
+	}
+
+	if ( valueParts ) {
+		initialInUnit = +initialInUnit || +initial || 0;
+
+		// Apply relative offset (+=/-=) if specified
+		adjusted = valueParts[ 1 ] ?
+			initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] :
+			+valueParts[ 2 ];
+		if ( tween ) {
+			tween.unit = unit;
+			tween.start = initialInUnit;
+			tween.end = adjusted;
+		}
+	}
+	return adjusted;
+}
+
+
+var defaultDisplayMap = {};
+
+function getDefaultDisplay( elem ) {
+	var temp,
+		doc = elem.ownerDocument,
+		nodeName = elem.nodeName,
+		display = defaultDisplayMap[ nodeName ];
+
+	if ( display ) {
+		return display;
+	}
+
+	temp = doc.body.appendChild( doc.createElement( nodeName ) );
+	display = jQuery.css( temp, "display" );
+
+	temp.parentNode.removeChild( temp );
+
+	if ( display === "none" ) {
+		display = "block";
+	}
+	defaultDisplayMap[ nodeName ] = display;
+
+	return display;
+}
+
+function showHide( elements, show ) {
+	var display, elem,
+		values = [],
+		index = 0,
+		length = elements.length;
+
+	// Determine new display value for elements that need to change
+	for ( ; index < length; index++ ) {
+		elem = elements[ index ];
+		if ( !elem.style ) {
+			continue;
+		}
+
+		display = elem.style.display;
+		if ( show ) {
+
+			// Since we force visibility upon cascade-hidden elements, an immediate (and slow)
+			// check is required in this first loop unless we have a nonempty display value (either
+			// inline or about-to-be-restored)
+			if ( display === "none" ) {
+				values[ index ] = dataPriv.get( elem, "display" ) || null;
+				if ( !values[ index ] ) {
+					elem.style.display = "";
+				}
+			}
+			if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) {
+				values[ index ] = getDefaultDisplay( elem );
+			}
+		} else {
+			if ( display !== "none" ) {
+				values[ index ] = "none";
+
+				// Remember what we're overwriting
+				dataPriv.set( elem, "display", display );
+			}
+		}
+	}
+
+	// Set the display of the elements in a second loop to avoid constant reflow
+	for ( index = 0; index < length; index++ ) {
+		if ( values[ index ] != null ) {
+			elements[ index ].style.display = values[ index ];
+		}
+	}
+
+	return elements;
+}
+
+jQuery.fn.extend( {
+	show: function() {
+		return showHide( this, true );
+	},
+	hide: function() {
+		return showHide( this );
+	},
+	toggle: function( state ) {
+		if ( typeof state === "boolean" ) {
+			return state ? this.show() : this.hide();
+		}
+
+		return this.each( function() {
+			if ( isHiddenWithinTree( this ) ) {
+				jQuery( this ).show();
+			} else {
+				jQuery( this ).hide();
+			}
+		} );
+	}
+} );
+var rcheckableType = ( /^(?:checkbox|radio)$/i );
+
+var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i );
+
+var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i );
+
+
+
+( function() {
+	var fragment = document.createDocumentFragment(),
+		div = fragment.appendChild( document.createElement( "div" ) ),
+		input = document.createElement( "input" );
+
+	// Support: Android 4.0 - 4.3 only
+	// Check state lost if the name is set (#11217)
+	// Support: Windows Web Apps (WWA)
+	// `name` and `type` must use .setAttribute for WWA (#14901)
+	input.setAttribute( "type", "radio" );
+	input.setAttribute( "checked", "checked" );
+	input.setAttribute( "name", "t" );
+
+	div.appendChild( input );
+
+	// Support: Android <=4.1 only
+	// Older WebKit doesn't clone checked state correctly in fragments
+	support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked;
+
+	// Support: IE <=11 only
+	// Make sure textarea (and checkbox) defaultValue is properly cloned
+	div.innerHTML = "";
+	support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue;
+
+	// Support: IE <=9 only
+	// IE <=9 replaces ";
+	support.option = !!div.lastChild;
+} )();
+
+
+// We have to close these tags to support XHTML (#13200)
+var wrapMap = {
+
+	// XHTML parsers do not magically insert elements in the
+	// same way that tag soup parsers do. So we cannot shorten
+	// this by omitting  or other required elements.
+	thead: [ 1, "", "
    " ],
+	col: [ 2, "", "
    " ],
+	tr: [ 2, "", "
    " ],
+	td: [ 3, "", "
    " ],
+
+	_default: [ 0, "", "" ]
+};
+
+wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead;
+wrapMap.th = wrapMap.td;
+
+// Support: IE <=9 only
+if ( !support.option ) {
+	wrapMap.optgroup = wrapMap.option = [ 1, "" ];
+}
+
+
+function getAll( context, tag ) {
+
+	// Support: IE <=9 - 11 only
+	// Use typeof to avoid zero-argument method invocation on host objects (#15151)
+	var ret;
+
+	if ( typeof context.getElementsByTagName !== "undefined" ) {
+		ret = context.getElementsByTagName( tag || "*" );
+
+	} else if ( typeof context.querySelectorAll !== "undefined" ) {
+		ret = context.querySelectorAll( tag || "*" );
+
+	} else {
+		ret = [];
+	}
+
+	if ( tag === undefined || tag && nodeName( context, tag ) ) {
+		return jQuery.merge( [ context ], ret );
+	}
+
+	return ret;
+}
+
+
+// Mark scripts as having already been evaluated
+function setGlobalEval( elems, refElements ) {
+	var i = 0,
+		l = elems.length;
+
+	for ( ; i < l; i++ ) {
+		dataPriv.set(
+			elems[ i ],
+			"globalEval",
+			!refElements || dataPriv.get( refElements[ i ], "globalEval" )
+		);
+	}
+}
+
+
+var rhtml = /<|&#?\w+;/;
+
+function buildFragment( elems, context, scripts, selection, ignored ) {
+	var elem, tmp, tag, wrap, attached, j,
+		fragment = context.createDocumentFragment(),
+		nodes = [],
+		i = 0,
+		l = elems.length;
+
+	for ( ; i < l; i++ ) {
+		elem = elems[ i ];
+
+		if ( elem || elem === 0 ) {
+
+			// Add nodes directly
+			if ( toType( elem ) === "object" ) {
+
+				// Support: Android <=4.0 only, PhantomJS 1 only
+				// push.apply(_, arraylike) throws on ancient WebKit
+				jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem );
+
+			// Convert non-html into a text node
+			} else if ( !rhtml.test( elem ) ) {
+				nodes.push( context.createTextNode( elem ) );
+
+			// Convert html into DOM nodes
+			} else {
+				tmp = tmp || fragment.appendChild( context.createElement( "div" ) );
+
+				// Deserialize a standard representation
+				tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase();
+				wrap = wrapMap[ tag ] || wrapMap._default;
+				tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ];
+
+				// Descend through wrappers to the right content
+				j = wrap[ 0 ];
+				while ( j-- ) {
+					tmp = tmp.lastChild;
+				}
+
+				// Support: Android <=4.0 only, PhantomJS 1 only
+				// push.apply(_, arraylike) throws on ancient WebKit
+				jQuery.merge( nodes, tmp.childNodes );
+
+				// Remember the top-level container
+				tmp = fragment.firstChild;
+
+				// Ensure the created nodes are orphaned (#12392)
+				tmp.textContent = "";
+			}
+		}
+	}
+
+	// Remove wrapper from fragment
+	fragment.textContent = "";
+
+	i = 0;
+	while ( ( elem = nodes[ i++ ] ) ) {
+
+		// Skip elements already in the context collection (trac-4087)
+		if ( selection && jQuery.inArray( elem, selection ) > -1 ) {
+			if ( ignored ) {
+				ignored.push( elem );
+			}
+			continue;
+		}
+
+		attached = isAttached( elem );
+
+		// Append to fragment
+		tmp = getAll( fragment.appendChild( elem ), "script" );
+
+		// Preserve script evaluation history
+		if ( attached ) {
+			setGlobalEval( tmp );
+		}
+
+		// Capture executables
+		if ( scripts ) {
+			j = 0;
+			while ( ( elem = tmp[ j++ ] ) ) {
+				if ( rscriptType.test( elem.type || "" ) ) {
+					scripts.push( elem );
+				}
+			}
+		}
+	}
+
+	return fragment;
+}
+
+
+var rtypenamespace = /^([^.]*)(?:\.(.+)|)/;
+
+function returnTrue() {
+	return true;
+}
+
+function returnFalse() {
+	return false;
+}
+
+// Support: IE <=9 - 11+
+// focus() and blur() are asynchronous, except when they are no-op.
+// So expect focus to be synchronous when the element is already active,
+// and blur to be synchronous when the element is not already active.
+// (focus and blur are always synchronous in other supported browsers,
+// this just defines when we can count on it).
+function expectSync( elem, type ) {
+	return ( elem === safeActiveElement() ) === ( type === "focus" );
+}
+
+// Support: IE <=9 only
+// Accessing document.activeElement can throw unexpectedly
+// https://bugs.jquery.com/ticket/13393
+function safeActiveElement() {
+	try {
+		return document.activeElement;
+	} catch ( err ) { }
+}
+
+function on( elem, types, selector, data, fn, one ) {
+	var origFn, type;
+
+	// Types can be a map of types/handlers
+	if ( typeof types === "object" ) {
+
+		// ( types-Object, selector, data )
+		if ( typeof selector !== "string" ) {
+
+			// ( types-Object, data )
+			data = data || selector;
+			selector = undefined;
+		}
+		for ( type in types ) {
+			on( elem, type, selector, data, types[ type ], one );
+		}
+		return elem;
+	}
+
+	if ( data == null && fn == null ) {
+
+		// ( types, fn )
+		fn = selector;
+		data = selector = undefined;
+	} else if ( fn == null ) {
+		if ( typeof selector === "string" ) {
+
+			// ( types, selector, fn )
+			fn = data;
+			data = undefined;
+		} else {
+
+			// ( types, data, fn )
+			fn = data;
+			data = selector;
+			selector = undefined;
+		}
+	}
+	if ( fn === false ) {
+		fn = returnFalse;
+	} else if ( !fn ) {
+		return elem;
+	}
+
+	if ( one === 1 ) {
+		origFn = fn;
+		fn = function( event ) {
+
+			// Can use an empty set, since event contains the info
+			jQuery().off( event );
+			return origFn.apply( this, arguments );
+		};
+
+		// Use same guid so caller can remove using origFn
+		fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ );
+	}
+	return elem.each( function() {
+		jQuery.event.add( this, types, fn, data, selector );
+	} );
+}
+
+/*
+ * Helper functions for managing events -- not part of the public interface.
+ * Props to Dean Edwards' addEvent library for many of the ideas.
+ */
+jQuery.event = {
+
+	global: {},
+
+	add: function( elem, types, handler, data, selector ) {
+
+		var handleObjIn, eventHandle, tmp,
+			events, t, handleObj,
+			special, handlers, type, namespaces, origType,
+			elemData = dataPriv.get( elem );
+
+		// Only attach events to objects that accept data
+		if ( !acceptData( elem ) ) {
+			return;
+		}
+
+		// Caller can pass in an object of custom data in lieu of the handler
+		if ( handler.handler ) {
+			handleObjIn = handler;
+			handler = handleObjIn.handler;
+			selector = handleObjIn.selector;
+		}
+
+		// Ensure that invalid selectors throw exceptions at attach time
+		// Evaluate against documentElement in case elem is a non-element node (e.g., document)
+		if ( selector ) {
+			jQuery.find.matchesSelector( documentElement, selector );
+		}
+
+		// Make sure that the handler has a unique ID, used to find/remove it later
+		if ( !handler.guid ) {
+			handler.guid = jQuery.guid++;
+		}
+
+		// Init the element's event structure and main handler, if this is the first
+		if ( !( events = elemData.events ) ) {
+			events = elemData.events = Object.create( null );
+		}
+		if ( !( eventHandle = elemData.handle ) ) {
+			eventHandle = elemData.handle = function( e ) {
+
+				// Discard the second event of a jQuery.event.trigger() and
+				// when an event is called after a page has unloaded
+				return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ?
+					jQuery.event.dispatch.apply( elem, arguments ) : undefined;
+			};
+		}
+
+		// Handle multiple events separated by a space
+		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+		t = types.length;
+		while ( t-- ) {
+			tmp = rtypenamespace.exec( types[ t ] ) || [];
+			type = origType = tmp[ 1 ];
+			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+			// There *must* be a type, no attaching namespace-only handlers
+			if ( !type ) {
+				continue;
+			}
+
+			// If event changes its type, use the special event handlers for the changed type
+			special = jQuery.event.special[ type ] || {};
+
+			// If selector defined, determine special event api type, otherwise given type
+			type = ( selector ? special.delegateType : special.bindType ) || type;
+
+			// Update special based on newly reset type
+			special = jQuery.event.special[ type ] || {};
+
+			// handleObj is passed to all event handlers
+			handleObj = jQuery.extend( {
+				type: type,
+				origType: origType,
+				data: data,
+				handler: handler,
+				guid: handler.guid,
+				selector: selector,
+				needsContext: selector && jQuery.expr.match.needsContext.test( selector ),
+				namespace: namespaces.join( "." )
+			}, handleObjIn );
+
+			// Init the event handler queue if we're the first
+			if ( !( handlers = events[ type ] ) ) {
+				handlers = events[ type ] = [];
+				handlers.delegateCount = 0;
+
+				// Only use addEventListener if the special events handler returns false
+				if ( !special.setup ||
+					special.setup.call( elem, data, namespaces, eventHandle ) === false ) {
+
+					if ( elem.addEventListener ) {
+						elem.addEventListener( type, eventHandle );
+					}
+				}
+			}
+
+			if ( special.add ) {
+				special.add.call( elem, handleObj );
+
+				if ( !handleObj.handler.guid ) {
+					handleObj.handler.guid = handler.guid;
+				}
+			}
+
+			// Add to the element's handler list, delegates in front
+			if ( selector ) {
+				handlers.splice( handlers.delegateCount++, 0, handleObj );
+			} else {
+				handlers.push( handleObj );
+			}
+
+			// Keep track of which events have ever been used, for event optimization
+			jQuery.event.global[ type ] = true;
+		}
+
+	},
+
+	// Detach an event or set of events from an element
+	remove: function( elem, types, handler, selector, mappedTypes ) {
+
+		var j, origCount, tmp,
+			events, t, handleObj,
+			special, handlers, type, namespaces, origType,
+			elemData = dataPriv.hasData( elem ) && dataPriv.get( elem );
+
+		if ( !elemData || !( events = elemData.events ) ) {
+			return;
+		}
+
+		// Once for each type.namespace in types; type may be omitted
+		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+		t = types.length;
+		while ( t-- ) {
+			tmp = rtypenamespace.exec( types[ t ] ) || [];
+			type = origType = tmp[ 1 ];
+			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+			// Unbind all events (on this namespace, if provided) for the element
+			if ( !type ) {
+				for ( type in events ) {
+					jQuery.event.remove( elem, type + types[ t ], handler, selector, true );
+				}
+				continue;
+			}
+
+			special = jQuery.event.special[ type ] || {};
+			type = ( selector ? special.delegateType : special.bindType ) || type;
+			handlers = events[ type ] || [];
+			tmp = tmp[ 2 ] &&
+				new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" );
+
+			// Remove matching events
+			origCount = j = handlers.length;
+			while ( j-- ) {
+				handleObj = handlers[ j ];
+
+				if ( ( mappedTypes || origType === handleObj.origType ) &&
+					( !handler || handler.guid === handleObj.guid ) &&
+					( !tmp || tmp.test( handleObj.namespace ) ) &&
+					( !selector || selector === handleObj.selector ||
+						selector === "**" && handleObj.selector ) ) {
+					handlers.splice( j, 1 );
+
+					if ( handleObj.selector ) {
+						handlers.delegateCount--;
+					}
+					if ( special.remove ) {
+						special.remove.call( elem, handleObj );
+					}
+				}
+			}
+
+			// Remove generic event handler if we removed something and no more handlers exist
+			// (avoids potential for endless recursion during removal of special event handlers)
+			if ( origCount && !handlers.length ) {
+				if ( !special.teardown ||
+					special.teardown.call( elem, namespaces, elemData.handle ) === false ) {
+
+					jQuery.removeEvent( elem, type, elemData.handle );
+				}
+
+				delete events[ type ];
+			}
+		}
+
+		// Remove data and the expando if it's no longer used
+		if ( jQuery.isEmptyObject( events ) ) {
+			dataPriv.remove( elem, "handle events" );
+		}
+	},
+
+	dispatch: function( nativeEvent ) {
+
+		var i, j, ret, matched, handleObj, handlerQueue,
+			args = new Array( arguments.length ),
+
+			// Make a writable jQuery.Event from the native event object
+			event = jQuery.event.fix( nativeEvent ),
+
+			handlers = (
+				dataPriv.get( this, "events" ) || Object.create( null )
+			)[ event.type ] || [],
+			special = jQuery.event.special[ event.type ] || {};
+
+		// Use the fix-ed jQuery.Event rather than the (read-only) native event
+		args[ 0 ] = event;
+
+		for ( i = 1; i < arguments.length; i++ ) {
+			args[ i ] = arguments[ i ];
+		}
+
+		event.delegateTarget = this;
+
+		// Call the preDispatch hook for the mapped type, and let it bail if desired
+		if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) {
+			return;
+		}
+
+		// Determine handlers
+		handlerQueue = jQuery.event.handlers.call( this, event, handlers );
+
+		// Run delegates first; they may want to stop propagation beneath us
+		i = 0;
+		while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) {
+			event.currentTarget = matched.elem;
+
+			j = 0;
+			while ( ( handleObj = matched.handlers[ j++ ] ) &&
+				!event.isImmediatePropagationStopped() ) {
+
+				// If the event is namespaced, then each handler is only invoked if it is
+				// specially universal or its namespaces are a superset of the event's.
+				if ( !event.rnamespace || handleObj.namespace === false ||
+					event.rnamespace.test( handleObj.namespace ) ) {
+
+					event.handleObj = handleObj;
+					event.data = handleObj.data;
+
+					ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle ||
+						handleObj.handler ).apply( matched.elem, args );
+
+					if ( ret !== undefined ) {
+						if ( ( event.result = ret ) === false ) {
+							event.preventDefault();
+							event.stopPropagation();
+						}
+					}
+				}
+			}
+		}
+
+		// Call the postDispatch hook for the mapped type
+		if ( special.postDispatch ) {
+			special.postDispatch.call( this, event );
+		}
+
+		return event.result;
+	},
+
+	handlers: function( event, handlers ) {
+		var i, handleObj, sel, matchedHandlers, matchedSelectors,
+			handlerQueue = [],
+			delegateCount = handlers.delegateCount,
+			cur = event.target;
+
+		// Find delegate handlers
+		if ( delegateCount &&
+
+			// Support: IE <=9
+			// Black-hole SVG  instance trees (trac-13180)
+			cur.nodeType &&
+
+			// Support: Firefox <=42
+			// Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861)
+			// https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click
+			// Support: IE 11 only
+			// ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343)
+			!( event.type === "click" && event.button >= 1 ) ) {
+
+			for ( ; cur !== this; cur = cur.parentNode || this ) {
+
+				// Don't check non-elements (#13208)
+				// Don't process clicks on disabled elements (#6911, #8165, #11382, #11764)
+				if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) {
+					matchedHandlers = [];
+					matchedSelectors = {};
+					for ( i = 0; i < delegateCount; i++ ) {
+						handleObj = handlers[ i ];
+
+						// Don't conflict with Object.prototype properties (#13203)
+						sel = handleObj.selector + " ";
+
+						if ( matchedSelectors[ sel ] === undefined ) {
+							matchedSelectors[ sel ] = handleObj.needsContext ?
+								jQuery( sel, this ).index( cur ) > -1 :
+								jQuery.find( sel, this, null, [ cur ] ).length;
+						}
+						if ( matchedSelectors[ sel ] ) {
+							matchedHandlers.push( handleObj );
+						}
+					}
+					if ( matchedHandlers.length ) {
+						handlerQueue.push( { elem: cur, handlers: matchedHandlers } );
+					}
+				}
+			}
+		}
+
+		// Add the remaining (directly-bound) handlers
+		cur = this;
+		if ( delegateCount < handlers.length ) {
+			handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } );
+		}
+
+		return handlerQueue;
+	},
+
+	addProp: function( name, hook ) {
+		Object.defineProperty( jQuery.Event.prototype, name, {
+			enumerable: true,
+			configurable: true,
+
+			get: isFunction( hook ) ?
+				function() {
+					if ( this.originalEvent ) {
+						return hook( this.originalEvent );
+					}
+				} :
+				function() {
+					if ( this.originalEvent ) {
+						return this.originalEvent[ name ];
+					}
+				},
+
+			set: function( value ) {
+				Object.defineProperty( this, name, {
+					enumerable: true,
+					configurable: true,
+					writable: true,
+					value: value
+				} );
+			}
+		} );
+	},
+
+	fix: function( originalEvent ) {
+		return originalEvent[ jQuery.expando ] ?
+			originalEvent :
+			new jQuery.Event( originalEvent );
+	},
+
+	special: {
+		load: {
+
+			// Prevent triggered image.load events from bubbling to window.load
+			noBubble: true
+		},
+		click: {
+
+			// Utilize native event to ensure correct state for checkable inputs
+			setup: function( data ) {
+
+				// For mutual compressibility with _default, replace `this` access with a local var.
+				// `|| data` is dead code meant only to preserve the variable through minification.
+				var el = this || data;
+
+				// Claim the first handler
+				if ( rcheckableType.test( el.type ) &&
+					el.click && nodeName( el, "input" ) ) {
+
+					// dataPriv.set( el, "click", ... )
+					leverageNative( el, "click", returnTrue );
+				}
+
+				// Return false to allow normal processing in the caller
+				return false;
+			},
+			trigger: function( data ) {
+
+				// For mutual compressibility with _default, replace `this` access with a local var.
+				// `|| data` is dead code meant only to preserve the variable through minification.
+				var el = this || data;
+
+				// Force setup before triggering a click
+				if ( rcheckableType.test( el.type ) &&
+					el.click && nodeName( el, "input" ) ) {
+
+					leverageNative( el, "click" );
+				}
+
+				// Return non-false to allow normal event-path propagation
+				return true;
+			},
+
+			// For cross-browser consistency, suppress native .click() on links
+			// Also prevent it if we're currently inside a leveraged native-event stack
+			_default: function( event ) {
+				var target = event.target;
+				return rcheckableType.test( target.type ) &&
+					target.click && nodeName( target, "input" ) &&
+					dataPriv.get( target, "click" ) ||
+					nodeName( target, "a" );
+			}
+		},
+
+		beforeunload: {
+			postDispatch: function( event ) {
+
+				// Support: Firefox 20+
+				// Firefox doesn't alert if the returnValue field is not set.
+				if ( event.result !== undefined && event.originalEvent ) {
+					event.originalEvent.returnValue = event.result;
+				}
+			}
+		}
+	}
+};
+
+// Ensure the presence of an event listener that handles manually-triggered
+// synthetic events by interrupting progress until reinvoked in response to
+// *native* events that it fires directly, ensuring that state changes have
+// already occurred before other listeners are invoked.
+function leverageNative( el, type, expectSync ) {
+
+	// Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add
+	if ( !expectSync ) {
+		if ( dataPriv.get( el, type ) === undefined ) {
+			jQuery.event.add( el, type, returnTrue );
+		}
+		return;
+	}
+
+	// Register the controller as a special universal handler for all event namespaces
+	dataPriv.set( el, type, false );
+	jQuery.event.add( el, type, {
+		namespace: false,
+		handler: function( event ) {
+			var notAsync, result,
+				saved = dataPriv.get( this, type );
+
+			if ( ( event.isTrigger & 1 ) && this[ type ] ) {
+
+				// Interrupt processing of the outer synthetic .trigger()ed event
+				// Saved data should be false in such cases, but might be a leftover capture object
+				// from an async native handler (gh-4350)
+				if ( !saved.length ) {
+
+					// Store arguments for use when handling the inner native event
+					// There will always be at least one argument (an event object), so this array
+					// will not be confused with a leftover capture object.
+					saved = slice.call( arguments );
+					dataPriv.set( this, type, saved );
+
+					// Trigger the native event and capture its result
+					// Support: IE <=9 - 11+
+					// focus() and blur() are asynchronous
+					notAsync = expectSync( this, type );
+					this[ type ]();
+					result = dataPriv.get( this, type );
+					if ( saved !== result || notAsync ) {
+						dataPriv.set( this, type, false );
+					} else {
+						result = {};
+					}
+					if ( saved !== result ) {
+
+						// Cancel the outer synthetic event
+						event.stopImmediatePropagation();
+						event.preventDefault();
+
+						// Support: Chrome 86+
+						// In Chrome, if an element having a focusout handler is blurred by
+						// clicking outside of it, it invokes the handler synchronously. If
+						// that handler calls `.remove()` on the element, the data is cleared,
+						// leaving `result` undefined. We need to guard against this.
+						return result && result.value;
+					}
+
+				// If this is an inner synthetic event for an event with a bubbling surrogate
+				// (focus or blur), assume that the surrogate already propagated from triggering the
+				// native event and prevent that from happening again here.
+				// This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the
+				// bubbling surrogate propagates *after* the non-bubbling base), but that seems
+				// less bad than duplication.
+				} else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) {
+					event.stopPropagation();
+				}
+
+			// If this is a native event triggered above, everything is now in order
+			// Fire an inner synthetic event with the original arguments
+			} else if ( saved.length ) {
+
+				// ...and capture the result
+				dataPriv.set( this, type, {
+					value: jQuery.event.trigger(
+
+						// Support: IE <=9 - 11+
+						// Extend with the prototype to reset the above stopImmediatePropagation()
+						jQuery.extend( saved[ 0 ], jQuery.Event.prototype ),
+						saved.slice( 1 ),
+						this
+					)
+				} );
+
+				// Abort handling of the native event
+				event.stopImmediatePropagation();
+			}
+		}
+	} );
+}
+
+jQuery.removeEvent = function( elem, type, handle ) {
+
+	// This "if" is needed for plain objects
+	if ( elem.removeEventListener ) {
+		elem.removeEventListener( type, handle );
+	}
+};
+
+jQuery.Event = function( src, props ) {
+
+	// Allow instantiation without the 'new' keyword
+	if ( !( this instanceof jQuery.Event ) ) {
+		return new jQuery.Event( src, props );
+	}
+
+	// Event object
+	if ( src && src.type ) {
+		this.originalEvent = src;
+		this.type = src.type;
+
+		// Events bubbling up the document may have been marked as prevented
+		// by a handler lower down the tree; reflect the correct value.
+		this.isDefaultPrevented = src.defaultPrevented ||
+				src.defaultPrevented === undefined &&
+
+				// Support: Android <=2.3 only
+				src.returnValue === false ?
+			returnTrue :
+			returnFalse;
+
+		// Create target properties
+		// Support: Safari <=6 - 7 only
+		// Target should not be a text node (#504, #13143)
+		this.target = ( src.target && src.target.nodeType === 3 ) ?
+			src.target.parentNode :
+			src.target;
+
+		this.currentTarget = src.currentTarget;
+		this.relatedTarget = src.relatedTarget;
+
+	// Event type
+	} else {
+		this.type = src;
+	}
+
+	// Put explicitly provided properties onto the event object
+	if ( props ) {
+		jQuery.extend( this, props );
+	}
+
+	// Create a timestamp if incoming event doesn't have one
+	this.timeStamp = src && src.timeStamp || Date.now();
+
+	// Mark it as fixed
+	this[ jQuery.expando ] = true;
+};
+
+// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding
+// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html
+jQuery.Event.prototype = {
+	constructor: jQuery.Event,
+	isDefaultPrevented: returnFalse,
+	isPropagationStopped: returnFalse,
+	isImmediatePropagationStopped: returnFalse,
+	isSimulated: false,
+
+	preventDefault: function() {
+		var e = this.originalEvent;
+
+		this.isDefaultPrevented = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.preventDefault();
+		}
+	},
+	stopPropagation: function() {
+		var e = this.originalEvent;
+
+		this.isPropagationStopped = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.stopPropagation();
+		}
+	},
+	stopImmediatePropagation: function() {
+		var e = this.originalEvent;
+
+		this.isImmediatePropagationStopped = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.stopImmediatePropagation();
+		}
+
+		this.stopPropagation();
+	}
+};
+
+// Includes all common event props including KeyEvent and MouseEvent specific props
+jQuery.each( {
+	altKey: true,
+	bubbles: true,
+	cancelable: true,
+	changedTouches: true,
+	ctrlKey: true,
+	detail: true,
+	eventPhase: true,
+	metaKey: true,
+	pageX: true,
+	pageY: true,
+	shiftKey: true,
+	view: true,
+	"char": true,
+	code: true,
+	charCode: true,
+	key: true,
+	keyCode: true,
+	button: true,
+	buttons: true,
+	clientX: true,
+	clientY: true,
+	offsetX: true,
+	offsetY: true,
+	pointerId: true,
+	pointerType: true,
+	screenX: true,
+	screenY: true,
+	targetTouches: true,
+	toElement: true,
+	touches: true,
+	which: true
+}, jQuery.event.addProp );
+
+jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) {
+	jQuery.event.special[ type ] = {
+
+		// Utilize native event if possible so blur/focus sequence is correct
+		setup: function() {
+
+			// Claim the first handler
+			// dataPriv.set( this, "focus", ... )
+			// dataPriv.set( this, "blur", ... )
+			leverageNative( this, type, expectSync );
+
+			// Return false to allow normal processing in the caller
+			return false;
+		},
+		trigger: function() {
+
+			// Force setup before trigger
+			leverageNative( this, type );
+
+			// Return non-false to allow normal event-path propagation
+			return true;
+		},
+
+		// Suppress native focus or blur as it's already being fired
+		// in leverageNative.
+		_default: function() {
+			return true;
+		},
+
+		delegateType: delegateType
+	};
+} );
+
+// Create mouseenter/leave events using mouseover/out and event-time checks
+// so that event delegation works in jQuery.
+// Do the same for pointerenter/pointerleave and pointerover/pointerout
+//
+// Support: Safari 7 only
+// Safari sends mouseenter too often; see:
+// https://bugs.chromium.org/p/chromium/issues/detail?id=470258
+// for the description of the bug (it existed in older Chrome versions as well).
+jQuery.each( {
+	mouseenter: "mouseover",
+	mouseleave: "mouseout",
+	pointerenter: "pointerover",
+	pointerleave: "pointerout"
+}, function( orig, fix ) {
+	jQuery.event.special[ orig ] = {
+		delegateType: fix,
+		bindType: fix,
+
+		handle: function( event ) {
+			var ret,
+				target = this,
+				related = event.relatedTarget,
+				handleObj = event.handleObj;
+
+			// For mouseenter/leave call the handler if related is outside the target.
+			// NB: No relatedTarget if the mouse left/entered the browser window
+			if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) {
+				event.type = handleObj.origType;
+				ret = handleObj.handler.apply( this, arguments );
+				event.type = fix;
+			}
+			return ret;
+		}
+	};
+} );
+
+jQuery.fn.extend( {
+
+	on: function( types, selector, data, fn ) {
+		return on( this, types, selector, data, fn );
+	},
+	one: function( types, selector, data, fn ) {
+		return on( this, types, selector, data, fn, 1 );
+	},
+	off: function( types, selector, fn ) {
+		var handleObj, type;
+		if ( types && types.preventDefault && types.handleObj ) {
+
+			// ( event )  dispatched jQuery.Event
+			handleObj = types.handleObj;
+			jQuery( types.delegateTarget ).off(
+				handleObj.namespace ?
+					handleObj.origType + "." + handleObj.namespace :
+					handleObj.origType,
+				handleObj.selector,
+				handleObj.handler
+			);
+			return this;
+		}
+		if ( typeof types === "object" ) {
+
+			// ( types-object [, selector] )
+			for ( type in types ) {
+				this.off( type, selector, types[ type ] );
+			}
+			return this;
+		}
+		if ( selector === false || typeof selector === "function" ) {
+
+			// ( types [, fn] )
+			fn = selector;
+			selector = undefined;
+		}
+		if ( fn === false ) {
+			fn = returnFalse;
+		}
+		return this.each( function() {
+			jQuery.event.remove( this, types, fn, selector );
+		} );
+	}
+} );
+
+
+var
+
+	// Support: IE <=10 - 11, Edge 12 - 13 only
+	// In IE/Edge using regex groups here causes severe slowdowns.
+	// See https://connect.microsoft.com/IE/feedback/details/1736512/
+	rnoInnerhtml = /\s*$/g;
+
+// Prefer a tbody over its parent table for containing new rows
+function manipulationTarget( elem, content ) {
+	if ( nodeName( elem, "table" ) &&
+		nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) {
+
+		return jQuery( elem ).children( "tbody" )[ 0 ] || elem;
+	}
+
+	return elem;
+}
+
+// Replace/restore the type attribute of script elements for safe DOM manipulation
+function disableScript( elem ) {
+	elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type;
+	return elem;
+}
+function restoreScript( elem ) {
+	if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) {
+		elem.type = elem.type.slice( 5 );
+	} else {
+		elem.removeAttribute( "type" );
+	}
+
+	return elem;
+}
+
+function cloneCopyEvent( src, dest ) {
+	var i, l, type, pdataOld, udataOld, udataCur, events;
+
+	if ( dest.nodeType !== 1 ) {
+		return;
+	}
+
+	// 1. Copy private data: events, handlers, etc.
+	if ( dataPriv.hasData( src ) ) {
+		pdataOld = dataPriv.get( src );
+		events = pdataOld.events;
+
+		if ( events ) {
+			dataPriv.remove( dest, "handle events" );
+
+			for ( type in events ) {
+				for ( i = 0, l = events[ type ].length; i < l; i++ ) {
+					jQuery.event.add( dest, type, events[ type ][ i ] );
+				}
+			}
+		}
+	}
+
+	// 2. Copy user data
+	if ( dataUser.hasData( src ) ) {
+		udataOld = dataUser.access( src );
+		udataCur = jQuery.extend( {}, udataOld );
+
+		dataUser.set( dest, udataCur );
+	}
+}
+
+// Fix IE bugs, see support tests
+function fixInput( src, dest ) {
+	var nodeName = dest.nodeName.toLowerCase();
+
+	// Fails to persist the checked state of a cloned checkbox or radio button.
+	if ( nodeName === "input" && rcheckableType.test( src.type ) ) {
+		dest.checked = src.checked;
+
+	// Fails to return the selected option to the default selected state when cloning options
+	} else if ( nodeName === "input" || nodeName === "textarea" ) {
+		dest.defaultValue = src.defaultValue;
+	}
+}
+
+function domManip( collection, args, callback, ignored ) {
+
+	// Flatten any nested arrays
+	args = flat( args );
+
+	var fragment, first, scripts, hasScripts, node, doc,
+		i = 0,
+		l = collection.length,
+		iNoClone = l - 1,
+		value = args[ 0 ],
+		valueIsFunction = isFunction( value );
+
+	// We can't cloneNode fragments that contain checked, in WebKit
+	if ( valueIsFunction ||
+			( l > 1 && typeof value === "string" &&
+				!support.checkClone && rchecked.test( value ) ) ) {
+		return collection.each( function( index ) {
+			var self = collection.eq( index );
+			if ( valueIsFunction ) {
+				args[ 0 ] = value.call( this, index, self.html() );
+			}
+			domManip( self, args, callback, ignored );
+		} );
+	}
+
+	if ( l ) {
+		fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored );
+		first = fragment.firstChild;
+
+		if ( fragment.childNodes.length === 1 ) {
+			fragment = first;
+		}
+
+		// Require either new content or an interest in ignored elements to invoke the callback
+		if ( first || ignored ) {
+			scripts = jQuery.map( getAll( fragment, "script" ), disableScript );
+			hasScripts = scripts.length;
+
+			// Use the original fragment for the last item
+			// instead of the first because it can end up
+			// being emptied incorrectly in certain situations (#8070).
+			for ( ; i < l; i++ ) {
+				node = fragment;
+
+				if ( i !== iNoClone ) {
+					node = jQuery.clone( node, true, true );
+
+					// Keep references to cloned scripts for later restoration
+					if ( hasScripts ) {
+
+						// Support: Android <=4.0 only, PhantomJS 1 only
+						// push.apply(_, arraylike) throws on ancient WebKit
+						jQuery.merge( scripts, getAll( node, "script" ) );
+					}
+				}
+
+				callback.call( collection[ i ], node, i );
+			}
+
+			if ( hasScripts ) {
+				doc = scripts[ scripts.length - 1 ].ownerDocument;
+
+				// Reenable scripts
+				jQuery.map( scripts, restoreScript );
+
+				// Evaluate executable scripts on first document insertion
+				for ( i = 0; i < hasScripts; i++ ) {
+					node = scripts[ i ];
+					if ( rscriptType.test( node.type || "" ) &&
+						!dataPriv.access( node, "globalEval" ) &&
+						jQuery.contains( doc, node ) ) {
+
+						if ( node.src && ( node.type || "" ).toLowerCase()  !== "module" ) {
+
+							// Optional AJAX dependency, but won't run scripts if not present
+							if ( jQuery._evalUrl && !node.noModule ) {
+								jQuery._evalUrl( node.src, {
+									nonce: node.nonce || node.getAttribute( "nonce" )
+								}, doc );
+							}
+						} else {
+							DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc );
+						}
+					}
+				}
+			}
+		}
+	}
+
+	return collection;
+}
+
+function remove( elem, selector, keepData ) {
+	var node,
+		nodes = selector ? jQuery.filter( selector, elem ) : elem,
+		i = 0;
+
+	for ( ; ( node = nodes[ i ] ) != null; i++ ) {
+		if ( !keepData && node.nodeType === 1 ) {
+			jQuery.cleanData( getAll( node ) );
+		}
+
+		if ( node.parentNode ) {
+			if ( keepData && isAttached( node ) ) {
+				setGlobalEval( getAll( node, "script" ) );
+			}
+			node.parentNode.removeChild( node );
+		}
+	}
+
+	return elem;
+}
+
+jQuery.extend( {
+	htmlPrefilter: function( html ) {
+		return html;
+	},
+
+	clone: function( elem, dataAndEvents, deepDataAndEvents ) {
+		var i, l, srcElements, destElements,
+			clone = elem.cloneNode( true ),
+			inPage = isAttached( elem );
+
+		// Fix IE cloning issues
+		if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) &&
+				!jQuery.isXMLDoc( elem ) ) {
+
+			// We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2
+			destElements = getAll( clone );
+			srcElements = getAll( elem );
+
+			for ( i = 0, l = srcElements.length; i < l; i++ ) {
+				fixInput( srcElements[ i ], destElements[ i ] );
+			}
+		}
+
+		// Copy the events from the original to the clone
+		if ( dataAndEvents ) {
+			if ( deepDataAndEvents ) {
+				srcElements = srcElements || getAll( elem );
+				destElements = destElements || getAll( clone );
+
+				for ( i = 0, l = srcElements.length; i < l; i++ ) {
+					cloneCopyEvent( srcElements[ i ], destElements[ i ] );
+				}
+			} else {
+				cloneCopyEvent( elem, clone );
+			}
+		}
+
+		// Preserve script evaluation history
+		destElements = getAll( clone, "script" );
+		if ( destElements.length > 0 ) {
+			setGlobalEval( destElements, !inPage && getAll( elem, "script" ) );
+		}
+
+		// Return the cloned set
+		return clone;
+	},
+
+	cleanData: function( elems ) {
+		var data, elem, type,
+			special = jQuery.event.special,
+			i = 0;
+
+		for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) {
+			if ( acceptData( elem ) ) {
+				if ( ( data = elem[ dataPriv.expando ] ) ) {
+					if ( data.events ) {
+						for ( type in data.events ) {
+							if ( special[ type ] ) {
+								jQuery.event.remove( elem, type );
+
+							// This is a shortcut to avoid jQuery.event.remove's overhead
+							} else {
+								jQuery.removeEvent( elem, type, data.handle );
+							}
+						}
+					}
+
+					// Support: Chrome <=35 - 45+
+					// Assign undefined instead of using delete, see Data#remove
+					elem[ dataPriv.expando ] = undefined;
+				}
+				if ( elem[ dataUser.expando ] ) {
+
+					// Support: Chrome <=35 - 45+
+					// Assign undefined instead of using delete, see Data#remove
+					elem[ dataUser.expando ] = undefined;
+				}
+			}
+		}
+	}
+} );
+
+jQuery.fn.extend( {
+	detach: function( selector ) {
+		return remove( this, selector, true );
+	},
+
+	remove: function( selector ) {
+		return remove( this, selector );
+	},
+
+	text: function( value ) {
+		return access( this, function( value ) {
+			return value === undefined ?
+				jQuery.text( this ) :
+				this.empty().each( function() {
+					if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+						this.textContent = value;
+					}
+				} );
+		}, null, value, arguments.length );
+	},
+
+	append: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+				var target = manipulationTarget( this, elem );
+				target.appendChild( elem );
+			}
+		} );
+	},
+
+	prepend: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+				var target = manipulationTarget( this, elem );
+				target.insertBefore( elem, target.firstChild );
+			}
+		} );
+	},
+
+	before: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.parentNode ) {
+				this.parentNode.insertBefore( elem, this );
+			}
+		} );
+	},
+
+	after: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.parentNode ) {
+				this.parentNode.insertBefore( elem, this.nextSibling );
+			}
+		} );
+	},
+
+	empty: function() {
+		var elem,
+			i = 0;
+
+		for ( ; ( elem = this[ i ] ) != null; i++ ) {
+			if ( elem.nodeType === 1 ) {
+
+				// Prevent memory leaks
+				jQuery.cleanData( getAll( elem, false ) );
+
+				// Remove any remaining nodes
+				elem.textContent = "";
+			}
+		}
+
+		return this;
+	},
+
+	clone: function( dataAndEvents, deepDataAndEvents ) {
+		dataAndEvents = dataAndEvents == null ? false : dataAndEvents;
+		deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents;
+
+		return this.map( function() {
+			return jQuery.clone( this, dataAndEvents, deepDataAndEvents );
+		} );
+	},
+
+	html: function( value ) {
+		return access( this, function( value ) {
+			var elem = this[ 0 ] || {},
+				i = 0,
+				l = this.length;
+
+			if ( value === undefined && elem.nodeType === 1 ) {
+				return elem.innerHTML;
+			}
+
+			// See if we can take a shortcut and just use innerHTML
+			if ( typeof value === "string" && !rnoInnerhtml.test( value ) &&
+				!wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) {
+
+				value = jQuery.htmlPrefilter( value );
+
+				try {
+					for ( ; i < l; i++ ) {
+						elem = this[ i ] || {};
+
+						// Remove element nodes and prevent memory leaks
+						if ( elem.nodeType === 1 ) {
+							jQuery.cleanData( getAll( elem, false ) );
+							elem.innerHTML = value;
+						}
+					}
+
+					elem = 0;
+
+				// If using innerHTML throws an exception, use the fallback method
+				} catch ( e ) {}
+			}
+
+			if ( elem ) {
+				this.empty().append( value );
+			}
+		}, null, value, arguments.length );
+	},
+
+	replaceWith: function() {
+		var ignored = [];
+
+		// Make the changes, replacing each non-ignored context element with the new content
+		return domManip( this, arguments, function( elem ) {
+			var parent = this.parentNode;
+
+			if ( jQuery.inArray( this, ignored ) < 0 ) {
+				jQuery.cleanData( getAll( this ) );
+				if ( parent ) {
+					parent.replaceChild( elem, this );
+				}
+			}
+
+		// Force callback invocation
+		}, ignored );
+	}
+} );
+
+jQuery.each( {
+	appendTo: "append",
+	prependTo: "prepend",
+	insertBefore: "before",
+	insertAfter: "after",
+	replaceAll: "replaceWith"
+}, function( name, original ) {
+	jQuery.fn[ name ] = function( selector ) {
+		var elems,
+			ret = [],
+			insert = jQuery( selector ),
+			last = insert.length - 1,
+			i = 0;
+
+		for ( ; i <= last; i++ ) {
+			elems = i === last ? this : this.clone( true );
+			jQuery( insert[ i ] )[ original ]( elems );
+
+			// Support: Android <=4.0 only, PhantomJS 1 only
+			// .get() because push.apply(_, arraylike) throws on ancient WebKit
+			push.apply( ret, elems.get() );
+		}
+
+		return this.pushStack( ret );
+	};
+} );
+var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" );
+
+var getStyles = function( elem ) {
+
+		// Support: IE <=11 only, Firefox <=30 (#15098, #14150)
+		// IE throws on elements created in popups
+		// FF meanwhile throws on frame elements through "defaultView.getComputedStyle"
+		var view = elem.ownerDocument.defaultView;
+
+		if ( !view || !view.opener ) {
+			view = window;
+		}
+
+		return view.getComputedStyle( elem );
+	};
+
+var swap = function( elem, options, callback ) {
+	var ret, name,
+		old = {};
+
+	// Remember the old values, and insert the new ones
+	for ( name in options ) {
+		old[ name ] = elem.style[ name ];
+		elem.style[ name ] = options[ name ];
+	}
+
+	ret = callback.call( elem );
+
+	// Revert the old values
+	for ( name in options ) {
+		elem.style[ name ] = old[ name ];
+	}
+
+	return ret;
+};
+
+
+var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" );
+
+
+
+( function() {
+
+	// Executing both pixelPosition & boxSizingReliable tests require only one layout
+	// so they're executed at the same time to save the second computation.
+	function computeStyleTests() {
+
+		// This is a singleton, we need to execute it only once
+		if ( !div ) {
+			return;
+		}
+
+		container.style.cssText = "position:absolute;left:-11111px;width:60px;" +
+			"margin-top:1px;padding:0;border:0";
+		div.style.cssText =
+			"position:relative;display:block;box-sizing:border-box;overflow:scroll;" +
+			"margin:auto;border:1px;padding:1px;" +
+			"width:60%;top:1%";
+		documentElement.appendChild( container ).appendChild( div );
+
+		var divStyle = window.getComputedStyle( div );
+		pixelPositionVal = divStyle.top !== "1%";
+
+		// Support: Android 4.0 - 4.3 only, Firefox <=3 - 44
+		reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12;
+
+		// Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3
+		// Some styles come back with percentage values, even though they shouldn't
+		div.style.right = "60%";
+		pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36;
+
+		// Support: IE 9 - 11 only
+		// Detect misreporting of content dimensions for box-sizing:border-box elements
+		boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36;
+
+		// Support: IE 9 only
+		// Detect overflow:scroll screwiness (gh-3699)
+		// Support: Chrome <=64
+		// Don't get tricked when zoom affects offsetWidth (gh-4029)
+		div.style.position = "absolute";
+		scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12;
+
+		documentElement.removeChild( container );
+
+		// Nullify the div so it wouldn't be stored in the memory and
+		// it will also be a sign that checks already performed
+		div = null;
+	}
+
+	function roundPixelMeasures( measure ) {
+		return Math.round( parseFloat( measure ) );
+	}
+
+	var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal,
+		reliableTrDimensionsVal, reliableMarginLeftVal,
+		container = document.createElement( "div" ),
+		div = document.createElement( "div" );
+
+	// Finish early in limited (non-browser) environments
+	if ( !div.style ) {
+		return;
+	}
+
+	// Support: IE <=9 - 11 only
+	// Style of cloned element affects source element cloned (#8908)
+	div.style.backgroundClip = "content-box";
+	div.cloneNode( true ).style.backgroundClip = "";
+	support.clearCloneStyle = div.style.backgroundClip === "content-box";
+
+	jQuery.extend( support, {
+		boxSizingReliable: function() {
+			computeStyleTests();
+			return boxSizingReliableVal;
+		},
+		pixelBoxStyles: function() {
+			computeStyleTests();
+			return pixelBoxStylesVal;
+		},
+		pixelPosition: function() {
+			computeStyleTests();
+			return pixelPositionVal;
+		},
+		reliableMarginLeft: function() {
+			computeStyleTests();
+			return reliableMarginLeftVal;
+		},
+		scrollboxSize: function() {
+			computeStyleTests();
+			return scrollboxSizeVal;
+		},
+
+		// Support: IE 9 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Behavior in IE 9 is more subtle than in newer versions & it passes
+		// some versions of this test; make sure not to make it pass there!
+		//
+		// Support: Firefox 70+
+		// Only Firefox includes border widths
+		// in computed dimensions. (gh-4529)
+		reliableTrDimensions: function() {
+			var table, tr, trChild, trStyle;
+			if ( reliableTrDimensionsVal == null ) {
+				table = document.createElement( "table" );
+				tr = document.createElement( "tr" );
+				trChild = document.createElement( "div" );
+
+				table.style.cssText = "position:absolute;left:-11111px;border-collapse:separate";
+				tr.style.cssText = "border:1px solid";
+
+				// Support: Chrome 86+
+				// Height set through cssText does not get applied.
+				// Computed height then comes back as 0.
+				tr.style.height = "1px";
+				trChild.style.height = "9px";
+
+				// Support: Android 8 Chrome 86+
+				// In our bodyBackground.html iframe,
+				// display for all div elements is set to "inline",
+				// which causes a problem only in Android 8 Chrome 86.
+				// Ensuring the div is display: block
+				// gets around this issue.
+				trChild.style.display = "block";
+
+				documentElement
+					.appendChild( table )
+					.appendChild( tr )
+					.appendChild( trChild );
+
+				trStyle = window.getComputedStyle( tr );
+				reliableTrDimensionsVal = ( parseInt( trStyle.height, 10 ) +
+					parseInt( trStyle.borderTopWidth, 10 ) +
+					parseInt( trStyle.borderBottomWidth, 10 ) ) === tr.offsetHeight;
+
+				documentElement.removeChild( table );
+			}
+			return reliableTrDimensionsVal;
+		}
+	} );
+} )();
+
+
+function curCSS( elem, name, computed ) {
+	var width, minWidth, maxWidth, ret,
+
+		// Support: Firefox 51+
+		// Retrieving style before computed somehow
+		// fixes an issue with getting wrong values
+		// on detached elements
+		style = elem.style;
+
+	computed = computed || getStyles( elem );
+
+	// getPropertyValue is needed for:
+	//   .css('filter') (IE 9 only, #12537)
+	//   .css('--customProperty) (#3144)
+	if ( computed ) {
+		ret = computed.getPropertyValue( name ) || computed[ name ];
+
+		if ( ret === "" && !isAttached( elem ) ) {
+			ret = jQuery.style( elem, name );
+		}
+
+		// A tribute to the "awesome hack by Dean Edwards"
+		// Android Browser returns percentage for some values,
+		// but width seems to be reliably pixels.
+		// This is against the CSSOM draft spec:
+		// https://drafts.csswg.org/cssom/#resolved-values
+		if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) {
+
+			// Remember the original values
+			width = style.width;
+			minWidth = style.minWidth;
+			maxWidth = style.maxWidth;
+
+			// Put in the new values to get a computed value out
+			style.minWidth = style.maxWidth = style.width = ret;
+			ret = computed.width;
+
+			// Revert the changed values
+			style.width = width;
+			style.minWidth = minWidth;
+			style.maxWidth = maxWidth;
+		}
+	}
+
+	return ret !== undefined ?
+
+		// Support: IE <=9 - 11 only
+		// IE returns zIndex value as an integer.
+		ret + "" :
+		ret;
+}
+
+
+function addGetHookIf( conditionFn, hookFn ) {
+
+	// Define the hook, we'll check on the first run if it's really needed.
+	return {
+		get: function() {
+			if ( conditionFn() ) {
+
+				// Hook not needed (or it's not possible to use it due
+				// to missing dependency), remove it.
+				delete this.get;
+				return;
+			}
+
+			// Hook needed; redefine it so that the support test is not executed again.
+			return ( this.get = hookFn ).apply( this, arguments );
+		}
+	};
+}
+
+
+var cssPrefixes = [ "Webkit", "Moz", "ms" ],
+	emptyStyle = document.createElement( "div" ).style,
+	vendorProps = {};
+
+// Return a vendor-prefixed property or undefined
+function vendorPropName( name ) {
+
+	// Check for vendor prefixed names
+	var capName = name[ 0 ].toUpperCase() + name.slice( 1 ),
+		i = cssPrefixes.length;
+
+	while ( i-- ) {
+		name = cssPrefixes[ i ] + capName;
+		if ( name in emptyStyle ) {
+			return name;
+		}
+	}
+}
+
+// Return a potentially-mapped jQuery.cssProps or vendor prefixed property
+function finalPropName( name ) {
+	var final = jQuery.cssProps[ name ] || vendorProps[ name ];
+
+	if ( final ) {
+		return final;
+	}
+	if ( name in emptyStyle ) {
+		return name;
+	}
+	return vendorProps[ name ] = vendorPropName( name ) || name;
+}
+
+
+var
+
+	// Swappable if display is none or starts with table
+	// except "table", "table-cell", or "table-caption"
+	// See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display
+	rdisplayswap = /^(none|table(?!-c[ea]).+)/,
+	rcustomProp = /^--/,
+	cssShow = { position: "absolute", visibility: "hidden", display: "block" },
+	cssNormalTransform = {
+		letterSpacing: "0",
+		fontWeight: "400"
+	};
+
+function setPositiveNumber( _elem, value, subtract ) {
+
+	// Any relative (+/-) values have already been
+	// normalized at this point
+	var matches = rcssNum.exec( value );
+	return matches ?
+
+		// Guard against undefined "subtract", e.g., when used as in cssHooks
+		Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) :
+		value;
+}
+
+function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) {
+	var i = dimension === "width" ? 1 : 0,
+		extra = 0,
+		delta = 0;
+
+	// Adjustment may not be necessary
+	if ( box === ( isBorderBox ? "border" : "content" ) ) {
+		return 0;
+	}
+
+	for ( ; i < 4; i += 2 ) {
+
+		// Both box models exclude margin
+		if ( box === "margin" ) {
+			delta += jQuery.css( elem, box + cssExpand[ i ], true, styles );
+		}
+
+		// If we get here with a content-box, we're seeking "padding" or "border" or "margin"
+		if ( !isBorderBox ) {
+
+			// Add padding
+			delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+
+			// For "border" or "margin", add border
+			if ( box !== "padding" ) {
+				delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+
+			// But still keep track of it otherwise
+			} else {
+				extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+			}
+
+		// If we get here with a border-box (content + padding + border), we're seeking "content" or
+		// "padding" or "margin"
+		} else {
+
+			// For "content", subtract padding
+			if ( box === "content" ) {
+				delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+			}
+
+			// For "content" or "padding", subtract border
+			if ( box !== "margin" ) {
+				delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+			}
+		}
+	}
+
+	// Account for positive content-box scroll gutter when requested by providing computedVal
+	if ( !isBorderBox && computedVal >= 0 ) {
+
+		// offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border
+		// Assuming integer scroll gutter, subtract the rest and round down
+		delta += Math.max( 0, Math.ceil(
+			elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+			computedVal -
+			delta -
+			extra -
+			0.5
+
+		// If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter
+		// Use an explicit zero to avoid NaN (gh-3964)
+		) ) || 0;
+	}
+
+	return delta;
+}
+
+function getWidthOrHeight( elem, dimension, extra ) {
+
+	// Start with computed style
+	var styles = getStyles( elem ),
+
+		// To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322).
+		// Fake content-box until we know it's needed to know the true value.
+		boxSizingNeeded = !support.boxSizingReliable() || extra,
+		isBorderBox = boxSizingNeeded &&
+			jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+		valueIsBorderBox = isBorderBox,
+
+		val = curCSS( elem, dimension, styles ),
+		offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 );
+
+	// Support: Firefox <=54
+	// Return a confounding non-pixel value or feign ignorance, as appropriate.
+	if ( rnumnonpx.test( val ) ) {
+		if ( !extra ) {
+			return val;
+		}
+		val = "auto";
+	}
+
+
+	// Support: IE 9 - 11 only
+	// Use offsetWidth/offsetHeight for when box sizing is unreliable.
+	// In those cases, the computed value can be trusted to be border-box.
+	if ( ( !support.boxSizingReliable() && isBorderBox ||
+
+		// Support: IE 10 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Interestingly, in some cases IE 9 doesn't suffer from this issue.
+		!support.reliableTrDimensions() && nodeName( elem, "tr" ) ||
+
+		// Fall back to offsetWidth/offsetHeight when value is "auto"
+		// This happens for inline elements with no explicit setting (gh-3571)
+		val === "auto" ||
+
+		// Support: Android <=4.1 - 4.3 only
+		// Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602)
+		!parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) &&
+
+		// Make sure the element is visible & connected
+		elem.getClientRects().length ) {
+
+		isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box";
+
+		// Where available, offsetWidth/offsetHeight approximate border box dimensions.
+		// Where not available (e.g., SVG), assume unreliable box-sizing and interpret the
+		// retrieved value as a content box dimension.
+		valueIsBorderBox = offsetProp in elem;
+		if ( valueIsBorderBox ) {
+			val = elem[ offsetProp ];
+		}
+	}
+
+	// Normalize "" and auto
+	val = parseFloat( val ) || 0;
+
+	// Adjust for the element's box model
+	return ( val +
+		boxModelAdjustment(
+			elem,
+			dimension,
+			extra || ( isBorderBox ? "border" : "content" ),
+			valueIsBorderBox,
+			styles,
+
+			// Provide the current computed size to request scroll gutter calculation (gh-3589)
+			val
+		)
+	) + "px";
+}
+
+jQuery.extend( {
+
+	// Add in style property hooks for overriding the default
+	// behavior of getting and setting a style property
+	cssHooks: {
+		opacity: {
+			get: function( elem, computed ) {
+				if ( computed ) {
+
+					// We should always get a number back from opacity
+					var ret = curCSS( elem, "opacity" );
+					return ret === "" ? "1" : ret;
+				}
+			}
+		}
+	},
+
+	// Don't automatically add "px" to these possibly-unitless properties
+	cssNumber: {
+		"animationIterationCount": true,
+		"columnCount": true,
+		"fillOpacity": true,
+		"flexGrow": true,
+		"flexShrink": true,
+		"fontWeight": true,
+		"gridArea": true,
+		"gridColumn": true,
+		"gridColumnEnd": true,
+		"gridColumnStart": true,
+		"gridRow": true,
+		"gridRowEnd": true,
+		"gridRowStart": true,
+		"lineHeight": true,
+		"opacity": true,
+		"order": true,
+		"orphans": true,
+		"widows": true,
+		"zIndex": true,
+		"zoom": true
+	},
+
+	// Add in properties whose names you wish to fix before
+	// setting or getting the value
+	cssProps: {},
+
+	// Get and set the style property on a DOM Node
+	style: function( elem, name, value, extra ) {
+
+		// Don't set styles on text and comment nodes
+		if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) {
+			return;
+		}
+
+		// Make sure that we're working with the right name
+		var ret, type, hooks,
+			origName = camelCase( name ),
+			isCustomProp = rcustomProp.test( name ),
+			style = elem.style;
+
+		// Make sure that we're working with the right name. We don't
+		// want to query the value if it is a CSS custom property
+		// since they are user-defined.
+		if ( !isCustomProp ) {
+			name = finalPropName( origName );
+		}
+
+		// Gets hook for the prefixed version, then unprefixed version
+		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+		// Check if we're setting a value
+		if ( value !== undefined ) {
+			type = typeof value;
+
+			// Convert "+=" or "-=" to relative numbers (#7345)
+			if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) {
+				value = adjustCSS( elem, name, ret );
+
+				// Fixes bug #9237
+				type = "number";
+			}
+
+			// Make sure that null and NaN values aren't set (#7116)
+			if ( value == null || value !== value ) {
+				return;
+			}
+
+			// If a number was passed in, add the unit (except for certain CSS properties)
+			// The isCustomProp check can be removed in jQuery 4.0 when we only auto-append
+			// "px" to a few hardcoded values.
+			if ( type === "number" && !isCustomProp ) {
+				value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" );
+			}
+
+			// background-* props affect original clone's values
+			if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) {
+				style[ name ] = "inherit";
+			}
+
+			// If a hook was provided, use that value, otherwise just set the specified value
+			if ( !hooks || !( "set" in hooks ) ||
+				( value = hooks.set( elem, value, extra ) ) !== undefined ) {
+
+				if ( isCustomProp ) {
+					style.setProperty( name, value );
+				} else {
+					style[ name ] = value;
+				}
+			}
+
+		} else {
+
+			// If a hook was provided get the non-computed value from there
+			if ( hooks && "get" in hooks &&
+				( ret = hooks.get( elem, false, extra ) ) !== undefined ) {
+
+				return ret;
+			}
+
+			// Otherwise just get the value from the style object
+			return style[ name ];
+		}
+	},
+
+	css: function( elem, name, extra, styles ) {
+		var val, num, hooks,
+			origName = camelCase( name ),
+			isCustomProp = rcustomProp.test( name );
+
+		// Make sure that we're working with the right name. We don't
+		// want to modify the value if it is a CSS custom property
+		// since they are user-defined.
+		if ( !isCustomProp ) {
+			name = finalPropName( origName );
+		}
+
+		// Try prefixed name followed by the unprefixed name
+		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+		// If a hook was provided get the computed value from there
+		if ( hooks && "get" in hooks ) {
+			val = hooks.get( elem, true, extra );
+		}
+
+		// Otherwise, if a way to get the computed value exists, use that
+		if ( val === undefined ) {
+			val = curCSS( elem, name, styles );
+		}
+
+		// Convert "normal" to computed value
+		if ( val === "normal" && name in cssNormalTransform ) {
+			val = cssNormalTransform[ name ];
+		}
+
+		// Make numeric if forced or a qualifier was provided and val looks numeric
+		if ( extra === "" || extra ) {
+			num = parseFloat( val );
+			return extra === true || isFinite( num ) ? num || 0 : val;
+		}
+
+		return val;
+	}
+} );
+
+jQuery.each( [ "height", "width" ], function( _i, dimension ) {
+	jQuery.cssHooks[ dimension ] = {
+		get: function( elem, computed, extra ) {
+			if ( computed ) {
+
+				// Certain elements can have dimension info if we invisibly show them
+				// but it must have a current display style that would benefit
+				return rdisplayswap.test( jQuery.css( elem, "display" ) ) &&
+
+					// Support: Safari 8+
+					// Table columns in Safari have non-zero offsetWidth & zero
+					// getBoundingClientRect().width unless display is changed.
+					// Support: IE <=11 only
+					// Running getBoundingClientRect on a disconnected node
+					// in IE throws an error.
+					( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ?
+					swap( elem, cssShow, function() {
+						return getWidthOrHeight( elem, dimension, extra );
+					} ) :
+					getWidthOrHeight( elem, dimension, extra );
+			}
+		},
+
+		set: function( elem, value, extra ) {
+			var matches,
+				styles = getStyles( elem ),
+
+				// Only read styles.position if the test has a chance to fail
+				// to avoid forcing a reflow.
+				scrollboxSizeBuggy = !support.scrollboxSize() &&
+					styles.position === "absolute",
+
+				// To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991)
+				boxSizingNeeded = scrollboxSizeBuggy || extra,
+				isBorderBox = boxSizingNeeded &&
+					jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+				subtract = extra ?
+					boxModelAdjustment(
+						elem,
+						dimension,
+						extra,
+						isBorderBox,
+						styles
+					) :
+					0;
+
+			// Account for unreliable border-box dimensions by comparing offset* to computed and
+			// faking a content-box to get border and padding (gh-3699)
+			if ( isBorderBox && scrollboxSizeBuggy ) {
+				subtract -= Math.ceil(
+					elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+					parseFloat( styles[ dimension ] ) -
+					boxModelAdjustment( elem, dimension, "border", false, styles ) -
+					0.5
+				);
+			}
+
+			// Convert to pixels if value adjustment is needed
+			if ( subtract && ( matches = rcssNum.exec( value ) ) &&
+				( matches[ 3 ] || "px" ) !== "px" ) {
+
+				elem.style[ dimension ] = value;
+				value = jQuery.css( elem, dimension );
+			}
+
+			return setPositiveNumber( elem, value, subtract );
+		}
+	};
+} );
+
+jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft,
+	function( elem, computed ) {
+		if ( computed ) {
+			return ( parseFloat( curCSS( elem, "marginLeft" ) ) ||
+				elem.getBoundingClientRect().left -
+					swap( elem, { marginLeft: 0 }, function() {
+						return elem.getBoundingClientRect().left;
+					} )
+			) + "px";
+		}
+	}
+);
+
+// These hooks are used by animate to expand properties
+jQuery.each( {
+	margin: "",
+	padding: "",
+	border: "Width"
+}, function( prefix, suffix ) {
+	jQuery.cssHooks[ prefix + suffix ] = {
+		expand: function( value ) {
+			var i = 0,
+				expanded = {},
+
+				// Assumes a single number if not a string
+				parts = typeof value === "string" ? value.split( " " ) : [ value ];
+
+			for ( ; i < 4; i++ ) {
+				expanded[ prefix + cssExpand[ i ] + suffix ] =
+					parts[ i ] || parts[ i - 2 ] || parts[ 0 ];
+			}
+
+			return expanded;
+		}
+	};
+
+	if ( prefix !== "margin" ) {
+		jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber;
+	}
+} );
+
+jQuery.fn.extend( {
+	css: function( name, value ) {
+		return access( this, function( elem, name, value ) {
+			var styles, len,
+				map = {},
+				i = 0;
+
+			if ( Array.isArray( name ) ) {
+				styles = getStyles( elem );
+				len = name.length;
+
+				for ( ; i < len; i++ ) {
+					map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles );
+				}
+
+				return map;
+			}
+
+			return value !== undefined ?
+				jQuery.style( elem, name, value ) :
+				jQuery.css( elem, name );
+		}, name, value, arguments.length > 1 );
+	}
+} );
+
+
+function Tween( elem, options, prop, end, easing ) {
+	return new Tween.prototype.init( elem, options, prop, end, easing );
+}
+jQuery.Tween = Tween;
+
+Tween.prototype = {
+	constructor: Tween,
+	init: function( elem, options, prop, end, easing, unit ) {
+		this.elem = elem;
+		this.prop = prop;
+		this.easing = easing || jQuery.easing._default;
+		this.options = options;
+		this.start = this.now = this.cur();
+		this.end = end;
+		this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" );
+	},
+	cur: function() {
+		var hooks = Tween.propHooks[ this.prop ];
+
+		return hooks && hooks.get ?
+			hooks.get( this ) :
+			Tween.propHooks._default.get( this );
+	},
+	run: function( percent ) {
+		var eased,
+			hooks = Tween.propHooks[ this.prop ];
+
+		if ( this.options.duration ) {
+			this.pos = eased = jQuery.easing[ this.easing ](
+				percent, this.options.duration * percent, 0, 1, this.options.duration
+			);
+		} else {
+			this.pos = eased = percent;
+		}
+		this.now = ( this.end - this.start ) * eased + this.start;
+
+		if ( this.options.step ) {
+			this.options.step.call( this.elem, this.now, this );
+		}
+
+		if ( hooks && hooks.set ) {
+			hooks.set( this );
+		} else {
+			Tween.propHooks._default.set( this );
+		}
+		return this;
+	}
+};
+
+Tween.prototype.init.prototype = Tween.prototype;
+
+Tween.propHooks = {
+	_default: {
+		get: function( tween ) {
+			var result;
+
+			// Use a property on the element directly when it is not a DOM element,
+			// or when there is no matching style property that exists.
+			if ( tween.elem.nodeType !== 1 ||
+				tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) {
+				return tween.elem[ tween.prop ];
+			}
+
+			// Passing an empty string as a 3rd parameter to .css will automatically
+			// attempt a parseFloat and fallback to a string if the parse fails.
+			// Simple values such as "10px" are parsed to Float;
+			// complex values such as "rotate(1rad)" are returned as-is.
+			result = jQuery.css( tween.elem, tween.prop, "" );
+
+			// Empty strings, null, undefined and "auto" are converted to 0.
+			return !result || result === "auto" ? 0 : result;
+		},
+		set: function( tween ) {
+
+			// Use step hook for back compat.
+			// Use cssHook if its there.
+			// Use .style if available and use plain properties where available.
+			if ( jQuery.fx.step[ tween.prop ] ) {
+				jQuery.fx.step[ tween.prop ]( tween );
+			} else if ( tween.elem.nodeType === 1 && (
+				jQuery.cssHooks[ tween.prop ] ||
+					tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) {
+				jQuery.style( tween.elem, tween.prop, tween.now + tween.unit );
+			} else {
+				tween.elem[ tween.prop ] = tween.now;
+			}
+		}
+	}
+};
+
+// Support: IE <=9 only
+// Panic based approach to setting things on disconnected nodes
+Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = {
+	set: function( tween ) {
+		if ( tween.elem.nodeType && tween.elem.parentNode ) {
+			tween.elem[ tween.prop ] = tween.now;
+		}
+	}
+};
+
+jQuery.easing = {
+	linear: function( p ) {
+		return p;
+	},
+	swing: function( p ) {
+		return 0.5 - Math.cos( p * Math.PI ) / 2;
+	},
+	_default: "swing"
+};
+
+jQuery.fx = Tween.prototype.init;
+
+// Back compat <1.8 extension point
+jQuery.fx.step = {};
+
+
+
+
+var
+	fxNow, inProgress,
+	rfxtypes = /^(?:toggle|show|hide)$/,
+	rrun = /queueHooks$/;
+
+function schedule() {
+	if ( inProgress ) {
+		if ( document.hidden === false && window.requestAnimationFrame ) {
+			window.requestAnimationFrame( schedule );
+		} else {
+			window.setTimeout( schedule, jQuery.fx.interval );
+		}
+
+		jQuery.fx.tick();
+	}
+}
+
+// Animations created synchronously will run synchronously
+function createFxNow() {
+	window.setTimeout( function() {
+		fxNow = undefined;
+	} );
+	return ( fxNow = Date.now() );
+}
+
+// Generate parameters to create a standard animation
+function genFx( type, includeWidth ) {
+	var which,
+		i = 0,
+		attrs = { height: type };
+
+	// If we include width, step value is 1 to do all cssExpand values,
+	// otherwise step value is 2 to skip over Left and Right
+	includeWidth = includeWidth ? 1 : 0;
+	for ( ; i < 4; i += 2 - includeWidth ) {
+		which = cssExpand[ i ];
+		attrs[ "margin" + which ] = attrs[ "padding" + which ] = type;
+	}
+
+	if ( includeWidth ) {
+		attrs.opacity = attrs.width = type;
+	}
+
+	return attrs;
+}
+
+function createTween( value, prop, animation ) {
+	var tween,
+		collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ),
+		index = 0,
+		length = collection.length;
+	for ( ; index < length; index++ ) {
+		if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) {
+
+			// We're done with this property
+			return tween;
+		}
+	}
+}
+
+function defaultPrefilter( elem, props, opts ) {
+	var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display,
+		isBox = "width" in props || "height" in props,
+		anim = this,
+		orig = {},
+		style = elem.style,
+		hidden = elem.nodeType && isHiddenWithinTree( elem ),
+		dataShow = dataPriv.get( elem, "fxshow" );
+
+	// Queue-skipping animations hijack the fx hooks
+	if ( !opts.queue ) {
+		hooks = jQuery._queueHooks( elem, "fx" );
+		if ( hooks.unqueued == null ) {
+			hooks.unqueued = 0;
+			oldfire = hooks.empty.fire;
+			hooks.empty.fire = function() {
+				if ( !hooks.unqueued ) {
+					oldfire();
+				}
+			};
+		}
+		hooks.unqueued++;
+
+		anim.always( function() {
+
+			// Ensure the complete handler is called before this completes
+			anim.always( function() {
+				hooks.unqueued--;
+				if ( !jQuery.queue( elem, "fx" ).length ) {
+					hooks.empty.fire();
+				}
+			} );
+		} );
+	}
+
+	// Detect show/hide animations
+	for ( prop in props ) {
+		value = props[ prop ];
+		if ( rfxtypes.test( value ) ) {
+			delete props[ prop ];
+			toggle = toggle || value === "toggle";
+			if ( value === ( hidden ? "hide" : "show" ) ) {
+
+				// Pretend to be hidden if this is a "show" and
+				// there is still data from a stopped show/hide
+				if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) {
+					hidden = true;
+
+				// Ignore all other no-op show/hide data
+				} else {
+					continue;
+				}
+			}
+			orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop );
+		}
+	}
+
+	// Bail out if this is a no-op like .hide().hide()
+	propTween = !jQuery.isEmptyObject( props );
+	if ( !propTween && jQuery.isEmptyObject( orig ) ) {
+		return;
+	}
+
+	// Restrict "overflow" and "display" styles during box animations
+	if ( isBox && elem.nodeType === 1 ) {
+
+		// Support: IE <=9 - 11, Edge 12 - 15
+		// Record all 3 overflow attributes because IE does not infer the shorthand
+		// from identically-valued overflowX and overflowY and Edge just mirrors
+		// the overflowX value there.
+		opts.overflow = [ style.overflow, style.overflowX, style.overflowY ];
+
+		// Identify a display type, preferring old show/hide data over the CSS cascade
+		restoreDisplay = dataShow && dataShow.display;
+		if ( restoreDisplay == null ) {
+			restoreDisplay = dataPriv.get( elem, "display" );
+		}
+		display = jQuery.css( elem, "display" );
+		if ( display === "none" ) {
+			if ( restoreDisplay ) {
+				display = restoreDisplay;
+			} else {
+
+				// Get nonempty value(s) by temporarily forcing visibility
+				showHide( [ elem ], true );
+				restoreDisplay = elem.style.display || restoreDisplay;
+				display = jQuery.css( elem, "display" );
+				showHide( [ elem ] );
+			}
+		}
+
+		// Animate inline elements as inline-block
+		if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) {
+			if ( jQuery.css( elem, "float" ) === "none" ) {
+
+				// Restore the original display value at the end of pure show/hide animations
+				if ( !propTween ) {
+					anim.done( function() {
+						style.display = restoreDisplay;
+					} );
+					if ( restoreDisplay == null ) {
+						display = style.display;
+						restoreDisplay = display === "none" ? "" : display;
+					}
+				}
+				style.display = "inline-block";
+			}
+		}
+	}
+
+	if ( opts.overflow ) {
+		style.overflow = "hidden";
+		anim.always( function() {
+			style.overflow = opts.overflow[ 0 ];
+			style.overflowX = opts.overflow[ 1 ];
+			style.overflowY = opts.overflow[ 2 ];
+		} );
+	}
+
+	// Implement show/hide animations
+	propTween = false;
+	for ( prop in orig ) {
+
+		// General show/hide setup for this element animation
+		if ( !propTween ) {
+			if ( dataShow ) {
+				if ( "hidden" in dataShow ) {
+					hidden = dataShow.hidden;
+				}
+			} else {
+				dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } );
+			}
+
+			// Store hidden/visible for toggle so `.stop().toggle()` "reverses"
+			if ( toggle ) {
+				dataShow.hidden = !hidden;
+			}
+
+			// Show elements before animating them
+			if ( hidden ) {
+				showHide( [ elem ], true );
+			}
+
+			/* eslint-disable no-loop-func */
+
+			anim.done( function() {
+
+				/* eslint-enable no-loop-func */
+
+				// The final step of a "hide" animation is actually hiding the element
+				if ( !hidden ) {
+					showHide( [ elem ] );
+				}
+				dataPriv.remove( elem, "fxshow" );
+				for ( prop in orig ) {
+					jQuery.style( elem, prop, orig[ prop ] );
+				}
+			} );
+		}
+
+		// Per-property setup
+		propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim );
+		if ( !( prop in dataShow ) ) {
+			dataShow[ prop ] = propTween.start;
+			if ( hidden ) {
+				propTween.end = propTween.start;
+				propTween.start = 0;
+			}
+		}
+	}
+}
+
+function propFilter( props, specialEasing ) {
+	var index, name, easing, value, hooks;
+
+	// camelCase, specialEasing and expand cssHook pass
+	for ( index in props ) {
+		name = camelCase( index );
+		easing = specialEasing[ name ];
+		value = props[ index ];
+		if ( Array.isArray( value ) ) {
+			easing = value[ 1 ];
+			value = props[ index ] = value[ 0 ];
+		}
+
+		if ( index !== name ) {
+			props[ name ] = value;
+			delete props[ index ];
+		}
+
+		hooks = jQuery.cssHooks[ name ];
+		if ( hooks && "expand" in hooks ) {
+			value = hooks.expand( value );
+			delete props[ name ];
+
+			// Not quite $.extend, this won't overwrite existing keys.
+			// Reusing 'index' because we have the correct "name"
+			for ( index in value ) {
+				if ( !( index in props ) ) {
+					props[ index ] = value[ index ];
+					specialEasing[ index ] = easing;
+				}
+			}
+		} else {
+			specialEasing[ name ] = easing;
+		}
+	}
+}
+
+function Animation( elem, properties, options ) {
+	var result,
+		stopped,
+		index = 0,
+		length = Animation.prefilters.length,
+		deferred = jQuery.Deferred().always( function() {
+
+			// Don't match elem in the :animated selector
+			delete tick.elem;
+		} ),
+		tick = function() {
+			if ( stopped ) {
+				return false;
+			}
+			var currentTime = fxNow || createFxNow(),
+				remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ),
+
+				// Support: Android 2.3 only
+				// Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497)
+				temp = remaining / animation.duration || 0,
+				percent = 1 - temp,
+				index = 0,
+				length = animation.tweens.length;
+
+			for ( ; index < length; index++ ) {
+				animation.tweens[ index ].run( percent );
+			}
+
+			deferred.notifyWith( elem, [ animation, percent, remaining ] );
+
+			// If there's more to do, yield
+			if ( percent < 1 && length ) {
+				return remaining;
+			}
+
+			// If this was an empty animation, synthesize a final progress notification
+			if ( !length ) {
+				deferred.notifyWith( elem, [ animation, 1, 0 ] );
+			}
+
+			// Resolve the animation and report its conclusion
+			deferred.resolveWith( elem, [ animation ] );
+			return false;
+		},
+		animation = deferred.promise( {
+			elem: elem,
+			props: jQuery.extend( {}, properties ),
+			opts: jQuery.extend( true, {
+				specialEasing: {},
+				easing: jQuery.easing._default
+			}, options ),
+			originalProperties: properties,
+			originalOptions: options,
+			startTime: fxNow || createFxNow(),
+			duration: options.duration,
+			tweens: [],
+			createTween: function( prop, end ) {
+				var tween = jQuery.Tween( elem, animation.opts, prop, end,
+					animation.opts.specialEasing[ prop ] || animation.opts.easing );
+				animation.tweens.push( tween );
+				return tween;
+			},
+			stop: function( gotoEnd ) {
+				var index = 0,
+
+					// If we are going to the end, we want to run all the tweens
+					// otherwise we skip this part
+					length = gotoEnd ? animation.tweens.length : 0;
+				if ( stopped ) {
+					return this;
+				}
+				stopped = true;
+				for ( ; index < length; index++ ) {
+					animation.tweens[ index ].run( 1 );
+				}
+
+				// Resolve when we played the last frame; otherwise, reject
+				if ( gotoEnd ) {
+					deferred.notifyWith( elem, [ animation, 1, 0 ] );
+					deferred.resolveWith( elem, [ animation, gotoEnd ] );
+				} else {
+					deferred.rejectWith( elem, [ animation, gotoEnd ] );
+				}
+				return this;
+			}
+		} ),
+		props = animation.props;
+
+	propFilter( props, animation.opts.specialEasing );
+
+	for ( ; index < length; index++ ) {
+		result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts );
+		if ( result ) {
+			if ( isFunction( result.stop ) ) {
+				jQuery._queueHooks( animation.elem, animation.opts.queue ).stop =
+					result.stop.bind( result );
+			}
+			return result;
+		}
+	}
+
+	jQuery.map( props, createTween, animation );
+
+	if ( isFunction( animation.opts.start ) ) {
+		animation.opts.start.call( elem, animation );
+	}
+
+	// Attach callbacks from options
+	animation
+		.progress( animation.opts.progress )
+		.done( animation.opts.done, animation.opts.complete )
+		.fail( animation.opts.fail )
+		.always( animation.opts.always );
+
+	jQuery.fx.timer(
+		jQuery.extend( tick, {
+			elem: elem,
+			anim: animation,
+			queue: animation.opts.queue
+		} )
+	);
+
+	return animation;
+}
+
+jQuery.Animation = jQuery.extend( Animation, {
+
+	tweeners: {
+		"*": [ function( prop, value ) {
+			var tween = this.createTween( prop, value );
+			adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween );
+			return tween;
+		} ]
+	},
+
+	tweener: function( props, callback ) {
+		if ( isFunction( props ) ) {
+			callback = props;
+			props = [ "*" ];
+		} else {
+			props = props.match( rnothtmlwhite );
+		}
+
+		var prop,
+			index = 0,
+			length = props.length;
+
+		for ( ; index < length; index++ ) {
+			prop = props[ index ];
+			Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || [];
+			Animation.tweeners[ prop ].unshift( callback );
+		}
+	},
+
+	prefilters: [ defaultPrefilter ],
+
+	prefilter: function( callback, prepend ) {
+		if ( prepend ) {
+			Animation.prefilters.unshift( callback );
+		} else {
+			Animation.prefilters.push( callback );
+		}
+	}
+} );
+
+jQuery.speed = function( speed, easing, fn ) {
+	var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : {
+		complete: fn || !fn && easing ||
+			isFunction( speed ) && speed,
+		duration: speed,
+		easing: fn && easing || easing && !isFunction( easing ) && easing
+	};
+
+	// Go to the end state if fx are off
+	if ( jQuery.fx.off ) {
+		opt.duration = 0;
+
+	} else {
+		if ( typeof opt.duration !== "number" ) {
+			if ( opt.duration in jQuery.fx.speeds ) {
+				opt.duration = jQuery.fx.speeds[ opt.duration ];
+
+			} else {
+				opt.duration = jQuery.fx.speeds._default;
+			}
+		}
+	}
+
+	// Normalize opt.queue - true/undefined/null -> "fx"
+	if ( opt.queue == null || opt.queue === true ) {
+		opt.queue = "fx";
+	}
+
+	// Queueing
+	opt.old = opt.complete;
+
+	opt.complete = function() {
+		if ( isFunction( opt.old ) ) {
+			opt.old.call( this );
+		}
+
+		if ( opt.queue ) {
+			jQuery.dequeue( this, opt.queue );
+		}
+	};
+
+	return opt;
+};
+
+jQuery.fn.extend( {
+	fadeTo: function( speed, to, easing, callback ) {
+
+		// Show any hidden elements after setting opacity to 0
+		return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show()
+
+			// Animate to the value specified
+			.end().animate( { opacity: to }, speed, easing, callback );
+	},
+	animate: function( prop, speed, easing, callback ) {
+		var empty = jQuery.isEmptyObject( prop ),
+			optall = jQuery.speed( speed, easing, callback ),
+			doAnimation = function() {
+
+				// Operate on a copy of prop so per-property easing won't be lost
+				var anim = Animation( this, jQuery.extend( {}, prop ), optall );
+
+				// Empty animations, or finishing resolves immediately
+				if ( empty || dataPriv.get( this, "finish" ) ) {
+					anim.stop( true );
+				}
+			};
+
+		doAnimation.finish = doAnimation;
+
+		return empty || optall.queue === false ?
+			this.each( doAnimation ) :
+			this.queue( optall.queue, doAnimation );
+	},
+	stop: function( type, clearQueue, gotoEnd ) {
+		var stopQueue = function( hooks ) {
+			var stop = hooks.stop;
+			delete hooks.stop;
+			stop( gotoEnd );
+		};
+
+		if ( typeof type !== "string" ) {
+			gotoEnd = clearQueue;
+			clearQueue = type;
+			type = undefined;
+		}
+		if ( clearQueue ) {
+			this.queue( type || "fx", [] );
+		}
+
+		return this.each( function() {
+			var dequeue = true,
+				index = type != null && type + "queueHooks",
+				timers = jQuery.timers,
+				data = dataPriv.get( this );
+
+			if ( index ) {
+				if ( data[ index ] && data[ index ].stop ) {
+					stopQueue( data[ index ] );
+				}
+			} else {
+				for ( index in data ) {
+					if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) {
+						stopQueue( data[ index ] );
+					}
+				}
+			}
+
+			for ( index = timers.length; index--; ) {
+				if ( timers[ index ].elem === this &&
+					( type == null || timers[ index ].queue === type ) ) {
+
+					timers[ index ].anim.stop( gotoEnd );
+					dequeue = false;
+					timers.splice( index, 1 );
+				}
+			}
+
+			// Start the next in the queue if the last step wasn't forced.
+			// Timers currently will call their complete callbacks, which
+			// will dequeue but only if they were gotoEnd.
+			if ( dequeue || !gotoEnd ) {
+				jQuery.dequeue( this, type );
+			}
+		} );
+	},
+	finish: function( type ) {
+		if ( type !== false ) {
+			type = type || "fx";
+		}
+		return this.each( function() {
+			var index,
+				data = dataPriv.get( this ),
+				queue = data[ type + "queue" ],
+				hooks = data[ type + "queueHooks" ],
+				timers = jQuery.timers,
+				length = queue ? queue.length : 0;
+
+			// Enable finishing flag on private data
+			data.finish = true;
+
+			// Empty the queue first
+			jQuery.queue( this, type, [] );
+
+			if ( hooks && hooks.stop ) {
+				hooks.stop.call( this, true );
+			}
+
+			// Look for any active animations, and finish them
+			for ( index = timers.length; index--; ) {
+				if ( timers[ index ].elem === this && timers[ index ].queue === type ) {
+					timers[ index ].anim.stop( true );
+					timers.splice( index, 1 );
+				}
+			}
+
+			// Look for any animations in the old queue and finish them
+			for ( index = 0; index < length; index++ ) {
+				if ( queue[ index ] && queue[ index ].finish ) {
+					queue[ index ].finish.call( this );
+				}
+			}
+
+			// Turn off finishing flag
+			delete data.finish;
+		} );
+	}
+} );
+
+jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) {
+	var cssFn = jQuery.fn[ name ];
+	jQuery.fn[ name ] = function( speed, easing, callback ) {
+		return speed == null || typeof speed === "boolean" ?
+			cssFn.apply( this, arguments ) :
+			this.animate( genFx( name, true ), speed, easing, callback );
+	};
+} );
+
+// Generate shortcuts for custom animations
+jQuery.each( {
+	slideDown: genFx( "show" ),
+	slideUp: genFx( "hide" ),
+	slideToggle: genFx( "toggle" ),
+	fadeIn: { opacity: "show" },
+	fadeOut: { opacity: "hide" },
+	fadeToggle: { opacity: "toggle" }
+}, function( name, props ) {
+	jQuery.fn[ name ] = function( speed, easing, callback ) {
+		return this.animate( props, speed, easing, callback );
+	};
+} );
+
+jQuery.timers = [];
+jQuery.fx.tick = function() {
+	var timer,
+		i = 0,
+		timers = jQuery.timers;
+
+	fxNow = Date.now();
+
+	for ( ; i < timers.length; i++ ) {
+		timer = timers[ i ];
+
+		// Run the timer and safely remove it when done (allowing for external removal)
+		if ( !timer() && timers[ i ] === timer ) {
+			timers.splice( i--, 1 );
+		}
+	}
+
+	if ( !timers.length ) {
+		jQuery.fx.stop();
+	}
+	fxNow = undefined;
+};
+
+jQuery.fx.timer = function( timer ) {
+	jQuery.timers.push( timer );
+	jQuery.fx.start();
+};
+
+jQuery.fx.interval = 13;
+jQuery.fx.start = function() {
+	if ( inProgress ) {
+		return;
+	}
+
+	inProgress = true;
+	schedule();
+};
+
+jQuery.fx.stop = function() {
+	inProgress = null;
+};
+
+jQuery.fx.speeds = {
+	slow: 600,
+	fast: 200,
+
+	// Default speed
+	_default: 400
+};
+
+
+// Based off of the plugin by Clint Helfers, with permission.
+// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/
+jQuery.fn.delay = function( time, type ) {
+	time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time;
+	type = type || "fx";
+
+	return this.queue( type, function( next, hooks ) {
+		var timeout = window.setTimeout( next, time );
+		hooks.stop = function() {
+			window.clearTimeout( timeout );
+		};
+	} );
+};
+
+
+( function() {
+	var input = document.createElement( "input" ),
+		select = document.createElement( "select" ),
+		opt = select.appendChild( document.createElement( "option" ) );
+
+	input.type = "checkbox";
+
+	// Support: Android <=4.3 only
+	// Default value for a checkbox should be "on"
+	support.checkOn = input.value !== "";
+
+	// Support: IE <=11 only
+	// Must access selectedIndex to make default options select
+	support.optSelected = opt.selected;
+
+	// Support: IE <=11 only
+	// An input loses its value after becoming a radio
+	input = document.createElement( "input" );
+	input.value = "t";
+	input.type = "radio";
+	support.radioValue = input.value === "t";
+} )();
+
+
+var boolHook,
+	attrHandle = jQuery.expr.attrHandle;
+
+jQuery.fn.extend( {
+	attr: function( name, value ) {
+		return access( this, jQuery.attr, name, value, arguments.length > 1 );
+	},
+
+	removeAttr: function( name ) {
+		return this.each( function() {
+			jQuery.removeAttr( this, name );
+		} );
+	}
+} );
+
+jQuery.extend( {
+	attr: function( elem, name, value ) {
+		var ret, hooks,
+			nType = elem.nodeType;
+
+		// Don't get/set attributes on text, comment and attribute nodes
+		if ( nType === 3 || nType === 8 || nType === 2 ) {
+			return;
+		}
+
+		// Fallback to prop when attributes are not supported
+		if ( typeof elem.getAttribute === "undefined" ) {
+			return jQuery.prop( elem, name, value );
+		}
+
+		// Attribute hooks are determined by the lowercase version
+		// Grab necessary hook if one is defined
+		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+			hooks = jQuery.attrHooks[ name.toLowerCase() ] ||
+				( jQuery.expr.match.bool.test( name ) ? boolHook : undefined );
+		}
+
+		if ( value !== undefined ) {
+			if ( value === null ) {
+				jQuery.removeAttr( elem, name );
+				return;
+			}
+
+			if ( hooks && "set" in hooks &&
+				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+				return ret;
+			}
+
+			elem.setAttribute( name, value + "" );
+			return value;
+		}
+
+		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+			return ret;
+		}
+
+		ret = jQuery.find.attr( elem, name );
+
+		// Non-existent attributes return null, we normalize to undefined
+		return ret == null ? undefined : ret;
+	},
+
+	attrHooks: {
+		type: {
+			set: function( elem, value ) {
+				if ( !support.radioValue && value === "radio" &&
+					nodeName( elem, "input" ) ) {
+					var val = elem.value;
+					elem.setAttribute( "type", value );
+					if ( val ) {
+						elem.value = val;
+					}
+					return value;
+				}
+			}
+		}
+	},
+
+	removeAttr: function( elem, value ) {
+		var name,
+			i = 0,
+
+			// Attribute names can contain non-HTML whitespace characters
+			// https://html.spec.whatwg.org/multipage/syntax.html#attributes-2
+			attrNames = value && value.match( rnothtmlwhite );
+
+		if ( attrNames && elem.nodeType === 1 ) {
+			while ( ( name = attrNames[ i++ ] ) ) {
+				elem.removeAttribute( name );
+			}
+		}
+	}
+} );
+
+// Hooks for boolean attributes
+boolHook = {
+	set: function( elem, value, name ) {
+		if ( value === false ) {
+
+			// Remove boolean attributes when set to false
+			jQuery.removeAttr( elem, name );
+		} else {
+			elem.setAttribute( name, name );
+		}
+		return name;
+	}
+};
+
+jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) {
+	var getter = attrHandle[ name ] || jQuery.find.attr;
+
+	attrHandle[ name ] = function( elem, name, isXML ) {
+		var ret, handle,
+			lowercaseName = name.toLowerCase();
+
+		if ( !isXML ) {
+
+			// Avoid an infinite loop by temporarily removing this function from the getter
+			handle = attrHandle[ lowercaseName ];
+			attrHandle[ lowercaseName ] = ret;
+			ret = getter( elem, name, isXML ) != null ?
+				lowercaseName :
+				null;
+			attrHandle[ lowercaseName ] = handle;
+		}
+		return ret;
+	};
+} );
+
+
+
+
+var rfocusable = /^(?:input|select|textarea|button)$/i,
+	rclickable = /^(?:a|area)$/i;
+
+jQuery.fn.extend( {
+	prop: function( name, value ) {
+		return access( this, jQuery.prop, name, value, arguments.length > 1 );
+	},
+
+	removeProp: function( name ) {
+		return this.each( function() {
+			delete this[ jQuery.propFix[ name ] || name ];
+		} );
+	}
+} );
+
+jQuery.extend( {
+	prop: function( elem, name, value ) {
+		var ret, hooks,
+			nType = elem.nodeType;
+
+		// Don't get/set properties on text, comment and attribute nodes
+		if ( nType === 3 || nType === 8 || nType === 2 ) {
+			return;
+		}
+
+		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+
+			// Fix name and attach hooks
+			name = jQuery.propFix[ name ] || name;
+			hooks = jQuery.propHooks[ name ];
+		}
+
+		if ( value !== undefined ) {
+			if ( hooks && "set" in hooks &&
+				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+				return ret;
+			}
+
+			return ( elem[ name ] = value );
+		}
+
+		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+			return ret;
+		}
+
+		return elem[ name ];
+	},
+
+	propHooks: {
+		tabIndex: {
+			get: function( elem ) {
+
+				// Support: IE <=9 - 11 only
+				// elem.tabIndex doesn't always return the
+				// correct value when it hasn't been explicitly set
+				// https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/
+				// Use proper attribute retrieval(#12072)
+				var tabindex = jQuery.find.attr( elem, "tabindex" );
+
+				if ( tabindex ) {
+					return parseInt( tabindex, 10 );
+				}
+
+				if (
+					rfocusable.test( elem.nodeName ) ||
+					rclickable.test( elem.nodeName ) &&
+					elem.href
+				) {
+					return 0;
+				}
+
+				return -1;
+			}
+		}
+	},
+
+	propFix: {
+		"for": "htmlFor",
+		"class": "className"
+	}
+} );
+
+// Support: IE <=11 only
+// Accessing the selectedIndex property
+// forces the browser to respect setting selected
+// on the option
+// The getter ensures a default option is selected
+// when in an optgroup
+// eslint rule "no-unused-expressions" is disabled for this code
+// since it considers such accessions noop
+if ( !support.optSelected ) {
+	jQuery.propHooks.selected = {
+		get: function( elem ) {
+
+			/* eslint no-unused-expressions: "off" */
+
+			var parent = elem.parentNode;
+			if ( parent && parent.parentNode ) {
+				parent.parentNode.selectedIndex;
+			}
+			return null;
+		},
+		set: function( elem ) {
+
+			/* eslint no-unused-expressions: "off" */
+
+			var parent = elem.parentNode;
+			if ( parent ) {
+				parent.selectedIndex;
+
+				if ( parent.parentNode ) {
+					parent.parentNode.selectedIndex;
+				}
+			}
+		}
+	};
+}
+
+jQuery.each( [
+	"tabIndex",
+	"readOnly",
+	"maxLength",
+	"cellSpacing",
+	"cellPadding",
+	"rowSpan",
+	"colSpan",
+	"useMap",
+	"frameBorder",
+	"contentEditable"
+], function() {
+	jQuery.propFix[ this.toLowerCase() ] = this;
+} );
+
+
+
+
+	// Strip and collapse whitespace according to HTML spec
+	// https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace
+	function stripAndCollapse( value ) {
+		var tokens = value.match( rnothtmlwhite ) || [];
+		return tokens.join( " " );
+	}
+
+
+function getClass( elem ) {
+	return elem.getAttribute && elem.getAttribute( "class" ) || "";
+}
+
+function classesToArray( value ) {
+	if ( Array.isArray( value ) ) {
+		return value;
+	}
+	if ( typeof value === "string" ) {
+		return value.match( rnothtmlwhite ) || [];
+	}
+	return [];
+}
+
+jQuery.fn.extend( {
+	addClass: function( value ) {
+		var classes, elem, cur, curValue, clazz, j, finalValue,
+			i = 0;
+
+		if ( isFunction( value ) ) {
+			return this.each( function( j ) {
+				jQuery( this ).addClass( value.call( this, j, getClass( this ) ) );
+			} );
+		}
+
+		classes = classesToArray( value );
+
+		if ( classes.length ) {
+			while ( ( elem = this[ i++ ] ) ) {
+				curValue = getClass( elem );
+				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+				if ( cur ) {
+					j = 0;
+					while ( ( clazz = classes[ j++ ] ) ) {
+						if ( cur.indexOf( " " + clazz + " " ) < 0 ) {
+							cur += clazz + " ";
+						}
+					}
+
+					// Only assign if different to avoid unneeded rendering.
+					finalValue = stripAndCollapse( cur );
+					if ( curValue !== finalValue ) {
+						elem.setAttribute( "class", finalValue );
+					}
+				}
+			}
+		}
+
+		return this;
+	},
+
+	removeClass: function( value ) {
+		var classes, elem, cur, curValue, clazz, j, finalValue,
+			i = 0;
+
+		if ( isFunction( value ) ) {
+			return this.each( function( j ) {
+				jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) );
+			} );
+		}
+
+		if ( !arguments.length ) {
+			return this.attr( "class", "" );
+		}
+
+		classes = classesToArray( value );
+
+		if ( classes.length ) {
+			while ( ( elem = this[ i++ ] ) ) {
+				curValue = getClass( elem );
+
+				// This expression is here for better compressibility (see addClass)
+				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+				if ( cur ) {
+					j = 0;
+					while ( ( clazz = classes[ j++ ] ) ) {
+
+						// Remove *all* instances
+						while ( cur.indexOf( " " + clazz + " " ) > -1 ) {
+							cur = cur.replace( " " + clazz + " ", " " );
+						}
+					}
+
+					// Only assign if different to avoid unneeded rendering.
+					finalValue = stripAndCollapse( cur );
+					if ( curValue !== finalValue ) {
+						elem.setAttribute( "class", finalValue );
+					}
+				}
+			}
+		}
+
+		return this;
+	},
+
+	toggleClass: function( value, stateVal ) {
+		var type = typeof value,
+			isValidValue = type === "string" || Array.isArray( value );
+
+		if ( typeof stateVal === "boolean" && isValidValue ) {
+			return stateVal ? this.addClass( value ) : this.removeClass( value );
+		}
+
+		if ( isFunction( value ) ) {
+			return this.each( function( i ) {
+				jQuery( this ).toggleClass(
+					value.call( this, i, getClass( this ), stateVal ),
+					stateVal
+				);
+			} );
+		}
+
+		return this.each( function() {
+			var className, i, self, classNames;
+
+			if ( isValidValue ) {
+
+				// Toggle individual class names
+				i = 0;
+				self = jQuery( this );
+				classNames = classesToArray( value );
+
+				while ( ( className = classNames[ i++ ] ) ) {
+
+					// Check each className given, space separated list
+					if ( self.hasClass( className ) ) {
+						self.removeClass( className );
+					} else {
+						self.addClass( className );
+					}
+				}
+
+			// Toggle whole class name
+			} else if ( value === undefined || type === "boolean" ) {
+				className = getClass( this );
+				if ( className ) {
+
+					// Store className if set
+					dataPriv.set( this, "__className__", className );
+				}
+
+				// If the element has a class name or if we're passed `false`,
+				// then remove the whole classname (if there was one, the above saved it).
+				// Otherwise bring back whatever was previously saved (if anything),
+				// falling back to the empty string if nothing was stored.
+				if ( this.setAttribute ) {
+					this.setAttribute( "class",
+						className || value === false ?
+							"" :
+							dataPriv.get( this, "__className__" ) || ""
+					);
+				}
+			}
+		} );
+	},
+
+	hasClass: function( selector ) {
+		var className, elem,
+			i = 0;
+
+		className = " " + selector + " ";
+		while ( ( elem = this[ i++ ] ) ) {
+			if ( elem.nodeType === 1 &&
+				( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) {
+				return true;
+			}
+		}
+
+		return false;
+	}
+} );
+
+
+
+
+var rreturn = /\r/g;
+
+jQuery.fn.extend( {
+	val: function( value ) {
+		var hooks, ret, valueIsFunction,
+			elem = this[ 0 ];
+
+		if ( !arguments.length ) {
+			if ( elem ) {
+				hooks = jQuery.valHooks[ elem.type ] ||
+					jQuery.valHooks[ elem.nodeName.toLowerCase() ];
+
+				if ( hooks &&
+					"get" in hooks &&
+					( ret = hooks.get( elem, "value" ) ) !== undefined
+				) {
+					return ret;
+				}
+
+				ret = elem.value;
+
+				// Handle most common string cases
+				if ( typeof ret === "string" ) {
+					return ret.replace( rreturn, "" );
+				}
+
+				// Handle cases where value is null/undef or number
+				return ret == null ? "" : ret;
+			}
+
+			return;
+		}
+
+		valueIsFunction = isFunction( value );
+
+		return this.each( function( i ) {
+			var val;
+
+			if ( this.nodeType !== 1 ) {
+				return;
+			}
+
+			if ( valueIsFunction ) {
+				val = value.call( this, i, jQuery( this ).val() );
+			} else {
+				val = value;
+			}
+
+			// Treat null/undefined as ""; convert numbers to string
+			if ( val == null ) {
+				val = "";
+
+			} else if ( typeof val === "number" ) {
+				val += "";
+
+			} else if ( Array.isArray( val ) ) {
+				val = jQuery.map( val, function( value ) {
+					return value == null ? "" : value + "";
+				} );
+			}
+
+			hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ];
+
+			// If set returns undefined, fall back to normal setting
+			if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) {
+				this.value = val;
+			}
+		} );
+	}
+} );
+
+jQuery.extend( {
+	valHooks: {
+		option: {
+			get: function( elem ) {
+
+				var val = jQuery.find.attr( elem, "value" );
+				return val != null ?
+					val :
+
+					// Support: IE <=10 - 11 only
+					// option.text throws exceptions (#14686, #14858)
+					// Strip and collapse whitespace
+					// https://html.spec.whatwg.org/#strip-and-collapse-whitespace
+					stripAndCollapse( jQuery.text( elem ) );
+			}
+		},
+		select: {
+			get: function( elem ) {
+				var value, option, i,
+					options = elem.options,
+					index = elem.selectedIndex,
+					one = elem.type === "select-one",
+					values = one ? null : [],
+					max = one ? index + 1 : options.length;
+
+				if ( index < 0 ) {
+					i = max;
+
+				} else {
+					i = one ? index : 0;
+				}
+
+				// Loop through all the selected options
+				for ( ; i < max; i++ ) {
+					option = options[ i ];
+
+					// Support: IE <=9 only
+					// IE8-9 doesn't update selected after form reset (#2551)
+					if ( ( option.selected || i === index ) &&
+
+							// Don't return options that are disabled or in a disabled optgroup
+							!option.disabled &&
+							( !option.parentNode.disabled ||
+								!nodeName( option.parentNode, "optgroup" ) ) ) {
+
+						// Get the specific value for the option
+						value = jQuery( option ).val();
+
+						// We don't need an array for one selects
+						if ( one ) {
+							return value;
+						}
+
+						// Multi-Selects return an array
+						values.push( value );
+					}
+				}
+
+				return values;
+			},
+
+			set: function( elem, value ) {
+				var optionSet, option,
+					options = elem.options,
+					values = jQuery.makeArray( value ),
+					i = options.length;
+
+				while ( i-- ) {
+					option = options[ i ];
+
+					/* eslint-disable no-cond-assign */
+
+					if ( option.selected =
+						jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1
+					) {
+						optionSet = true;
+					}
+
+					/* eslint-enable no-cond-assign */
+				}
+
+				// Force browsers to behave consistently when non-matching value is set
+				if ( !optionSet ) {
+					elem.selectedIndex = -1;
+				}
+				return values;
+			}
+		}
+	}
+} );
+
+// Radios and checkboxes getter/setter
+jQuery.each( [ "radio", "checkbox" ], function() {
+	jQuery.valHooks[ this ] = {
+		set: function( elem, value ) {
+			if ( Array.isArray( value ) ) {
+				return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 );
+			}
+		}
+	};
+	if ( !support.checkOn ) {
+		jQuery.valHooks[ this ].get = function( elem ) {
+			return elem.getAttribute( "value" ) === null ? "on" : elem.value;
+		};
+	}
+} );
+
+
+
+
+// Return jQuery for attributes-only inclusion
+
+
+support.focusin = "onfocusin" in window;
+
+
+var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/,
+	stopPropagationCallback = function( e ) {
+		e.stopPropagation();
+	};
+
+jQuery.extend( jQuery.event, {
+
+	trigger: function( event, data, elem, onlyHandlers ) {
+
+		var i, cur, tmp, bubbleType, ontype, handle, special, lastElement,
+			eventPath = [ elem || document ],
+			type = hasOwn.call( event, "type" ) ? event.type : event,
+			namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : [];
+
+		cur = lastElement = tmp = elem = elem || document;
+
+		// Don't do events on text and comment nodes
+		if ( elem.nodeType === 3 || elem.nodeType === 8 ) {
+			return;
+		}
+
+		// focus/blur morphs to focusin/out; ensure we're not firing them right now
+		if ( rfocusMorph.test( type + jQuery.event.triggered ) ) {
+			return;
+		}
+
+		if ( type.indexOf( "." ) > -1 ) {
+
+			// Namespaced trigger; create a regexp to match event type in handle()
+			namespaces = type.split( "." );
+			type = namespaces.shift();
+			namespaces.sort();
+		}
+		ontype = type.indexOf( ":" ) < 0 && "on" + type;
+
+		// Caller can pass in a jQuery.Event object, Object, or just an event type string
+		event = event[ jQuery.expando ] ?
+			event :
+			new jQuery.Event( type, typeof event === "object" && event );
+
+		// Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true)
+		event.isTrigger = onlyHandlers ? 2 : 3;
+		event.namespace = namespaces.join( "." );
+		event.rnamespace = event.namespace ?
+			new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) :
+			null;
+
+		// Clean up the event in case it is being reused
+		event.result = undefined;
+		if ( !event.target ) {
+			event.target = elem;
+		}
+
+		// Clone any incoming data and prepend the event, creating the handler arg list
+		data = data == null ?
+			[ event ] :
+			jQuery.makeArray( data, [ event ] );
+
+		// Allow special events to draw outside the lines
+		special = jQuery.event.special[ type ] || {};
+		if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) {
+			return;
+		}
+
+		// Determine event propagation path in advance, per W3C events spec (#9951)
+		// Bubble up to document, then to window; watch for a global ownerDocument var (#9724)
+		if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) {
+
+			bubbleType = special.delegateType || type;
+			if ( !rfocusMorph.test( bubbleType + type ) ) {
+				cur = cur.parentNode;
+			}
+			for ( ; cur; cur = cur.parentNode ) {
+				eventPath.push( cur );
+				tmp = cur;
+			}
+
+			// Only add window if we got to document (e.g., not plain obj or detached DOM)
+			if ( tmp === ( elem.ownerDocument || document ) ) {
+				eventPath.push( tmp.defaultView || tmp.parentWindow || window );
+			}
+		}
+
+		// Fire handlers on the event path
+		i = 0;
+		while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) {
+			lastElement = cur;
+			event.type = i > 1 ?
+				bubbleType :
+				special.bindType || type;
+
+			// jQuery handler
+			handle = ( dataPriv.get( cur, "events" ) || Object.create( null ) )[ event.type ] &&
+				dataPriv.get( cur, "handle" );
+			if ( handle ) {
+				handle.apply( cur, data );
+			}
+
+			// Native handler
+			handle = ontype && cur[ ontype ];
+			if ( handle && handle.apply && acceptData( cur ) ) {
+				event.result = handle.apply( cur, data );
+				if ( event.result === false ) {
+					event.preventDefault();
+				}
+			}
+		}
+		event.type = type;
+
+		// If nobody prevented the default action, do it now
+		if ( !onlyHandlers && !event.isDefaultPrevented() ) {
+
+			if ( ( !special._default ||
+				special._default.apply( eventPath.pop(), data ) === false ) &&
+				acceptData( elem ) ) {
+
+				// Call a native DOM method on the target with the same name as the event.
+				// Don't do default actions on window, that's where global variables be (#6170)
+				if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) {
+
+					// Don't re-trigger an onFOO event when we call its FOO() method
+					tmp = elem[ ontype ];
+
+					if ( tmp ) {
+						elem[ ontype ] = null;
+					}
+
+					// Prevent re-triggering of the same event, since we already bubbled it above
+					jQuery.event.triggered = type;
+
+					if ( event.isPropagationStopped() ) {
+						lastElement.addEventListener( type, stopPropagationCallback );
+					}
+
+					elem[ type ]();
+
+					if ( event.isPropagationStopped() ) {
+						lastElement.removeEventListener( type, stopPropagationCallback );
+					}
+
+					jQuery.event.triggered = undefined;
+
+					if ( tmp ) {
+						elem[ ontype ] = tmp;
+					}
+				}
+			}
+		}
+
+		return event.result;
+	},
+
+	// Piggyback on a donor event to simulate a different one
+	// Used only for `focus(in | out)` events
+	simulate: function( type, elem, event ) {
+		var e = jQuery.extend(
+			new jQuery.Event(),
+			event,
+			{
+				type: type,
+				isSimulated: true
+			}
+		);
+
+		jQuery.event.trigger( e, null, elem );
+	}
+
+} );
+
+jQuery.fn.extend( {
+
+	trigger: function( type, data ) {
+		return this.each( function() {
+			jQuery.event.trigger( type, data, this );
+		} );
+	},
+	triggerHandler: function( type, data ) {
+		var elem = this[ 0 ];
+		if ( elem ) {
+			return jQuery.event.trigger( type, data, elem, true );
+		}
+	}
+} );
+
+
+// Support: Firefox <=44
+// Firefox doesn't have focus(in | out) events
+// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787
+//
+// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1
+// focus(in | out) events fire after focus & blur events,
+// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order
+// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857
+if ( !support.focusin ) {
+	jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) {
+
+		// Attach a single capturing handler on the document while someone wants focusin/focusout
+		var handler = function( event ) {
+			jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) );
+		};
+
+		jQuery.event.special[ fix ] = {
+			setup: function() {
+
+				// Handle: regular nodes (via `this.ownerDocument`), window
+				// (via `this.document`) & document (via `this`).
+				var doc = this.ownerDocument || this.document || this,
+					attaches = dataPriv.access( doc, fix );
+
+				if ( !attaches ) {
+					doc.addEventListener( orig, handler, true );
+				}
+				dataPriv.access( doc, fix, ( attaches || 0 ) + 1 );
+			},
+			teardown: function() {
+				var doc = this.ownerDocument || this.document || this,
+					attaches = dataPriv.access( doc, fix ) - 1;
+
+				if ( !attaches ) {
+					doc.removeEventListener( orig, handler, true );
+					dataPriv.remove( doc, fix );
+
+				} else {
+					dataPriv.access( doc, fix, attaches );
+				}
+			}
+		};
+	} );
+}
+var location = window.location;
+
+var nonce = { guid: Date.now() };
+
+var rquery = ( /\?/ );
+
+
+
+// Cross-browser xml parsing
+jQuery.parseXML = function( data ) {
+	var xml, parserErrorElem;
+	if ( !data || typeof data !== "string" ) {
+		return null;
+	}
+
+	// Support: IE 9 - 11 only
+	// IE throws on parseFromString with invalid input.
+	try {
+		xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" );
+	} catch ( e ) {}
+
+	parserErrorElem = xml && xml.getElementsByTagName( "parsererror" )[ 0 ];
+	if ( !xml || parserErrorElem ) {
+		jQuery.error( "Invalid XML: " + (
+			parserErrorElem ?
+				jQuery.map( parserErrorElem.childNodes, function( el ) {
+					return el.textContent;
+				} ).join( "\n" ) :
+				data
+		) );
+	}
+	return xml;
+};
+
+
+var
+	rbracket = /\[\]$/,
+	rCRLF = /\r?\n/g,
+	rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i,
+	rsubmittable = /^(?:input|select|textarea|keygen)/i;
+
+function buildParams( prefix, obj, traditional, add ) {
+	var name;
+
+	if ( Array.isArray( obj ) ) {
+
+		// Serialize array item.
+		jQuery.each( obj, function( i, v ) {
+			if ( traditional || rbracket.test( prefix ) ) {
+
+				// Treat each array item as a scalar.
+				add( prefix, v );
+
+			} else {
+
+				// Item is non-scalar (array or object), encode its numeric index.
+				buildParams(
+					prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]",
+					v,
+					traditional,
+					add
+				);
+			}
+		} );
+
+	} else if ( !traditional && toType( obj ) === "object" ) {
+
+		// Serialize object item.
+		for ( name in obj ) {
+			buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add );
+		}
+
+	} else {
+
+		// Serialize scalar item.
+		add( prefix, obj );
+	}
+}
+
+// Serialize an array of form elements or a set of
+// key/values into a query string
+jQuery.param = function( a, traditional ) {
+	var prefix,
+		s = [],
+		add = function( key, valueOrFunction ) {
+
+			// If value is a function, invoke it and use its return value
+			var value = isFunction( valueOrFunction ) ?
+				valueOrFunction() :
+				valueOrFunction;
+
+			s[ s.length ] = encodeURIComponent( key ) + "=" +
+				encodeURIComponent( value == null ? "" : value );
+		};
+
+	if ( a == null ) {
+		return "";
+	}
+
+	// If an array was passed in, assume that it is an array of form elements.
+	if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) {
+
+		// Serialize the form elements
+		jQuery.each( a, function() {
+			add( this.name, this.value );
+		} );
+
+	} else {
+
+		// If traditional, encode the "old" way (the way 1.3.2 or older
+		// did it), otherwise encode params recursively.
+		for ( prefix in a ) {
+			buildParams( prefix, a[ prefix ], traditional, add );
+		}
+	}
+
+	// Return the resulting serialization
+	return s.join( "&" );
+};
+
+jQuery.fn.extend( {
+	serialize: function() {
+		return jQuery.param( this.serializeArray() );
+	},
+	serializeArray: function() {
+		return this.map( function() {
+
+			// Can add propHook for "elements" to filter or add form elements
+			var elements = jQuery.prop( this, "elements" );
+			return elements ? jQuery.makeArray( elements ) : this;
+		} ).filter( function() {
+			var type = this.type;
+
+			// Use .is( ":disabled" ) so that fieldset[disabled] works
+			return this.name && !jQuery( this ).is( ":disabled" ) &&
+				rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) &&
+				( this.checked || !rcheckableType.test( type ) );
+		} ).map( function( _i, elem ) {
+			var val = jQuery( this ).val();
+
+			if ( val == null ) {
+				return null;
+			}
+
+			if ( Array.isArray( val ) ) {
+				return jQuery.map( val, function( val ) {
+					return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+				} );
+			}
+
+			return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+		} ).get();
+	}
+} );
+
+
+var
+	r20 = /%20/g,
+	rhash = /#.*$/,
+	rantiCache = /([?&])_=[^&]*/,
+	rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg,
+
+	// #7653, #8125, #8152: local protocol detection
+	rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/,
+	rnoContent = /^(?:GET|HEAD)$/,
+	rprotocol = /^\/\//,
+
+	/* Prefilters
+	 * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example)
+	 * 2) These are called:
+	 *    - BEFORE asking for a transport
+	 *    - AFTER param serialization (s.data is a string if s.processData is true)
+	 * 3) key is the dataType
+	 * 4) the catchall symbol "*" can be used
+	 * 5) execution will start with transport dataType and THEN continue down to "*" if needed
+	 */
+	prefilters = {},
+
+	/* Transports bindings
+	 * 1) key is the dataType
+	 * 2) the catchall symbol "*" can be used
+	 * 3) selection will start with transport dataType and THEN go to "*" if needed
+	 */
+	transports = {},
+
+	// Avoid comment-prolog char sequence (#10098); must appease lint and evade compression
+	allTypes = "*/".concat( "*" ),
+
+	// Anchor tag for parsing the document origin
+	originAnchor = document.createElement( "a" );
+
+originAnchor.href = location.href;
+
+// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport
+function addToPrefiltersOrTransports( structure ) {
+
+	// dataTypeExpression is optional and defaults to "*"
+	return function( dataTypeExpression, func ) {
+
+		if ( typeof dataTypeExpression !== "string" ) {
+			func = dataTypeExpression;
+			dataTypeExpression = "*";
+		}
+
+		var dataType,
+			i = 0,
+			dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || [];
+
+		if ( isFunction( func ) ) {
+
+			// For each dataType in the dataTypeExpression
+			while ( ( dataType = dataTypes[ i++ ] ) ) {
+
+				// Prepend if requested
+				if ( dataType[ 0 ] === "+" ) {
+					dataType = dataType.slice( 1 ) || "*";
+					( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func );
+
+				// Otherwise append
+				} else {
+					( structure[ dataType ] = structure[ dataType ] || [] ).push( func );
+				}
+			}
+		}
+	};
+}
+
+// Base inspection function for prefilters and transports
+function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) {
+
+	var inspected = {},
+		seekingTransport = ( structure === transports );
+
+	function inspect( dataType ) {
+		var selected;
+		inspected[ dataType ] = true;
+		jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) {
+			var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR );
+			if ( typeof dataTypeOrTransport === "string" &&
+				!seekingTransport && !inspected[ dataTypeOrTransport ] ) {
+
+				options.dataTypes.unshift( dataTypeOrTransport );
+				inspect( dataTypeOrTransport );
+				return false;
+			} else if ( seekingTransport ) {
+				return !( selected = dataTypeOrTransport );
+			}
+		} );
+		return selected;
+	}
+
+	return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" );
+}
+
+// A special extend for ajax options
+// that takes "flat" options (not to be deep extended)
+// Fixes #9887
+function ajaxExtend( target, src ) {
+	var key, deep,
+		flatOptions = jQuery.ajaxSettings.flatOptions || {};
+
+	for ( key in src ) {
+		if ( src[ key ] !== undefined ) {
+			( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ];
+		}
+	}
+	if ( deep ) {
+		jQuery.extend( true, target, deep );
+	}
+
+	return target;
+}
+
+/* Handles responses to an ajax request:
+ * - finds the right dataType (mediates between content-type and expected dataType)
+ * - returns the corresponding response
+ */
+function ajaxHandleResponses( s, jqXHR, responses ) {
+
+	var ct, type, finalDataType, firstDataType,
+		contents = s.contents,
+		dataTypes = s.dataTypes;
+
+	// Remove auto dataType and get content-type in the process
+	while ( dataTypes[ 0 ] === "*" ) {
+		dataTypes.shift();
+		if ( ct === undefined ) {
+			ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" );
+		}
+	}
+
+	// Check if we're dealing with a known content-type
+	if ( ct ) {
+		for ( type in contents ) {
+			if ( contents[ type ] && contents[ type ].test( ct ) ) {
+				dataTypes.unshift( type );
+				break;
+			}
+		}
+	}
+
+	// Check to see if we have a response for the expected dataType
+	if ( dataTypes[ 0 ] in responses ) {
+		finalDataType = dataTypes[ 0 ];
+	} else {
+
+		// Try convertible dataTypes
+		for ( type in responses ) {
+			if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) {
+				finalDataType = type;
+				break;
+			}
+			if ( !firstDataType ) {
+				firstDataType = type;
+			}
+		}
+
+		// Or just use first one
+		finalDataType = finalDataType || firstDataType;
+	}
+
+	// If we found a dataType
+	// We add the dataType to the list if needed
+	// and return the corresponding response
+	if ( finalDataType ) {
+		if ( finalDataType !== dataTypes[ 0 ] ) {
+			dataTypes.unshift( finalDataType );
+		}
+		return responses[ finalDataType ];
+	}
+}
+
+/* Chain conversions given the request and the original response
+ * Also sets the responseXXX fields on the jqXHR instance
+ */
+function ajaxConvert( s, response, jqXHR, isSuccess ) {
+	var conv2, current, conv, tmp, prev,
+		converters = {},
+
+		// Work with a copy of dataTypes in case we need to modify it for conversion
+		dataTypes = s.dataTypes.slice();
+
+	// Create converters map with lowercased keys
+	if ( dataTypes[ 1 ] ) {
+		for ( conv in s.converters ) {
+			converters[ conv.toLowerCase() ] = s.converters[ conv ];
+		}
+	}
+
+	current = dataTypes.shift();
+
+	// Convert to each sequential dataType
+	while ( current ) {
+
+		if ( s.responseFields[ current ] ) {
+			jqXHR[ s.responseFields[ current ] ] = response;
+		}
+
+		// Apply the dataFilter if provided
+		if ( !prev && isSuccess && s.dataFilter ) {
+			response = s.dataFilter( response, s.dataType );
+		}
+
+		prev = current;
+		current = dataTypes.shift();
+
+		if ( current ) {
+
+			// There's only work to do if current dataType is non-auto
+			if ( current === "*" ) {
+
+				current = prev;
+
+			// Convert response if prev dataType is non-auto and differs from current
+			} else if ( prev !== "*" && prev !== current ) {
+
+				// Seek a direct converter
+				conv = converters[ prev + " " + current ] || converters[ "* " + current ];
+
+				// If none found, seek a pair
+				if ( !conv ) {
+					for ( conv2 in converters ) {
+
+						// If conv2 outputs current
+						tmp = conv2.split( " " );
+						if ( tmp[ 1 ] === current ) {
+
+							// If prev can be converted to accepted input
+							conv = converters[ prev + " " + tmp[ 0 ] ] ||
+								converters[ "* " + tmp[ 0 ] ];
+							if ( conv ) {
+
+								// Condense equivalence converters
+								if ( conv === true ) {
+									conv = converters[ conv2 ];
+
+								// Otherwise, insert the intermediate dataType
+								} else if ( converters[ conv2 ] !== true ) {
+									current = tmp[ 0 ];
+									dataTypes.unshift( tmp[ 1 ] );
+								}
+								break;
+							}
+						}
+					}
+				}
+
+				// Apply converter (if not an equivalence)
+				if ( conv !== true ) {
+
+					// Unless errors are allowed to bubble, catch and return them
+					if ( conv && s.throws ) {
+						response = conv( response );
+					} else {
+						try {
+							response = conv( response );
+						} catch ( e ) {
+							return {
+								state: "parsererror",
+								error: conv ? e : "No conversion from " + prev + " to " + current
+							};
+						}
+					}
+				}
+			}
+		}
+	}
+
+	return { state: "success", data: response };
+}
+
+jQuery.extend( {
+
+	// Counter for holding the number of active queries
+	active: 0,
+
+	// Last-Modified header cache for next request
+	lastModified: {},
+	etag: {},
+
+	ajaxSettings: {
+		url: location.href,
+		type: "GET",
+		isLocal: rlocalProtocol.test( location.protocol ),
+		global: true,
+		processData: true,
+		async: true,
+		contentType: "application/x-www-form-urlencoded; charset=UTF-8",
+
+		/*
+		timeout: 0,
+		data: null,
+		dataType: null,
+		username: null,
+		password: null,
+		cache: null,
+		throws: false,
+		traditional: false,
+		headers: {},
+		*/
+
+		accepts: {
+			"*": allTypes,
+			text: "text/plain",
+			html: "text/html",
+			xml: "application/xml, text/xml",
+			json: "application/json, text/javascript"
+		},
+
+		contents: {
+			xml: /\bxml\b/,
+			html: /\bhtml/,
+			json: /\bjson\b/
+		},
+
+		responseFields: {
+			xml: "responseXML",
+			text: "responseText",
+			json: "responseJSON"
+		},
+
+		// Data converters
+		// Keys separate source (or catchall "*") and destination types with a single space
+		converters: {
+
+			// Convert anything to text
+			"* text": String,
+
+			// Text to html (true = no transformation)
+			"text html": true,
+
+			// Evaluate text as a json expression
+			"text json": JSON.parse,
+
+			// Parse text as xml
+			"text xml": jQuery.parseXML
+		},
+
+		// For options that shouldn't be deep extended:
+		// you can add your own custom options here if
+		// and when you create one that shouldn't be
+		// deep extended (see ajaxExtend)
+		flatOptions: {
+			url: true,
+			context: true
+		}
+	},
+
+	// Creates a full fledged settings object into target
+	// with both ajaxSettings and settings fields.
+	// If target is omitted, writes into ajaxSettings.
+	ajaxSetup: function( target, settings ) {
+		return settings ?
+
+			// Building a settings object
+			ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) :
+
+			// Extending ajaxSettings
+			ajaxExtend( jQuery.ajaxSettings, target );
+	},
+
+	ajaxPrefilter: addToPrefiltersOrTransports( prefilters ),
+	ajaxTransport: addToPrefiltersOrTransports( transports ),
+
+	// Main method
+	ajax: function( url, options ) {
+
+		// If url is an object, simulate pre-1.5 signature
+		if ( typeof url === "object" ) {
+			options = url;
+			url = undefined;
+		}
+
+		// Force options to be an object
+		options = options || {};
+
+		var transport,
+
+			// URL without anti-cache param
+			cacheURL,
+
+			// Response headers
+			responseHeadersString,
+			responseHeaders,
+
+			// timeout handle
+			timeoutTimer,
+
+			// Url cleanup var
+			urlAnchor,
+
+			// Request state (becomes false upon send and true upon completion)
+			completed,
+
+			// To know if global events are to be dispatched
+			fireGlobals,
+
+			// Loop variable
+			i,
+
+			// uncached part of the url
+			uncached,
+
+			// Create the final options object
+			s = jQuery.ajaxSetup( {}, options ),
+
+			// Callbacks context
+			callbackContext = s.context || s,
+
+			// Context for global events is callbackContext if it is a DOM node or jQuery collection
+			globalEventContext = s.context &&
+				( callbackContext.nodeType || callbackContext.jquery ) ?
+				jQuery( callbackContext ) :
+				jQuery.event,
+
+			// Deferreds
+			deferred = jQuery.Deferred(),
+			completeDeferred = jQuery.Callbacks( "once memory" ),
+
+			// Status-dependent callbacks
+			statusCode = s.statusCode || {},
+
+			// Headers (they are sent all at once)
+			requestHeaders = {},
+			requestHeadersNames = {},
+
+			// Default abort message
+			strAbort = "canceled",
+
+			// Fake xhr
+			jqXHR = {
+				readyState: 0,
+
+				// Builds headers hashtable if needed
+				getResponseHeader: function( key ) {
+					var match;
+					if ( completed ) {
+						if ( !responseHeaders ) {
+							responseHeaders = {};
+							while ( ( match = rheaders.exec( responseHeadersString ) ) ) {
+								responseHeaders[ match[ 1 ].toLowerCase() + " " ] =
+									( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] )
+										.concat( match[ 2 ] );
+							}
+						}
+						match = responseHeaders[ key.toLowerCase() + " " ];
+					}
+					return match == null ? null : match.join( ", " );
+				},
+
+				// Raw string
+				getAllResponseHeaders: function() {
+					return completed ? responseHeadersString : null;
+				},
+
+				// Caches the header
+				setRequestHeader: function( name, value ) {
+					if ( completed == null ) {
+						name = requestHeadersNames[ name.toLowerCase() ] =
+							requestHeadersNames[ name.toLowerCase() ] || name;
+						requestHeaders[ name ] = value;
+					}
+					return this;
+				},
+
+				// Overrides response content-type header
+				overrideMimeType: function( type ) {
+					if ( completed == null ) {
+						s.mimeType = type;
+					}
+					return this;
+				},
+
+				// Status-dependent callbacks
+				statusCode: function( map ) {
+					var code;
+					if ( map ) {
+						if ( completed ) {
+
+							// Execute the appropriate callbacks
+							jqXHR.always( map[ jqXHR.status ] );
+						} else {
+
+							// Lazy-add the new callbacks in a way that preserves old ones
+							for ( code in map ) {
+								statusCode[ code ] = [ statusCode[ code ], map[ code ] ];
+							}
+						}
+					}
+					return this;
+				},
+
+				// Cancel the request
+				abort: function( statusText ) {
+					var finalText = statusText || strAbort;
+					if ( transport ) {
+						transport.abort( finalText );
+					}
+					done( 0, finalText );
+					return this;
+				}
+			};
+
+		// Attach deferreds
+		deferred.promise( jqXHR );
+
+		// Add protocol if not provided (prefilters might expect it)
+		// Handle falsy url in the settings object (#10093: consistency with old signature)
+		// We also use the url parameter if available
+		s.url = ( ( url || s.url || location.href ) + "" )
+			.replace( rprotocol, location.protocol + "//" );
+
+		// Alias method option to type as per ticket #12004
+		s.type = options.method || options.type || s.method || s.type;
+
+		// Extract dataTypes list
+		s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ];
+
+		// A cross-domain request is in order when the origin doesn't match the current origin.
+		if ( s.crossDomain == null ) {
+			urlAnchor = document.createElement( "a" );
+
+			// Support: IE <=8 - 11, Edge 12 - 15
+			// IE throws exception on accessing the href property if url is malformed,
+			// e.g. http://example.com:80x/
+			try {
+				urlAnchor.href = s.url;
+
+				// Support: IE <=8 - 11 only
+				// Anchor's host property isn't correctly set when s.url is relative
+				urlAnchor.href = urlAnchor.href;
+				s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !==
+					urlAnchor.protocol + "//" + urlAnchor.host;
+			} catch ( e ) {
+
+				// If there is an error parsing the URL, assume it is crossDomain,
+				// it can be rejected by the transport if it is invalid
+				s.crossDomain = true;
+			}
+		}
+
+		// Convert data if not already a string
+		if ( s.data && s.processData && typeof s.data !== "string" ) {
+			s.data = jQuery.param( s.data, s.traditional );
+		}
+
+		// Apply prefilters
+		inspectPrefiltersOrTransports( prefilters, s, options, jqXHR );
+
+		// If request was aborted inside a prefilter, stop there
+		if ( completed ) {
+			return jqXHR;
+		}
+
+		// We can fire global events as of now if asked to
+		// Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118)
+		fireGlobals = jQuery.event && s.global;
+
+		// Watch for a new set of requests
+		if ( fireGlobals && jQuery.active++ === 0 ) {
+			jQuery.event.trigger( "ajaxStart" );
+		}
+
+		// Uppercase the type
+		s.type = s.type.toUpperCase();
+
+		// Determine if request has content
+		s.hasContent = !rnoContent.test( s.type );
+
+		// Save the URL in case we're toying with the If-Modified-Since
+		// and/or If-None-Match header later on
+		// Remove hash to simplify url manipulation
+		cacheURL = s.url.replace( rhash, "" );
+
+		// More options handling for requests with no content
+		if ( !s.hasContent ) {
+
+			// Remember the hash so we can put it back
+			uncached = s.url.slice( cacheURL.length );
+
+			// If data is available and should be processed, append data to url
+			if ( s.data && ( s.processData || typeof s.data === "string" ) ) {
+				cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data;
+
+				// #9682: remove data so that it's not used in an eventual retry
+				delete s.data;
+			}
+
+			// Add or update anti-cache param if needed
+			if ( s.cache === false ) {
+				cacheURL = cacheURL.replace( rantiCache, "$1" );
+				uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) +
+					uncached;
+			}
+
+			// Put hash and anti-cache on the URL that will be requested (gh-1732)
+			s.url = cacheURL + uncached;
+
+		// Change '%20' to '+' if this is encoded form body content (gh-2658)
+		} else if ( s.data && s.processData &&
+			( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) {
+			s.data = s.data.replace( r20, "+" );
+		}
+
+		// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+		if ( s.ifModified ) {
+			if ( jQuery.lastModified[ cacheURL ] ) {
+				jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] );
+			}
+			if ( jQuery.etag[ cacheURL ] ) {
+				jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] );
+			}
+		}
+
+		// Set the correct header, if data is being sent
+		if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) {
+			jqXHR.setRequestHeader( "Content-Type", s.contentType );
+		}
+
+		// Set the Accepts header for the server, depending on the dataType
+		jqXHR.setRequestHeader(
+			"Accept",
+			s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ?
+				s.accepts[ s.dataTypes[ 0 ] ] +
+					( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) :
+				s.accepts[ "*" ]
+		);
+
+		// Check for headers option
+		for ( i in s.headers ) {
+			jqXHR.setRequestHeader( i, s.headers[ i ] );
+		}
+
+		// Allow custom headers/mimetypes and early abort
+		if ( s.beforeSend &&
+			( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) {
+
+			// Abort if not done already and return
+			return jqXHR.abort();
+		}
+
+		// Aborting is no longer a cancellation
+		strAbort = "abort";
+
+		// Install callbacks on deferreds
+		completeDeferred.add( s.complete );
+		jqXHR.done( s.success );
+		jqXHR.fail( s.error );
+
+		// Get transport
+		transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR );
+
+		// If no transport, we auto-abort
+		if ( !transport ) {
+			done( -1, "No Transport" );
+		} else {
+			jqXHR.readyState = 1;
+
+			// Send global event
+			if ( fireGlobals ) {
+				globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] );
+			}
+
+			// If request was aborted inside ajaxSend, stop there
+			if ( completed ) {
+				return jqXHR;
+			}
+
+			// Timeout
+			if ( s.async && s.timeout > 0 ) {
+				timeoutTimer = window.setTimeout( function() {
+					jqXHR.abort( "timeout" );
+				}, s.timeout );
+			}
+
+			try {
+				completed = false;
+				transport.send( requestHeaders, done );
+			} catch ( e ) {
+
+				// Rethrow post-completion exceptions
+				if ( completed ) {
+					throw e;
+				}
+
+				// Propagate others as results
+				done( -1, e );
+			}
+		}
+
+		// Callback for when everything is done
+		function done( status, nativeStatusText, responses, headers ) {
+			var isSuccess, success, error, response, modified,
+				statusText = nativeStatusText;
+
+			// Ignore repeat invocations
+			if ( completed ) {
+				return;
+			}
+
+			completed = true;
+
+			// Clear timeout if it exists
+			if ( timeoutTimer ) {
+				window.clearTimeout( timeoutTimer );
+			}
+
+			// Dereference transport for early garbage collection
+			// (no matter how long the jqXHR object will be used)
+			transport = undefined;
+
+			// Cache response headers
+			responseHeadersString = headers || "";
+
+			// Set readyState
+			jqXHR.readyState = status > 0 ? 4 : 0;
+
+			// Determine if successful
+			isSuccess = status >= 200 && status < 300 || status === 304;
+
+			// Get response data
+			if ( responses ) {
+				response = ajaxHandleResponses( s, jqXHR, responses );
+			}
+
+			// Use a noop converter for missing script but not if jsonp
+			if ( !isSuccess &&
+				jQuery.inArray( "script", s.dataTypes ) > -1 &&
+				jQuery.inArray( "json", s.dataTypes ) < 0 ) {
+				s.converters[ "text script" ] = function() {};
+			}
+
+			// Convert no matter what (that way responseXXX fields are always set)
+			response = ajaxConvert( s, response, jqXHR, isSuccess );
+
+			// If successful, handle type chaining
+			if ( isSuccess ) {
+
+				// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+				if ( s.ifModified ) {
+					modified = jqXHR.getResponseHeader( "Last-Modified" );
+					if ( modified ) {
+						jQuery.lastModified[ cacheURL ] = modified;
+					}
+					modified = jqXHR.getResponseHeader( "etag" );
+					if ( modified ) {
+						jQuery.etag[ cacheURL ] = modified;
+					}
+				}
+
+				// if no content
+				if ( status === 204 || s.type === "HEAD" ) {
+					statusText = "nocontent";
+
+				// if not modified
+				} else if ( status === 304 ) {
+					statusText = "notmodified";
+
+				// If we have data, let's convert it
+				} else {
+					statusText = response.state;
+					success = response.data;
+					error = response.error;
+					isSuccess = !error;
+				}
+			} else {
+
+				// Extract error from statusText and normalize for non-aborts
+				error = statusText;
+				if ( status || !statusText ) {
+					statusText = "error";
+					if ( status < 0 ) {
+						status = 0;
+					}
+				}
+			}
+
+			// Set data for the fake xhr object
+			jqXHR.status = status;
+			jqXHR.statusText = ( nativeStatusText || statusText ) + "";
+
+			// Success/Error
+			if ( isSuccess ) {
+				deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] );
+			} else {
+				deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] );
+			}
+
+			// Status-dependent callbacks
+			jqXHR.statusCode( statusCode );
+			statusCode = undefined;
+
+			if ( fireGlobals ) {
+				globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError",
+					[ jqXHR, s, isSuccess ? success : error ] );
+			}
+
+			// Complete
+			completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] );
+
+			if ( fireGlobals ) {
+				globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] );
+
+				// Handle the global AJAX counter
+				if ( !( --jQuery.active ) ) {
+					jQuery.event.trigger( "ajaxStop" );
+				}
+			}
+		}
+
+		return jqXHR;
+	},
+
+	getJSON: function( url, data, callback ) {
+		return jQuery.get( url, data, callback, "json" );
+	},
+
+	getScript: function( url, callback ) {
+		return jQuery.get( url, undefined, callback, "script" );
+	}
+} );
+
+jQuery.each( [ "get", "post" ], function( _i, method ) {
+	jQuery[ method ] = function( url, data, callback, type ) {
+
+		// Shift arguments if data argument was omitted
+		if ( isFunction( data ) ) {
+			type = type || callback;
+			callback = data;
+			data = undefined;
+		}
+
+		// The url can be an options object (which then must have .url)
+		return jQuery.ajax( jQuery.extend( {
+			url: url,
+			type: method,
+			dataType: type,
+			data: data,
+			success: callback
+		}, jQuery.isPlainObject( url ) && url ) );
+	};
+} );
+
+jQuery.ajaxPrefilter( function( s ) {
+	var i;
+	for ( i in s.headers ) {
+		if ( i.toLowerCase() === "content-type" ) {
+			s.contentType = s.headers[ i ] || "";
+		}
+	}
+} );
+
+
+jQuery._evalUrl = function( url, options, doc ) {
+	return jQuery.ajax( {
+		url: url,
+
+		// Make this explicit, since user can override this through ajaxSetup (#11264)
+		type: "GET",
+		dataType: "script",
+		cache: true,
+		async: false,
+		global: false,
+
+		// Only evaluate the response if it is successful (gh-4126)
+		// dataFilter is not invoked for failure responses, so using it instead
+		// of the default converter is kludgy but it works.
+		converters: {
+			"text script": function() {}
+		},
+		dataFilter: function( response ) {
+			jQuery.globalEval( response, options, doc );
+		}
+	} );
+};
+
+
+jQuery.fn.extend( {
+	wrapAll: function( html ) {
+		var wrap;
+
+		if ( this[ 0 ] ) {
+			if ( isFunction( html ) ) {
+				html = html.call( this[ 0 ] );
+			}
+
+			// The elements to wrap the target around
+			wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true );
+
+			if ( this[ 0 ].parentNode ) {
+				wrap.insertBefore( this[ 0 ] );
+			}
+
+			wrap.map( function() {
+				var elem = this;
+
+				while ( elem.firstElementChild ) {
+					elem = elem.firstElementChild;
+				}
+
+				return elem;
+			} ).append( this );
+		}
+
+		return this;
+	},
+
+	wrapInner: function( html ) {
+		if ( isFunction( html ) ) {
+			return this.each( function( i ) {
+				jQuery( this ).wrapInner( html.call( this, i ) );
+			} );
+		}
+
+		return this.each( function() {
+			var self = jQuery( this ),
+				contents = self.contents();
+
+			if ( contents.length ) {
+				contents.wrapAll( html );
+
+			} else {
+				self.append( html );
+			}
+		} );
+	},
+
+	wrap: function( html ) {
+		var htmlIsFunction = isFunction( html );
+
+		return this.each( function( i ) {
+			jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html );
+		} );
+	},
+
+	unwrap: function( selector ) {
+		this.parent( selector ).not( "body" ).each( function() {
+			jQuery( this ).replaceWith( this.childNodes );
+		} );
+		return this;
+	}
+} );
+
+
+jQuery.expr.pseudos.hidden = function( elem ) {
+	return !jQuery.expr.pseudos.visible( elem );
+};
+jQuery.expr.pseudos.visible = function( elem ) {
+	return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length );
+};
+
+
+
+
+jQuery.ajaxSettings.xhr = function() {
+	try {
+		return new window.XMLHttpRequest();
+	} catch ( e ) {}
+};
+
+var xhrSuccessStatus = {
+
+		// File protocol always yields status code 0, assume 200
+		0: 200,
+
+		// Support: IE <=9 only
+		// #1450: sometimes IE returns 1223 when it should be 204
+		1223: 204
+	},
+	xhrSupported = jQuery.ajaxSettings.xhr();
+
+support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported );
+support.ajax = xhrSupported = !!xhrSupported;
+
+jQuery.ajaxTransport( function( options ) {
+	var callback, errorCallback;
+
+	// Cross domain only allowed if supported through XMLHttpRequest
+	if ( support.cors || xhrSupported && !options.crossDomain ) {
+		return {
+			send: function( headers, complete ) {
+				var i,
+					xhr = options.xhr();
+
+				xhr.open(
+					options.type,
+					options.url,
+					options.async,
+					options.username,
+					options.password
+				);
+
+				// Apply custom fields if provided
+				if ( options.xhrFields ) {
+					for ( i in options.xhrFields ) {
+						xhr[ i ] = options.xhrFields[ i ];
+					}
+				}
+
+				// Override mime type if needed
+				if ( options.mimeType && xhr.overrideMimeType ) {
+					xhr.overrideMimeType( options.mimeType );
+				}
+
+				// X-Requested-With header
+				// For cross-domain requests, seeing as conditions for a preflight are
+				// akin to a jigsaw puzzle, we simply never set it to be sure.
+				// (it can always be set on a per-request basis or even using ajaxSetup)
+				// For same-domain requests, won't change header if already provided.
+				if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) {
+					headers[ "X-Requested-With" ] = "XMLHttpRequest";
+				}
+
+				// Set headers
+				for ( i in headers ) {
+					xhr.setRequestHeader( i, headers[ i ] );
+				}
+
+				// Callback
+				callback = function( type ) {
+					return function() {
+						if ( callback ) {
+							callback = errorCallback = xhr.onload =
+								xhr.onerror = xhr.onabort = xhr.ontimeout =
+									xhr.onreadystatechange = null;
+
+							if ( type === "abort" ) {
+								xhr.abort();
+							} else if ( type === "error" ) {
+
+								// Support: IE <=9 only
+								// On a manual native abort, IE9 throws
+								// errors on any property access that is not readyState
+								if ( typeof xhr.status !== "number" ) {
+									complete( 0, "error" );
+								} else {
+									complete(
+
+										// File: protocol always yields status 0; see #8605, #14207
+										xhr.status,
+										xhr.statusText
+									);
+								}
+							} else {
+								complete(
+									xhrSuccessStatus[ xhr.status ] || xhr.status,
+									xhr.statusText,
+
+									// Support: IE <=9 only
+									// IE9 has no XHR2 but throws on binary (trac-11426)
+									// For XHR2 non-text, let the caller handle it (gh-2498)
+									( xhr.responseType || "text" ) !== "text"  ||
+									typeof xhr.responseText !== "string" ?
+										{ binary: xhr.response } :
+										{ text: xhr.responseText },
+									xhr.getAllResponseHeaders()
+								);
+							}
+						}
+					};
+				};
+
+				// Listen to events
+				xhr.onload = callback();
+				errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" );
+
+				// Support: IE 9 only
+				// Use onreadystatechange to replace onabort
+				// to handle uncaught aborts
+				if ( xhr.onabort !== undefined ) {
+					xhr.onabort = errorCallback;
+				} else {
+					xhr.onreadystatechange = function() {
+
+						// Check readyState before timeout as it changes
+						if ( xhr.readyState === 4 ) {
+
+							// Allow onerror to be called first,
+							// but that will not handle a native abort
+							// Also, save errorCallback to a variable
+							// as xhr.onerror cannot be accessed
+							window.setTimeout( function() {
+								if ( callback ) {
+									errorCallback();
+								}
+							} );
+						}
+					};
+				}
+
+				// Create the abort callback
+				callback = callback( "abort" );
+
+				try {
+
+					// Do send the request (this may raise an exception)
+					xhr.send( options.hasContent && options.data || null );
+				} catch ( e ) {
+
+					// #14683: Only rethrow if this hasn't been notified as an error yet
+					if ( callback ) {
+						throw e;
+					}
+				}
+			},
+
+			abort: function() {
+				if ( callback ) {
+					callback();
+				}
+			}
+		};
+	}
+} );
+
+
+
+
+// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432)
+jQuery.ajaxPrefilter( function( s ) {
+	if ( s.crossDomain ) {
+		s.contents.script = false;
+	}
+} );
+
+// Install script dataType
+jQuery.ajaxSetup( {
+	accepts: {
+		script: "text/javascript, application/javascript, " +
+			"application/ecmascript, application/x-ecmascript"
+	},
+	contents: {
+		script: /\b(?:java|ecma)script\b/
+	},
+	converters: {
+		"text script": function( text ) {
+			jQuery.globalEval( text );
+			return text;
+		}
+	}
+} );
+
+// Handle cache's special case and crossDomain
+jQuery.ajaxPrefilter( "script", function( s ) {
+	if ( s.cache === undefined ) {
+		s.cache = false;
+	}
+	if ( s.crossDomain ) {
+		s.type = "GET";
+	}
+} );
+
+// Bind script tag hack transport
+jQuery.ajaxTransport( "script", function( s ) {
+
+	// This transport only deals with cross domain or forced-by-attrs requests
+	if ( s.crossDomain || s.scriptAttrs ) {
+		var script, callback;
+		return {
+			send: function( _, complete ) {
+				script = jQuery( "
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+
 
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+  
    
 
    spatialreg
 
    
 
    Actions Status CRAN
    
 
    
 
    spatialreg: spatial models estimation and testing
 
    
-
    A collection of all the estimation functions for spatial cross-sectional models (on lattice/areal data using spatial weights matrices) contained up to now in spdep. These model fitting functions include maximum likelihood methods for cross-sectional models proposed by Cliff and Ord (1973, ISBN: 0850860369) and (1981, ISBN: 0850860814), fitting methods initially described by Ord (1975) https://doi.org/10.1080/01621459.1975.10480272. The models are further described by Anselin (1988) https://doi.org/10.1007/978-94-015-7799-1. Spatial two stage least squares and spatial general method of moment models initially proposed by Kelejian and Prucha (1998) https://doi.org/10.1023/A:1007707430416 and (1999) https://doi.org/10.1111/1468-2354.00027 are provided. Impact methods and MCMC fitting methods proposed by LeSage and Pace (2009) https://doi.org/10.1201/9781420064254 are implemented for the family of cross-sectional spatial regression models. Methods for fitting the log determinant term in maximum likelihood and MCMC fitting are compared by Bivand et al. (2013) https://doi.org/10.1111/gean.12008, and model fitting methods by Bivand and Piras (2015) https://doi.org/10.18637/jss.v063.i18; both of these articles include extensive lists of references. A recent review is provided by Bivand, Millo and Piras (2021) https://doi.org/10.3390/math9111276. spatialreg >= 1.1-1 corresponds to spdep = 1.1-1, in which the model fitting functions are deprecated and pass through to spatialreg, but will mask those in spatialreg. From versions 1.2-1, the functions have been made defunct in spdep.
    
+
    A collection of all the estimation functions for spatial cross-sectional models (on lattice/areal data using spatial weights matrices) contained up to now in spdep. These model fitting functions include maximum likelihood methods for cross-sectional models proposed by Cliff and Ord (1973, ISBN: 0850860369) and (1981, ISBN: 0850860814), fitting methods initially described by Ord (1975) https://doi.org/10.1080/01621459.1975.10480272. The models are further described by Anselin (1988) https://doi.org/10.1007/978-94-015-7799-1. Spatial two stage least squares and spatial general method of moment models initially proposed by Kelejian and Prucha (1998) https://doi.org/10.1023/A:1007707430416 and (1999) https://doi.org/10.1111/1468-2354.00027 are provided. Impact methods and MCMC fitting methods proposed by LeSage and Pace (2009) https://doi.org/10.1201/9781420064254 are implemented for the family of cross-sectional spatial regression models. Methods for fitting the log determinant term in maximum likelihood and MCMC fitting are compared by Bivand et al. (2013) https://doi.org/10.1111/gean.12008, and model fitting methods by Bivand and Piras (2015) https://doi.org/10.18637/jss.v063.i18; both of these articles include extensive lists of references. A recent review is provided by Bivand, Millo and Piras (2021) https://doi.org/10.3390/math9111276. spatialreg >= 1.1-1 corresponds to spdep = 1.1-1, in which the model fitting functions are deprecated and pass through to spatialreg, but will mask those in spatialreg. From versions 1.2-1, the functions have been made defunct in spdep. From version 1.3-6, add Anselin-Kelejian (1997) test to stsls for residual spatial autocorrelation https://doi.org/10.1177/016001769702000109.
    
 
    Default branch now main.
    
 
    
 
    
-  
    
-
-  
 
-  
 
 
-  
+
 
   
 
diff --git a/docs/katex-auto.js b/docs/katex-auto.js
new file mode 100644
index 0000000..20651d9
--- /dev/null
+++ b/docs/katex-auto.js
@@ -0,0 +1,14 @@
+// https://github.com/jgm/pandoc/blob/29fa97ab96b8e2d62d48326e1b949a71dc41f47a/src/Text/Pandoc/Writers/HTML.hs#L332-L345
+document.addEventListener("DOMContentLoaded", function () {
+  var mathElements = document.getElementsByClassName("math");
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+      });
+    }}});
diff --git a/docs/lightswitch.js b/docs/lightswitch.js
new file mode 100644
index 0000000..9467125
--- /dev/null
+++ b/docs/lightswitch.js
@@ -0,0 +1,85 @@
+
+/*!
+ * Color mode toggler for Bootstrap's docs (https://getbootstrap.com/)
+ * Copyright 2011-2023 The Bootstrap Authors
+ * Licensed under the Creative Commons Attribution 3.0 Unported License.
+ * Updates for {pkgdown} by the {bslib} authors, also licensed under CC-BY-3.0.
+ */
+
+const getStoredTheme = () => localStorage.getItem('theme')
+const setStoredTheme = theme => localStorage.setItem('theme', theme)
+
+const getPreferredTheme = () => {
+  const storedTheme = getStoredTheme()
+  if (storedTheme) {
+    return storedTheme
+  }
+
+  return window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'
+}
+
+const setTheme = theme => {
+  if (theme === 'auto') {
+    document.documentElement.setAttribute('data-bs-theme', (window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'))
+  } else {
+    document.documentElement.setAttribute('data-bs-theme', theme)
+  }
+}
+
+function bsSetupThemeToggle () {
+  'use strict'
+
+  const showActiveTheme = (theme, focus = false) => {
+    var activeLabel, activeIcon;
+
+    document.querySelectorAll('[data-bs-theme-value]').forEach(element => {
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+      const isActive = buttonTheme == theme
+      
+      element.classList.toggle('active', isActive)
+      element.setAttribute('aria-pressed', isActive)
+
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+        activeIcon = element.querySelector('span').classList.value;
+      }
+    })
+
+    const themeSwitcher = document.querySelector('#dropdown-lightswitch')
+    if (!themeSwitcher) {
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+
+    themeSwitcher.setAttribute('aria-label', activeLabel)
+    themeSwitcher.querySelector('span').classList.value = activeIcon;
+
+    if (focus) {
+      themeSwitcher.focus()
+    }
+  }
+
+  window.matchMedia('(prefers-color-scheme: dark)').addEventListener('change', () => {
+    const storedTheme = getStoredTheme()
+    if (storedTheme !== 'light' && storedTheme !== 'dark') {
+      setTheme(getPreferredTheme())
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+
+  window.addEventListener('DOMContentLoaded', () => {
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+
+    document
+      .querySelectorAll('[data-bs-theme-value]')
+      .forEach(toggle => {
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+          setTheme(theme)
+          setStoredTheme(theme)
+          showActiveTheme(theme, true)
+        })
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+  })
+}
+
+setTheme(getPreferredTheme());
+bsSetupThemeToggle();
diff --git a/docs/news/index.html b/docs/news/index.html
index a73dc41..a792432 100644
--- a/docs/news/index.html
+++ b/docs/news/index.html
@@ -1,74 +1,60 @@
 
-Changelog • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-      
    Changelog 
    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Changelog
    
       Source: NEWS.md
     
    
 
     
    
-
    Version 1.3-4 (development)
    
+
    Version 1.3-6 (development)
    
+
    • #56 add Anselin-Kelejian (1997) test to stsls, reported in its summary method, analogous to the reporting in the summary method of lagsarlm of the Lagrange multiplier test, both for residual spatial autocorrelation
      • 
+
    • adding missing man page anchors
      • 
+
    
+    
    
+
    Version 1.3-5 (2024-08-19)
    CRAN release: 2024-08-19
    
+
    • conforming with STRICT_R_HEADERS=1
      • 
+
    • Condition on forthcoming tmap 4
      • 
+
    • #52 subgraph updates
      • 
+
    
+    
    
+
    Version 1.3-4 (2024-06-10)
    CRAN release: 2024-06-10
    
 
    • migrate from ESRI Shapefile to GeoPackage #50
      • 
 
    
     
    
-
    Version 1.3-3 (2024-05-31)2024-05-31
    
+
    Version 1.3-3 (2024-05-31)
    CRAN release: 2024-05-31
    
 
    • protect errorsarlm against missing Durbin= if only intercept
      • 
 
    • fix longstanding bugs in getVmate in a non-default side logic branch
      • 
 
    • add return_impacts= to lmSLX to work around issues with aliased variables; impacts should be improved to handle this case when time permits
      • 
@@ -76,19 +62,19 @@ 
      Versi
 
    • add igraph (>= 2.0.0) in DESCRIPTION for re-named igraph functions
      • 
 
    
     
    
-
    Version 1.3-2 (2024-02-06)2024-02-06
    
+
    Version 1.3-2 (2024-02-06)
    CRAN release: 2024-02-06
    
 
    • pass through SlX formula in call
      • 
 
    • re-corrected #19 because the fitted model weights component may be NULL
      • 
 
    • suppress warning from multcomp::glht as the test which throws the warning is discarded
      • 
 
    
     
    
-
    Version 1.3-1 (2023-11-23)2023-11-23
    
+
    Version 1.3-1 (2023-11-23)
    CRAN release: 2023-11-23
    
 
    • move expm from Imports to Suggests #42
      • 
 
    • added zero.policy pass-through to spdep::mat2listw calls in predict.Sarlm and to spdep::sn2listw in sids_models.Rmd; set spdep requirement to 1.3-1
      • 
 
    • corrected #19 because the fitted model weights component is never NULL, but may have a single unique value
      • 
 
    
     
    
-
    Version 1.2-9 (2023-05-25)2023-05-25
    
+
    Version 1.2-9 (2023-05-25)
    CRAN release: 2023-05-25
    
 
    • raised #39, no support for weights in SEM/SDEM/SLX #39
      • 
 
    • address #37; #38 remains (no formula Durbin support for prediction using any Sarlm object)
      • 
 
    • address #19 by not reporting AIC where case weights are used in spautolm or errorsarlm
      • 
@@ -96,38 +82,38 @@ 
      Versi
 
    • Further added checking for SLX/SDEM impacts and edge/corner cases; starting transition to use multcomp in place og gmodels
      • 
 
    
     
    
-
    Version 1.2-8 (2023-03-01)2023-03-01
    
+
    Version 1.2-8 (2023-03-01)
    CRAN release: 2023-03-01
    
 
    
     
    
-
    Version 1.2-6 (2022-10-07)2022-10-07
    
+
    Version 1.2-6 (2022-10-07)
    CRAN release: 2022-10-07
    
 
    • make local copy of gmodels::estimable() for lm objects only, add authors to package contributors
      • 
 
    • -Wstrict-prototypes fixes
      • 
 
    
     
    
-
    Version 1.2-5 (2022-08-16)2022-08-16
    
+
    Version 1.2-5 (2022-08-16)
    CRAN release: 2022-08-16
    
 
    • updating coercion for Matrix 1.4-2
      • 
 
    • updating dontrun/donttest for package split (previously unchecked, mostly in aple)
      • 
 
    
     
    
-
    Version 1.2-3 (2022-04-18)2022-04-18
    
+
    Version 1.2-3 (2022-04-18)
    CRAN release: 2022-04-18
    
 
    • protect definition of USE_FC_LEN_T
      • 
 
    • unescape underscores in help pages
      • 
 
    
     
    
-
    Version 1.2-1 (2021-11-11)2021-11-11
    
+
    Version 1.2-1 (2021-11-11)
    CRAN release: 2021-11-11
    
 
    • Add Fortran character handling USE_FC_LEN_T WRE §6.6.1
      • 
 
    • Add spdep split-out functionality
      • 
 
    
     
    
-
    Version 1.1-8 (2021-05-03)2021-05-03
    
+
    Version 1.1-8 (2021-05-03)
    CRAN release: 2021-05-03
    
 
    • #18 standardize use of coef() methods for (some) fitted model summary objects
      • 
 
    • https://github.com/tidymodels/broom/issues/1003#issuecomment-798694400 changing spatialreg model output class names: spdep sarlm -> spatialreg Sarlm, spautolm -> Spautolm, stsls -> Stsls, gmsar -> Gmsar, lagmess -> Lagmess, SLX -> , SlX, MCMC_s*_g -> MCMC_s*_G, SFResult -> SfResult, ME_res -> Me_res, lagImpact -> LagImpact, WXImpact -> WXimpact
      • 
 
    • #16 merged coordination of impacts methods (Gianfranco Piras)
      • 
 
    • #14 merged correction to SDEM and SLX impacts when a lagged intercept is present (Tobias Rüttenauer).
      • 
 
    
     
    
-
    Version 1.1-5 (2019-12-01)2019-12-01
    
+
    Version 1.1-5 (2019-12-01)
    CRAN release: 2019-12-01
    
 
    • #6, #11 na.action and precomputed eigenvalue bug
      • 
 
    • #9 Griddy Gibbs issue
      • 
 
    • #8 Predict method for SLX
      • 
@@ -135,32 +121,26 @@ 
      Versi
 
    • #5, #10 Panel Durbin= argument
      • 
 
    
     
    
-
    Version 1.1-3 (2019-04-01)2019-04-01
    
+
    Version 1.1-3 (2019-04-01)
    CRAN release: 2019-04-01
    
 
    • #2 Split spatialreg from spdep; spdep functions still present there as deprecated
      • 
 
    
-  
    
+  
    
 
-  
 
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
-
    
+    
    
 
-      
    
 
-  
 
 
-  
 
   
 
diff --git a/docs/pkgdown.js b/docs/pkgdown.js
index 6f0eee4..1a99c65 100644
--- a/docs/pkgdown.js
+++ b/docs/pkgdown.js
@@ -2,83 +2,43 @@
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   $(function() {
 
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+    $('nav.navbar').headroom();
 
-    $('body').css('padding-top', $('.navbar').height() + 10);
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+      $nav: $("#toc"),
+      $scope: $("main h2, main h3, main h4, main h5, main h6")
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-
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+    if ($('#toc').length) {
+      $('body').scrollspy({
+        target: '#toc',
+        offset: $("nav.navbar").outerHeight() + 1
+      });
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-    for (var i = 0; i < haystack.length; i++) {
-      if (needle[i] != haystack[i])
-        return(i);
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+    // Activate popovers
+    $('[data-bs-toggle="popover"]').popover({
+      container: 'body',
+      html: true,
+      trigger: 'focus',
+      placement: "top",
+      sanitize: false,
+    });
 
-    return(haystack.length);
-  }
+    $('[data-bs-toggle="tooltip"]').tooltip();
 
   /* Clipboard --------------------------*/
 
   function changeTooltipMessage(element, msg) {
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-    element.setAttribute('data-original-title', msg);
+    var tooltipOriginalTitle=element.getAttribute('data-bs-original-title');
+    element.setAttribute('data-bs-original-title', msg);
     $(element).tooltip('show');
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+    element.setAttribute('data-bs-original-title', tooltipOriginalTitle);
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+      var copyButton = "";
 
       $("div.sourceCode").addClass("hasCopyButton");
 
@@ -89,20 +49,114 @@
       $('.btn-copy-ex').tooltip({container: 'body'});
 
       // Initialize clipboard:
-      var clipboardBtnCopies = new ClipboardJS('[data-clipboard-copy]', {
+      var clipboard = new ClipboardJS('[data-clipboard-copy]', {
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+      clipboard.on('success', function(e) {
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+      clipboard.on('error', function(e) {
         changeTooltipMessage(e.trigger,'Press Ctrl+C or Command+C to copy');
       });
+
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+
+    /* Search marking --------------------------*/
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+    var toMark = url.searchParams.get("q");
+    var mark = new Mark("main#main");
+    if (toMark) {
+      mark.mark(toMark, {
+        accuracy: {
+          value: "complementary",
+          limiters: [",", ".", ":", "/"],
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+    }
+
+  /* Search --------------------------*/
+  /* Adapted from https://github.com/rstudio/bookdown/blob/2d692ba4b61f1e466c92e78fd712b0ab08c11d31/inst/resources/bs4_book/bs4_book.js#L25 */
+    // Initialise search index on focus
+  var fuse;
+  $("#search-input").focus(async function(e) {
+    if (fuse) {
+      return;
+    }
+
+    $(e.target).addClass("loading");
+    var response = await fetch($("#search-input").data("search-index"));
+    var data = await response.json();
+
+    var options = {
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+
+    $(e.target).removeClass("loading");
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+    minLength: 2,
+  };
+  var q;
+async function searchFuse(query, callback) {
+  await fuse;
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+  var items;
+  if (!fuse) {
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+    var results = fuse.search(query, { limit: 20 });
+    items = results
+      .filter((x) => x.score <= 0.75)
+      .map((x) => x.item);
+    if (items.length === 0) {
+      items = [{dir:"Sorry 😿",previous_headings:"",title:"No results found.",what:"No results found.",path:window.location.href}];
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+}
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+          } else {
+            return `${s.dir} >	
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     > ${s.previous_headings} > ${s.what}`;
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+        },
+      },
+    },
+  ]).on('autocomplete:selected', function(event, s) {
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+
+document.addEventListener('keydown', function(event) {
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diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
index 0f0366c..9559662 100644
--- a/docs/pkgdown.yml
+++ b/docs/pkgdown.yml
@@ -1,9 +1,11 @@
-pandoc: 3.1.3
-pkgdown: 2.0.9
+pandoc: 3.1.11.1
+pkgdown: 2.1.1
 pkgdown_sha: ~
 articles:
   nb_igraph: nb_igraph.html
   sids_models: sids_models.html
   SpatialFiltering: SpatialFiltering.html
-last_built: 2024-06-10T11:54Z
-
+last_built: 2024-11-19T11:32Z
+urls:
+  reference: https://r-spatial.github.io/spatialreg/reference
+  article: https://r-spatial.github.io/spatialreg/articles
diff --git a/docs/reference/GMargminImage.html b/docs/reference/GMargminImage.html
new file mode 100644
index 0000000..0cf5fc8
--- /dev/null
+++ b/docs/reference/GMargminImage.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/GMerrorsar.html b/docs/reference/GMerrorsar.html
index b15b9d5..6190af8 100644
--- a/docs/reference/GMerrorsar.html
+++ b/docs/reference/GMerrorsar.html
@@ -1,171 +1,146 @@
 
-Spatial simultaneous autoregressive error model estimation by GMM — GMerrorsar • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Spatial simultaneous autoregressive error model estimation by GMM
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Spatial simultaneous autoregressive error model estimation by GMM
    
+
+      
    GMerrorsar.Rd
    
     
    
 
-    
    
+    
    
     
    An implementation of Kelejian and Prucha's generalised moments estimator for the autoregressive parameter in a spatial model.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    GMerrorsar(formula, data = list(), listw, na.action = na.fail,
  zero.policy = attr(listw, "zero.policy"), method="nlminb", arnoldWied=FALSE, 
  control = list(), pars, scaleU=FALSE, verbose=NULL, legacy=FALSE,
  se.lambda=TRUE, returnHcov=FALSE, pWOrder=250, tol.Hcov=1.0e-10)
-# S3 method for Gmsar
+# S3 method for class 'Gmsar'
 summary(object, correlation = FALSE, Hausman=FALSE, ...)
 GMargminImage(obj, lambdaseq, s2seq)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    formula
    
-
    a symbolic description of the model to be fit. The details 
+    
    
+    
    Arguments
    
+    
    
+
    formula
    
+
    a symbolic description of the model to be fit. The details
 of model specification are given for lm()
    
 
-  
    data
    
-
    an optional data frame containing the variables in the model. 
-By default the variables are taken from the environment which the function 
+  
    data
    
+
    an optional data frame containing the variables in the model.
+By default the variables are taken from the environment which the function
 is called.
    
 
-  
    listw
    
+  
    listw
    
 
    a listw object created for example by nb2listw
    
 
-  
    na.action
    
+  
    na.action
    
 
    a function (default na.fail), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.
    
 
-  
    zero.policy
    
-
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without 
+  
    zero.policy
    
+
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without
 neighbours, if FALSE (default) assign NA - causing GMerrorsar() to terminate with an error
    
 
-  
    method
    
+  
    method
    
 
    default "nlminb", or optionally a method passed to optim to use an alternative optimizer
    
 
-  
    arnoldWied
    
+  
    arnoldWied
    
 
    default FALSE
    
 
-  
    control
    
+  
    control
    
 
    A list of control parameters. See details in optim or nlminb.
    
 
-  
    pars
    
+  
    pars
    
 
    starting values for \(\lambda\) and \(\sigma^2\) for GMM optimisation, if missing (default), approximated from initial OLS model as the autocorrelation coefficient corrected for weights style and model sigma squared
    
 
-  
    scaleU
    
+  
    scaleU
    
 
    Default FALSE: scale the OLS residuals before computing the moment matrices; only used if the pars argument is missing
    
 
-  
    verbose
    
+  
    verbose
    
 
    default NULL, use global option value; if TRUE, reports function values during optimization.
    
 
-  
    legacy
    
+  
    legacy
    
 
    default FALSE - compute using the unfiltered values of the response and right hand side variables; if TRUE - compute the fitted value and residuals from the spatially filtered model using the spatial error parameter
    
 
-  
    se.lambda
    
+  
    se.lambda
    
 
    default TRUE, use the analytical method described in http://econweb.umd.edu/~prucha/STATPROG/OLS/desols.pdf
    
 
-  
    returnHcov
    
+  
    returnHcov
    
 
    default FALSE, return the Vo matrix for a spatial Hausman test
    
 
-  
    tol.Hcov
    
+  
    tol.Hcov
    
 
    the tolerance for computing the Vo matrix (default=1.0e-10)
    
 
-  
    pWOrder
    
+  
    pWOrder
    
 
    default 250, if returnHcov=TRUE, pass this order to powerWeights as the power series maximum limit
    
 
-  
    object, obj
    
+  
    object, obj
    
 
    Gmsar object from GMerrorsar
    
 
-  
    correlation
    
+  
    correlation
    
 
    logical; (default=FALSE), TRUE not available
    
 
-  
    Hausman
    
+  
    Hausman
    
 
    if TRUE, the results of the Hausman test for error models are reported
    
 
-  
    ...
    
+  
    ...
    
 
    summary arguments passed through
    
 
-  
    lambdaseq
    
+  
    lambdaseq
    
 
    if given, an increasing sequence of lambda values for gridding
    
 
-  
    s2seq
    
+  
    s2seq
    
 
    if given, an increasing sequence of sigma squared values for gridding
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    When the control list is set with care, the function will converge to values close to the ML estimator without requiring computation of the Jacobian, the most resource-intensive part of ML estimation.
    
-
    Note that the fitted() function for the output object assumes that the response 
+
    Note that the fitted() function for the output object assumes that the response
 variable may be reconstructed as the sum of the trend, the signal, and the
 noise (residuals). Since the values of the response variable are known,
-their spatial lags are used to calculate signal components (Cressie 1993, p. 564). This differs from other software, including GeoDa, which does not use knowledge of the response 
+their spatial lags are used to calculate signal components (Cressie 1993, p. 564). This differs from other software, including GeoDa, which does not use knowledge of the response
 variable in making predictions for the fitting data.
    
 
    The GMargminImage may be used to visualize the shape of the surface of the argmin function used to find lambda.
    
     
    
-    
    
-    
    Value
    
-    
-
-
    A list object of class Gmsar
    
+    
    
+    
    Value
    
+    
    A list object of class Gmsar
    
 
    type
    
 
    "ERROR"
    
 
@@ -245,23 +220,23 @@ 
    Value
    
 
    (possibly) named vector of excluded or omitted observations if non-default na.action argument used
    
 
 
    
-    
    
-    
    References
    
-    
    Kelejian, H. H., and Prucha, I. R., 1999. A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. International Economic Review, 40, pp. 509--533; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York.
    
+    
    
+    
    References
    
+    
    Kelejian, H. H., and Prucha, I. R., 1999. A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. International Economic Review, 40, pp. 509–533; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York.
    
 
    Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. Journal of Statistical Software, 63(18), 1-36. doi:10.18637/jss.v063.i18
 .
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Luc Anselin and Roger Bivand
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    optim, nlminb, errorsarlm
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    #require("spdep", quietly=TRUE)
 data(oldcol, package="spdep")
 COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
@@ -451,27 +426,23 @@ 
    Examples
    
 #> 
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/HPDinterval.LagImpact.html b/docs/reference/HPDinterval.LagImpact.html
new file mode 100644
index 0000000..8259488
--- /dev/null
+++ b/docs/reference/HPDinterval.LagImpact.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/Hausman.test.Gmsar.html b/docs/reference/Hausman.test.Gmsar.html
new file mode 100644
index 0000000..0cf5fc8
--- /dev/null
+++ b/docs/reference/Hausman.test.Gmsar.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/Hausman.test.Sarlm.html b/docs/reference/Hausman.test.Sarlm.html
new file mode 100644
index 0000000..72496f8
--- /dev/null
+++ b/docs/reference/Hausman.test.Sarlm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/Hausman.test.html b/docs/reference/Hausman.test.html
new file mode 100644
index 0000000..72496f8
--- /dev/null
+++ b/docs/reference/Hausman.test.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/Jacobian_W.html b/docs/reference/Jacobian_W.html
new file mode 100644
index 0000000..210cb07
--- /dev/null
+++ b/docs/reference/Jacobian_W.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/LR1.Lagmess.html b/docs/reference/LR1.Lagmess.html
new file mode 100644
index 0000000..9b7573e
--- /dev/null
+++ b/docs/reference/LR1.Lagmess.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/LR1.Sarlm.html b/docs/reference/LR1.Sarlm.html
new file mode 100644
index 0000000..72496f8
--- /dev/null
+++ b/docs/reference/LR1.Sarlm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/LR1.Spautolm.html b/docs/reference/LR1.Spautolm.html
new file mode 100644
index 0000000..571745b
--- /dev/null
+++ b/docs/reference/LR1.Spautolm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/LU_prepermutate_setup.html b/docs/reference/LU_prepermutate_setup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/LU_prepermutate_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/LU_setup.html b/docs/reference/LU_setup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/LU_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/MCMCsamp.Sarlm.html b/docs/reference/MCMCsamp.Sarlm.html
new file mode 100644
index 0000000..7fd716c
--- /dev/null
+++ b/docs/reference/MCMCsamp.Sarlm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/MCMCsamp.Spautolm.html b/docs/reference/MCMCsamp.Spautolm.html
new file mode 100644
index 0000000..7fd716c
--- /dev/null
+++ b/docs/reference/MCMCsamp.Spautolm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/MCMCsamp.html b/docs/reference/MCMCsamp.html
index 1a6f95f..d578bc0 100644
--- a/docs/reference/MCMCsamp.html
+++ b/docs/reference/MCMCsamp.html
@@ -1,133 +1,110 @@
 
-MCMC sample from fitted spatial regression — MCMCsamp • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    MCMC sample from fitted spatial regression
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    MCMC sample from fitted spatial regression
    
+
+      
    MCMCsamp.Rd
    
     
    
 
-    
    
+    
    
     
    The MCMCsamp method uses rwmetrop, a random walk Metropolis algorithm, from LearnBayes to make MCMC samples from fitted maximum likelihood spatial regression models.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    MCMCsamp(object, mcmc = 1L, verbose = NULL, ...)
-# S3 method for Spautolm
+# S3 method for class 'Spautolm'
 MCMCsamp(object, mcmc = 1L, verbose = NULL, ...,
  burnin = 0L, scale=1, listw, control = list())
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 MCMCsamp(object, mcmc = 1L, verbose = NULL, ...,
     burnin=0L, scale=1, listw, listw2=NULL, control=list())
    
     
    
 
-    
    
-    
    Arguments
    
-    
    object
    
+    
    
+    
    Arguments
    
+    
    
+
    object
    
 
    A spatial regression model object fitted by maximum likelihood with spautolm
    
 
-  
    mcmc
    
+  
    mcmc
    
 
    The number of MCMC iterations after burnin
    
 
-  
    verbose
    
+  
    verbose
    
 
    default NULL, use global option value; if TRUE, reports progress
    
 
-  
    ...
    
+  
    ...
    
 
    Arguments passed through
    
 
-  
    burnin
    
+  
    burnin
    
 
    The number of burn-in iterations for the sampler
    
 
-  
    scale
    
+  
    scale
    
 
    a positive scale parameter
    
 
-  
    listw, listw2
    
+  
    listw, listw2
    
 
    listw objects created for example by nb2listw; should be the same object(s) used for fitting the model
    
 
-  
    control
    
+  
    control
    
 
    list of extra control arguments - see spautolm
    
 
 
    
-    
    
-    
    Value
    
+    
    
+    
    Value
    
     
    An object of class “mcmc” suited to coda, with attributes: “accept” acceptance rate; “type” input ML fitted model type “SAR”, “CAR”, “SMA”, “lag”, “mixed”, “error”, “sac”, “sacmixed”; “timings” run times
    
     
    
-    
    
-    
    Note
    
+    
    
+    
    Note
    
     
    If the acceptance rate is below 0.05, a warning will be issued; consider increasing mcmc.
    
     
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Jim Albert (2007) Bayesian Computation with R, Springer, New York, pp. 104-105.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    rwmetrop, spautolm, lagsarlm, errorsarlm, sacsarlm
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    require("sf", quietly=TRUE)
 nydata <- st_read(system.file("shapes/NY8_bna_utm18.gpkg", package="spData")[1], quiet=TRUE)
 suppressMessages(nyadjmat <- as.matrix(foreign::read.dbf(system.file(
@@ -870,27 +847,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/ME.html b/docs/reference/ME.html
index 9830382..c7dad73 100644
--- a/docs/reference/ME.html
+++ b/docs/reference/ME.html
@@ -1,128 +1,103 @@
 
-Moran eigenvector GLM filtering — ME • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Moran eigenvector GLM filtering
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Moran eigenvector GLM filtering
    
+
+      
    ME.Rd
    
     
    
 
-    
    
+    
    
     
    The Moran eigenvector filtering function is intended to remove spatial autocorrelation from the residuals of generalised linear models. It uses brute force eigenvector selection to reach a subset of such vectors to be added to the RHS of the GLM model to reduce residual autocorrelation to below the specified alpha value. Since eigenvector selection only works on symmetric weights, the weights are made symmetric before the eigenvectors are found (from spdep 0.5-50).
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    ME(formula, data=list(), family = gaussian, weights, offset,
  na.action=na.fail,listw=NULL, alpha=0.05, nsim=99, verbose=NULL,
  stdev=FALSE, zero.policy=NULL)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    formula
    
+    
    
+    
    Arguments
    
+    
    
+
    formula
    
 
    a symbolic description of the model to be fit
    
 
-  
    data
    
+  
    data
    
 
    an optional data frame containing the variables in the model
    
 
-  
    family
    
+  
    family
    
 
    a description of the error distribution and link function to
           be used in the model
    
 
-  
    weights
    
+  
    weights
    
 
    an optional vector of weights to be used in the fitting process
    
 
-  
    offset
    
+  
    offset
    
 
    this can be used to specify an a priori known component to be included in the linear predictor during fitting
    
 
-  
    na.action
    
+  
    na.action
    
 
    a function (default options("na.action")), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the spatial weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.
    
 
-  
    listw
    
+  
    listw
    
 
    a listw object created for example by nb2listw
    
 
-  
    alpha
    
+  
    alpha
    
 
    used as a stopping rule to choose all eigenvectors up to and including the one with a p-value exceeding alpha
    
 
-  
    nsim
    
+  
    nsim
    
 
    number of permutations for permutation bootstrap for finding p-values
    
 
-  
    verbose
    
+  
    verbose
    
 
    default NULL, use global option value; if TRUE report eigenvectors selected
    
 
-  
    stdev
    
+  
    stdev
    
 
    if TRUE, p-value calculated from bootstrap permutation standard deviate using pnorm with alternative="greater", if FALSE the Hope-type p-value
    
 
-  
    zero.policy
    
+  
    zero.policy
    
 
    default NULL, use global option value; if FALSE stop with error for any empty neighbour sets, if TRUE permit the weights list to be formed with zero-length weights vectors
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    The eigenvectors for inclusion are chosen by calculating the empirical Moran's I values for the initial model plus each of the doubly centred symmetric spatial weights matrix eigenvectors in turn. Then the first eigenvector is chosen as that with the lowest Moran's I value. The procedure is repeated until the lowest remaining Moran's I value has a permutation-based probability value above alpha. The probability value is either Hope-type or based on using the mean and standard deviation of the permutations to calculate ZI based on the stdev argument.
    
     
    
-    
    
-    
    Value
    
-    
-
-
    An object of class Me_res:
    
+    
    
+    
    Value
    
+    
    An object of class Me_res:
    
 
    selection
    
 
    a matrix summarising the selection of eigenvectors for inclusion, with columns:
    Eigenvector
    
 
    number of selected eigenvector
    
@@ -133,28 +108,28 @@ 
    Value
    
       
    pr(ZI)
    
 
    probability value: if stdev=TRUE of the permutation-based standardized deviate, if FALSE the Hope-type probability value, in both cases on-sided
    
 
-    
+
 
    The first row is the value at the start of the search
    
 
   
    vectors
    
 
    a matrix of the selected eigenvectors in order of selection
    
 
 
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Dray S, Legendre P and Peres-Neto PR (2005) Spatial modeling: a comprehensive framework for principle coordinate analysis of neigbbor matrices (PCNM), Ecological Modelling; Griffith DA and Peres-Neto PR (2006) Spatial modeling in ecology: the flexibility of eigenfunction spatial analyses.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand and Pedro Peres-Neto
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    SpatialFiltering, glm
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    #require("spdep", quietly=TRUE)
 data(hopkins, package="spData")
 hopkins_part <- hopkins[21:36,36:21]
@@ -168,7 +143,7 @@ 
    Examples
    
 #> eV[,1], I: 0.08290518 ZI: NA, pr(ZI): 0.04
 #> eV[,9], I: 0.06426565 ZI: NA, pr(ZI): 0.14
 #>    user  system elapsed 
-#>   1.188   0.004   1.197 
+#>   1.258   0.007   1.272 
 glmME <- glm(c(hopkins_part) ~ 1 + fitted(MEbinom1), family="binomial")
 #anova(glmME, test="Chisq")
 coef(summary(glmME))
@@ -220,7 +195,7 @@ 
    Examples
    
 #> eV[,6], I: 0.1178225 ZI: NA, pr(ZI): 0.08
 #> eV[,4], I: 0.06242664 ZI: NA, pr(ZI): 0.27
 #>    user  system elapsed 
-#>   0.518   0.000   0.520 
+#>   0.528   0.000   0.532 
 lagcol1
 #>   Eigenvector ZI pr(ZI)
 #> 0          NA NA   0.01
@@ -302,6 +277,7 @@ 
    Examples
    
 rn <- as.character(nc.sids$FIPS)
 ncCC89_nb <- spdep::read.gal(system.file("weights/ncCC89.gal", package="spData")[1],
  region.id=rn)
+#> Warning: neighbour object has 3 sub-graphs
 ncCR85_nb <- spdep::read.gal(system.file("weights/ncCR85.gal", package="spData")[1],
  region.id=rn)
 glmbase <- glm(SID74 ~ 1, data=nc.sids, offset=log(BIR74),
@@ -348,27 +324,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/ML_models.html b/docs/reference/ML_models.html
index b8b12cd..08fa755 100644
--- a/docs/reference/ML_models.html
+++ b/docs/reference/ML_models.html
@@ -1,5 +1,5 @@
 
-Spatial simultaneous autoregressive model estimation by maximum likelihood — ML_models • spatialregSpatial simultaneous autoregressive model estimation by maximum likelihood — ML_models • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Spatial simultaneous autoregressive model estimation by maximum likelihood
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Spatial simultaneous autoregressive model estimation by maximum likelihood
    
+
+      
    ML_models.Rd
    
     
    
 
-    
    
+    
    
     
    The lagsarlm function provides Maximum likelihood estimation of spatial simultaneous autoregressive lag and spatial Durbin (mixed) models of the form:
    
 
    $$y = \rho W y + X \beta + \varepsilon$$
    
 
    where \(\rho\) is found by optimize() first, and \(\beta\) and other parameters by generalized least squares subsequently (one-dimensional search using optim performs badly on some platforms). In the spatial Durbin (mixed) model, the spatially lagged independent variables are added to X. Note that interpretation of the fitted coefficients should use impact measures, because of the feedback loops induced by the data generation process for this model. With one of the sparse matrix methods, larger numbers of observations can be handled, but the interval= argument may need be set when the weights are not row-standardised.
    
@@ -92,7 +79,8 @@ 
    Spatial simultaneous autoregressive model estimation by maximum likelihood
 
-    
    
+    
    
+    
    Usage
    
     
    lagsarlm(formula, data = list(), listw, na.action, Durbin, type,
  method="eigen", quiet=NULL, zero.policy=NULL, interval=NULL,
  tol.solve=.Machine$double.eps, trs=NULL, control=list())
@@ -103,119 +91,120 @@ 
    Spatial simultaneous autoregressive model estimation by maximum likelihood method="eigen", quiet=NULL, zero.policy=NULL, tol.solve=.Machine$double.eps,
  llprof=NULL, interval1=NULL, interval2=NULL, trs1=NULL, trs2=NULL,
  control = list())
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 summary(object, correlation = FALSE, Nagelkerke = FALSE,
  Hausman=FALSE, adj.se=FALSE, ...)
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 print(x, ...)
-# S3 method for summary.Sarlm
+# S3 method for class 'summary.Sarlm'
 print(x, digits = max(5, .Options$digits - 3),
  signif.stars = FALSE, ...)
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 residuals(object, ...)
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 deviance(object, ...)
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 coef(object, ...)
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 vcov(object, ...)
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 fitted(object, ...)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    formula
    
-
    a symbolic description of the model to be fit. The details 
+    
    
+    
    Arguments
    
+    
    
+
    formula
    
+
    a symbolic description of the model to be fit. The details
 of model specification are given for lm()
    
 
-  
    data
    
-
    an optional data frame containing the variables in the model. 
-By default the variables are taken from the environment which the function 
+  
    data
    
+
    an optional data frame containing the variables in the model.
+By default the variables are taken from the environment which the function
 is called.
    
 
-  
    listw, listw2
    
+  
    listw, listw2
    
 
    a listw object created for example by nb2listw; if nb2listw not given, set to the same spatial weights as the listw argument
    
 
-  
    na.action
    
+  
    na.action
    
 
    a function (default options("na.action")), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.
    
 
-  
    weights
    
+  
    weights
    
 
    an optional vector of weights to be used in the fitting process. Non-NULL weights can be used to indicate that different observations have different variances (with the values in weights being inversely proportional to the variances); or equivalently, when the elements of weights are positive integers w_i, that each response y_i is the mean of w_i unit-weight observations (including the case that there are w_i observations equal to y_i and the data have been summarized) - lm
    
 
-  
    Durbin
    
+  
    Durbin
    
 
    default FALSE (spatial lag model); if TRUE, full spatial Durbin model; if a formula object, the subset of explanatory variables to lag
    
 
-  
    type
    
+  
    type
    
 
    (use the ‘Durbin=’ argument - retained for backwards compatibility only) default "lag", may be set to "mixed"; when "mixed", the lagged intercept is dropped for spatial weights style "W", that is row-standardised weights, but otherwise included; “Durbin” may be used instead of “mixed”
    
 
-  
    etype
    
+  
    etype
    
 
    (use the ‘Durbin=’ argument - retained for backwards compatibility only) default "error", may be set to "emixed" to include the spatially lagged independent variables added to X; when "emixed", the lagged intercept is dropped for spatial weights style "W", that is row-standardised weights, but otherwise included
    
 
-  
    method
    
-
    "eigen" (default) - the Jacobian is computed as the product 
+  
    method
    
+
    "eigen" (default) - the Jacobian is computed as the product
 of (1 - rho*eigenvalue) using eigenw, and "spam" or "Matrix_J" for strictly symmetric weights lists of styles "B" and "C", or made symmetric by similarity (Ord, 1975, Appendix C) if possible for styles "W" and "S", using code from the spam or Matrix packages to calculate the determinant; “Matrix” and “spam_update” provide updating Cholesky decomposition methods; "LU" provides an alternative sparse matrix decomposition approach. In addition, there are "Chebyshev" and Monte Carlo "MC" approximate log-determinant methods; the Smirnov/Anselin (2009) trace approximation is available as "moments". Three methods: "SE_classic", "SE_whichMin", and "SE_interp" are provided experimentally, the first to attempt to emulate the behaviour of Spatial Econometrics toolbox ML fitting functions. All use grids of log determinant values, and the latter two attempt to ameliorate some features of "SE_classic".
    
 
-  
    quiet
    
+  
    quiet
    
 
    default NULL, use !verbose global option value; if FALSE, reports function values during optimization.
    
 
-  
    zero.policy
    
-
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without 
+  
    zero.policy
    
+
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without
 neighbours, if FALSE (default) assign NA - causing lagsarlm() to terminate with an error
    
 
-  
    interval
    
+  
    interval
    
 
    default is NULL, search interval for autoregressive parameter
    
 
-  
    tol.solve
    
+  
    tol.solve
    
 
    the tolerance for detecting linear dependencies in the columns of matrices to be inverted - passed to solve() (default=1.0e-10). This may be used if necessary to extract coefficient standard errors (for instance lowering to 1e-12), but errors in solve() may constitute indications of poorly scaled variables: if the variables have scales differing much from the autoregressive coefficient, the values in this matrix may be very different in scale, and inverting such a matrix is analytically possible by definition, but numerically unstable; rescaling the RHS variables alleviates this better than setting tol.solve to a very small value
    
 
-  
    llprof
    
+  
    llprof
    
 
    default NULL, can either be an integer, to divide the feasible ranges into a grid of points, or a two-column matrix of spatial coefficient values, at which to evaluate the likelihood function
    
 
-  
    trs1, trs2
    
+  
    trs1, trs2
    
 
    default NULL, if given, vectors for each weights object of powered spatial weights matrix traces output by trW; when given, used in some Jacobian methods
    
 
-  
    interval1, interval2
    
+  
    interval1, interval2
    
 
    default is NULL, search intervals for each weights object for autoregressive parameters
    
 
-  
    trs
    
+  
    trs
    
 
    default NULL, if given, a vector of powered spatial weights matrix traces output by trW; when given, insert the asymptotic analytical values into the numerical Hessian instead of the approximated values; may be used to get around some problems raised when the numerical Hessian is poorly conditioned, generating NaNs in subsequent operations; the use of trs is recommended
    
 
- 
    control
    
+ 
    control
    
 
    list of extra control arguments - see section below
    
 
-  
    object
    
+  
    object
    
 
    Sarlm object from lagsarlm, errorsarlm or sacsarlm
    
 
-  
    correlation
    
+  
    correlation
    
 
    logical; if 'TRUE', the correlation matrix of the estimated parameters including sigma is returned and printed (default=FALSE)
    
 
-  
    Nagelkerke
    
+  
    Nagelkerke
    
 
    if TRUE, the Nagelkerke pseudo R-squared is reported
    
 
-  
    Hausman
    
+  
    Hausman
    
 
    if TRUE, the results of the Hausman test for error models are reported
    
 
-  
    adj.se
    
+  
    adj.se
    
 
    if TRUE, adjust the coefficient standard errors for the number of fitted coefficients
    
 
-  
    x
    
-
    Sarlm object from lagsarlm, errorsarlm or sacsarlm in print.Sarlm, summary object from summary.Sarlm for 
+  
    x
    
+
    Sarlm object from lagsarlm, errorsarlm or sacsarlm in print.Sarlm, summary object from summary.Sarlm for
 print.summary.Sarlm
    
 
-  
    digits
    
+  
    digits
    
 
    the number of significant digits to use when printing
    
 
-  
    signif.stars
    
+  
    signif.stars
    
 
    logical. If TRUE, "significance stars" are printed
           for each coefficient.
    
 
-  
    ...
    
+  
    ...
    
 
    further arguments passed to or from other methods
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    The asymptotic standard error of \(\rho\) is only computed when
 method=“eigen”, because the full matrix operations involved would be costly
 for large n typically associated with the choice of method="spam" or "Matrix". The same applies to the coefficient covariance matrix. Taken as the
@@ -224,19 +213,19 @@ 
    Details
    
 of magnitude in difference). It often happens that the tol.solve
 argument needs to be set to a smaller value than the default, or the RHS variables can be centred or reduced in range.
    
 
    Versions of the package from 0.4-38 include numerical Hessian values where asymptotic standard errors are not available. This change has been introduced to permit the simulation of distributions for impact measures. The warnings made above with regard to variable scaling also apply in this case.
    
-
    Note that the fitted() function for the output object assumes that the response 
+
    Note that the fitted() function for the output object assumes that the response
 variable may be reconstructed as the sum of the trend, the signal, and the
 noise (residuals). Since the values of the response variable are known,
-their spatial lags are used to calculate signal components (Cressie 1993, 
-p. 564). This differs from other software, including GeoDa, which does not use 
-knowledge of the response variable in making predictions for the fitting data. 
-Refer to the help page of predict.Sarlm for discussions and 
+their spatial lags are used to calculate signal components (Cressie 1993,
+p. 564). This differs from other software, including GeoDa, which does not use
+knowledge of the response variable in making predictions for the fitting data.
+Refer to the help page of predict.Sarlm for discussions and
 references.
    
 
    Because numerical optimisation is used to find the values of lambda and rho in sacsarlm, care needs to be shown. It has been found that the surface of the 2D likelihood function often forms a “banana trench” from (low rho, high lambda) through (high rho, high lambda) to (high rho, low lambda) values. In addition, sometimes the banana has optima towards both ends, one local, the other global, and conseqently the choice of the starting point for the final optimization becomes crucial. The default approach is not to use just (0, 0) as a starting point, nor the (rho, lambda) values from gstsls, which lie in a central part of the “trench”, but either four values at (low rho, high lambda), (0, 0), (high rho, high lambda), and (high rho, low lambda), and to use the best of these start points for the final optimization. Optionally, nine points can be used spanning the whole (lower, upper) space.
    
     
    
-    
    
-    
    Control arguments
    
-    
+    
    
+    
    Control arguments
    
+
 
    tol.opt:
    
 
    the desired accuracy of the optimization - passed to optimize() (default=square root of double precision machine tolerance, a larger root may be used needed, see help(boston) for an example)
    
 
@@ -335,8 +324,8 @@ 
    Control arguments
    
 
 
 
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion;
 Ord, J. K. 1975 Estimation methods for models of spatial interaction,
 Journal of the American Statistical Association, 70, 120-126;
@@ -347,24 +336,24 @@ 
    References
    
 Anselin L, Bera AK (1998) Spatial dependence in linear regression models
 with an introduction to spatial econometrics. In: Ullah A, Giles DEA
 (eds) Handbook of applied economic statistics. Marcel Dekker, New York,
-pp. 237-289; Nagelkerke NJD (1991) A note on a general definition of the 
+pp. 237-289; Nagelkerke NJD (1991) A note on a general definition of the
 coefficient of determination. Biometrika 78: 691-692; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York; LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton.
    
 
    Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. Journal of Statistical Software, 63(18), 1-36. doi:10.18637/jss.v063.i18
 .
    
 
    Bivand, R. S., Hauke, J., and Kossowski, T. (2013). Computing the Jacobian in Gaussian spatial autoregressive models: An illustrated comparison of available methods. Geographical Analysis, 45(2), 150-179.
    
     
    
-    
    
-    
    Author
    
-    
    Roger Bivand Roger.Bivand@nhh.no, with thanks to Andrew 
+    
    
+    
    Author
    
+    
    Roger Bivand Roger.Bivand@nhh.no, with thanks to Andrew
 Bernat for contributions to the asymptotic standard error code.
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    lm, impacts
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    data(oldcol, package="spdep")
 listw <- spdep::nb2listw(COL.nb, style="W")
 ev <- eigenw(listw)
@@ -587,7 +576,7 @@ 
    Examples
    
 #> Computing eigenvalues ...
 #> 
 #>    user  system elapsed 
-#>   0.141   0.000   0.142 
+#>   0.187   0.000   0.188 
 summary(COL.lag.M)
 #> 
 #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw, 
@@ -643,7 +632,7 @@ 
    Examples
    
 #> Computing eigenvalues ...
 #> 
 #>    user  system elapsed 
-#>   0.406   0.001   0.409 
+#>   0.449   0.003   0.454 
 summary(COL.lag.sp)
 #> 
 #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw, 
@@ -1428,79 +1417,79 @@ 
    Examples
    
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="eigen", control=list(pre_eig=ev))))
 #>    user  system elapsed 
-#>   0.148   0.000   0.149 
+#>   0.165   0.000   0.166 
 ocoef <- coefficients(COL.errW.eig)
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="eigen", control=list(pre_eig=ev, LAPACK=FALSE))))
 #>    user  system elapsed 
-#>   0.152   0.000   0.153 
+#>   0.161   0.000   0.161 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="eigen", control=list(pre_eig=ev, compiled_sse=TRUE))))
 #>    user  system elapsed 
-#>   0.147   0.000   0.149 
+#>   0.160   0.000   0.161 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="Matrix_J", control=list(super=TRUE))))
 #> Warning: the default value of argument 'sqrt' of method 'determinant(<CHMfactor>, <logical>)' may change from TRUE to FALSE as soon as the next release of Matrix; set 'sqrt' when programming
 #>    user  system elapsed 
-#>   0.169   0.000   0.176 
+#>   0.185   0.000   0.186 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="Matrix_J", control=list(super=FALSE))))
 #>    user  system elapsed 
-#>   0.166   0.000   0.166 
+#>   0.177   0.000   0.178 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="Matrix_J", control=list(super=as.logical(NA)))))
 #>    user  system elapsed 
-#>   0.164   0.000   0.165 
+#>   0.178   0.000   0.178 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="Matrix", control=list(super=TRUE))))
 #>    user  system elapsed 
-#>   0.153   0.000   0.155 
+#>   0.169   0.000   0.169 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="Matrix", control=list(super=FALSE))))
 #>    user  system elapsed 
-#>   0.151   0.000   0.152 
+#>   0.164   0.000   0.165 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="Matrix", control=list(super=as.logical(NA)))))
 #>    user  system elapsed 
-#>   0.152   0.000   0.153 
+#>   0.165   0.000   0.166 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="spam", control=list(spamPivot="MMD"))))
 #>    user  system elapsed 
-#>   0.162   0.000   0.162 
+#>   0.175   0.001   0.176 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="spam", control=list(spamPivot="RCM"))))
 #>    user  system elapsed 
-#>    0.16    0.00    0.16 
+#>   0.184   0.000   0.184 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="spam_update", control=list(spamPivot="MMD"))))
 #>    user  system elapsed 
-#>   0.155   0.000   0.157 
+#>   0.216   0.000   0.216 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
  listw, method="spam_update", control=list(spamPivot="RCM"))))
 #>    user  system elapsed 
-#>   0.156   0.000   0.157 
+#>   0.182   0.000   0.183 
 print(all.equal(ocoef, coefficients(COL.errW.eig)))
 #> [1] TRUE
 # }
@@ -1867,27 +1856,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/Matrix_J_setup.html b/docs/reference/Matrix_J_setup.html
new file mode 100644
index 0000000..ae0235d
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+++ b/docs/reference/Matrix_J_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/Matrix_setup.html b/docs/reference/Matrix_setup.html
new file mode 100644
index 0000000..ae0235d
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+++ b/docs/reference/Matrix_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
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deleted file mode 100644
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diff --git a/docs/reference/SET_MCMC.html b/docs/reference/SET_MCMC.html
index 0db166e..991b064 100644
--- a/docs/reference/SET_MCMC.html
+++ b/docs/reference/SET_MCMC.html
@@ -1,138 +1,115 @@
 
-Bayesian MCMC spatial simultaneous autoregressive model estimation — spBreg_lag • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Bayesian MCMC spatial simultaneous autoregressive model estimation
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Bayesian MCMC spatial simultaneous autoregressive model estimation
    
+
+      
    SET_MCMC.Rd
    
     
    
 
-    
    
+    
    
     
    The spBreg_lag function is an early-release version of the Matlab Spatial Econometrics Toolbox function sar_g.m, using drawing by inversion, and not accommodating heteroskedastic disturbances.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    spBreg_lag(formula, data = list(), listw, na.action, Durbin, type,
     zero.policy=NULL, control=list())
 spBreg_sac(formula, data = list(), listw, listw2=NULL, na.action, 
     Durbin, type, zero.policy=NULL, control=list())
 spBreg_err(formula, data = list(), listw, na.action, Durbin, etype,
     zero.policy=NULL, control=list())
-# S3 method for MCMC_sar_G
+# S3 method for class 'MCMC_sar_G'
 impacts(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL)
-# S3 method for MCMC_sem_G
+# S3 method for class 'MCMC_sem_G'
 impacts(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL)
-# S3 method for MCMC_sac_G
+# S3 method for class 'MCMC_sac_G'
 impacts(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    formula
    
-
    a symbolic description of the model to be fit. The details 
+    
    
+    
    Arguments
    
+    
    
+
    formula
    
+
    a symbolic description of the model to be fit. The details
 of model specification are given for lm()
    
 
-  
    data
    
-
    an optional data frame containing the variables in the model. 
-By default the variables are taken from the environment which the function 
+  
    data
    
+
    an optional data frame containing the variables in the model.
+By default the variables are taken from the environment which the function
 is called.
    
 
-  
    listw, listw2
    
+  
    listw, listw2
    
 
    a listw object created for example by nb2listw
    
 
-  
    na.action
    
+  
    na.action
    
 
    a function (default options("na.action")), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.
    
 
-  
    Durbin
    
+  
    Durbin
    
 
    default FALSE (spatial lag model); if TRUE, full spatial Durbin model; if a formula object, the subset of explanatory variables to lag
    
 
-  
    type, etype
    
+  
    type, etype
    
 
    (use the ‘Durbin=’ argument - retained for backwards compatibility only) default "lag", may be set to "mixed"; when "mixed", the lagged intercept is dropped for spatial weights style "W", that is row-standardised weights, but otherwise included; “Durbin” may be used instead of “mixed”
    
 
-  
    zero.policy
    
-
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without 
+  
    zero.policy
    
+
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without
 neighbours, if FALSE (default) assign NA
    
 
 
- 
    control
    
+ 
    control
    
 
    list of extra control arguments - see section below
    
 
-  
    obj
    
+  
    obj
    
 
    A spatial regression object
    
 
-  
    ...
    
+  
    ...
    
 
    Arguments passed through to methods in the coda package
    
 
-  
    tr
    
+  
    tr
    
 
    A vector of traces of powers of the spatial weights matrix created using trW, for approximate impact measures; if not given, listw must be given for exact measures (for small to moderate spatial weights matrices); the traces must be for the same spatial weights as were used in fitting the spatial regression, and must be row-standardised
    
 
-  
    evalues
    
+  
    evalues
    
 
    vector of eigenvalues of spatial weights matrix for impacts calculations
    
 
-  
    Q
    
+  
    Q
    
 
    default NULL, else an integer number of cumulative power series impacts to calculate if tr is given
    
 
 
    
-    
    
-    
    Control arguments
    
-    
+    
    
+    
    Control arguments
    
+
 
    tol.opt:
    
 
    the desired accuracy of the optimization - passed to optimize() (default=square root of double precision machine tolerance, a larger root may be used needed, see help(boston) for an example)
    
 
@@ -207,9 +184,9 @@ 
    Control arguments
    
 
 
 
    
-    
    
-    
    Extra Bayesian control arguments
    
-    
+    
    
+    
    Extra Bayesian control arguments
    
+
 
    ldet_method
    
 
    default “SE_classic”; equivalent to the method argument in lagsarlm
    
 
@@ -271,22 +248,22 @@ 
    Extra Bayesian control arguments
    
       
    cc2
    
 
    default 0.2; initial tuning parameter for M-H sampling
    
 
-    
+
 
    
 
 
 
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no, with thanks to Abhirup Mallik and Virgilio Gómez-Rubio for initial coding GSoC 2011
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    #require("spdep", quietly=TRUE)
 data(oldcol, package="spdep")
 lw <- spdep::nb2listw(COL.nb, style="W")
@@ -965,27 +942,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/SE_classic_setup.html b/docs/reference/SE_classic_setup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/SE_classic_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/SE_interp_setup.html b/docs/reference/SE_interp_setup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/SE_interp_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/SE_whichMin_setup.html b/docs/reference/SE_whichMin_setup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/SE_whichMin_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/SLX.html b/docs/reference/SLX.html
index 0d77240..ec5ae77 100644
--- a/docs/reference/SLX.html
+++ b/docs/reference/SLX.html
@@ -1,172 +1,147 @@
 
-Spatial Durbin linear (SLX, spatially lagged X) model — lmSLX • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Spatial Durbin linear (SLX, spatially lagged X) model
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Spatial Durbin linear (SLX, spatially lagged X) model
    
+
+      
    SLX.Rd
    
     
    
 
-    
    
+    
    
     
    lmSLX fits an lm model augmented with the spatially lagged RHS variables, including the lagged intercept when the spatial weights are not row-standardised. create_WX creates spatially lagged RHS variables, and is exposed for use in model fitting functions.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    lmSLX(formula, data = list(), listw, na.action, weights=NULL, Durbin=TRUE,
  zero.policy=NULL, return_impacts=TRUE)
-# S3 method for SlX
+# S3 method for class 'SlX'
 print(x, digits = max(3L, getOption("digits") - 3L), ...)
-# S3 method for SlX
+# S3 method for class 'SlX'
 summary(object, correlation = FALSE, symbolic.cor = FALSE, ...)
-# S3 method for summary.SlX
+# S3 method for class 'summary.SlX'
 print(x, digits = max(3L, getOption("digits") - 3L),
  symbolic.cor = x$symbolic.cor, signif.stars = getOption("show.signif.stars"), ...)
-# S3 method for SlX
+# S3 method for class 'SlX'
 impacts(obj, ...)
-# S3 method for WXimpact
+# S3 method for class 'WXimpact'
 print(x, ...)
-# S3 method for WXimpact
+# S3 method for class 'WXimpact'
 summary(object, ..., adjust_k=(attr(object, "type") == "SDEM"))
-# S3 method for SlX
+# S3 method for class 'SlX'
 predict(object, newdata, listw, zero.policy=NULL, ...)
 create_WX(x, listw, zero.policy=NULL, prefix="")
    
     
    
 
-    
    
-    
    Arguments
    
-    
    formula
    
-
    a symbolic description of the model to be fit. The details 
+    
    
+    
    Arguments
    
+    
    
+
    formula
    
+
    a symbolic description of the model to be fit. The details
 of model specification are given for lm()
    
 
-  
    data
    
-
    an optional data frame containing the variables in the model. 
-By default the variables are taken from the environment which the function 
+  
    data
    
+
    an optional data frame containing the variables in the model.
+By default the variables are taken from the environment which the function
 is called.
    
 
-  
    listw
    
+  
    listw
    
 
    a listw object created for example by nb2listw
    
 
-  
    na.action
    
+  
    na.action
    
 
    a function (default options("na.action")), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the spatial weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.
    
 
-  
    weights
    
+  
    weights
    
 
    an optional vector of weights to be used in the fitting process. Non-NULL weights can be used to indicate that different observations have different variances (with the values in weights being inversely proportional to the variances); or equivalently, when the elements of weights are positive integers w_i, that each response y_i is the mean of w_i unit-weight observations (including the case that there are w_i observations equal to y_i and the data have been summarized) - lm
    
 
-  
    Durbin
    
+  
    Durbin
    
 
    default TRUE for lmSLX (Durbin model including WX); if TRUE, full spatial Durbin model; if a formula object, the subset of explanatory variables to lag
    
 
-  
    zero.policy
    
+  
    zero.policy
    
 
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA
    
 
-  
    return_impacts
    
+  
    return_impacts
    
 
    default TRUE; may be set FALSE to avoid problems calculating impacts with aliased variables
    
 
-  
    digits
    
+  
    digits
    
 
    the number of significant digits to use when printing
    
 
-  
    correlation
    
+  
    correlation
    
 
    logical; if TRUE, the correlation matrix of the estimated parameters is returned and printed
    
 
-  
    symbolic.cor
    
+  
    symbolic.cor
    
 
    logical. If TRUE, print the correlations in a symbolic form (see 'symnum') rather than as numbers
    
 
-  
    signif.stars
    
+  
    signif.stars
    
 
    logical. If TRUE, 'significance stars' are printed for each coefficient
    
 
-  
    obj
    
+  
    obj
    
 
    A spatial regression object created by lmSLX
    
 
-  
    ...
    
+  
    ...
    
 
    Arguments passed through
    
 
-  
    prefix
    
+  
    prefix
    
 
    default empty string, may be “lag” in some cases
    
 
-  
    x, object
    
+  
    x, object
    
 
    model matrix to be lagged; lagImpact objects created by impacts methods
    
 
-  
    adjust_k
    
+  
    adjust_k
    
 
    default TRUE if SDEM else FALSE, adjust internal OLS SDEM standard errors by dividing by n rather than (n-k) (default changed and bug fixed after 0.7-8; standard errors now ML in SDEM summary and impacts summary and identical - for SLX use FALSE)
    
 
-  
    newdata
    
-
    data frame in which to predict --- if NULL, predictions are
+  
    newdata
    
+
    data frame in which to predict — if NULL, predictions are
 for the data on which the model was fitted. Should have row names corresponding to region.id. If row names are exactly the same than the ones used for training, it uses in-sample predictors for forecast.
    
 
 
    
-    
    
-    
    Value
    
-    
-
-
    The lmSLX function returns an “lm” object with a “mixedImps” list of three impact matrixes (impacts and standard errors) for direct, indirect and total impacts; total impacts calculated using a simplified local copy of the estimable function from the gmodels package.
    
+    
    
+    
    Value
    
+    
    The lmSLX function returns an “lm” object with a “mixedImps” list of three impact matrixes (impacts and standard errors) for direct, indirect and total impacts; total impacts calculated using a simplified local copy of the estimable function from the gmodels package.
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    lm
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    data(oldcol, package="spdep")
 lw <- spdep::nb2listw(COL.nb, style="W")
 COL.SLX <- lmSLX(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw)
@@ -397,27 +372,23 @@ 
    Examples
    
 #> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'mean': object 'pslx2' not found
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/SpatialFiltering.html b/docs/reference/SpatialFiltering.html
index d00a15b..b5a73b2 100644
--- a/docs/reference/SpatialFiltering.html
+++ b/docs/reference/SpatialFiltering.html
@@ -1,74 +1,50 @@
 
-Semi-parametric spatial filtering — SpatialFiltering • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Semi-parametric spatial filtering
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Semi-parametric spatial filtering
    
+
+      
    SpatialFiltering.Rd
    
     
    
 
-    
    
+    
    
     
    The function selects eigenvectors in a semi-parametric spatial filtering approach to removing spatial dependence from linear models. Selection is by brute force by finding the single eigenvector reducing the standard variate of Moran's I for regression residuals most, and continuing until no candidate eigenvector reduces the value by more than tol. It returns a summary table from the selection process and a matrix of selected eigenvectors for the specified model.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    SpatialFiltering(formula, lagformula=NULL, data=list(), na.action=na.fail,
  nb=NULL, glist = NULL,
  style = "C", zero.policy = NULL, tol = 0.1, zerovalue = 1e-04,
@@ -76,59 +52,58 @@ 
    Semi-parametric spatial filtering
    
  verbose=NULL)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    formula
    
+    
    
+    
    Arguments
    
+    
    
+
    formula
    
 
    a symbolic description of the model to be fit, assuming a spatial error representation; when lagformula is given, it should include only the response and the intercept term
    
 
-  
    lagformula
    
+  
    lagformula
    
 
    An extra one-sided formula to be used when a spatial lag representation is desired; the intercept is excluded within the function if present because it is part of the formula argument, but excluding it explicitly in the lagformula argument in the presence of factors generates a collinear model matrix
    
 
-  
    data
    
+  
    data
    
 
    an optional data frame containing the variables in the model
    
 
-  
    nb
    
+  
    nb
    
 
    an object of class nb
    
 
-  
    glist
    
+  
    glist
    
 
    list of general weights corresponding to neighbours
    
 
-  
    style
    
+  
    style
    
 
    style can take values W, B, C, U, and S
    
 
-  
    na.action
    
+  
    na.action
    
 
    a function (default options("na.action")), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the spatial weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.
    
 
-  
    zero.policy
    
+  
    zero.policy
    
 
    default NULL, use global option value; if FALSE stop with error for any empty neighbour sets, if TRUE permit the weights list to be formed with zero-length weights vectors
    
 
-  
    tol
    
+  
    tol
    
 
    tolerance value for convergence of spatial filtering
    
 
-  
    zerovalue
    
+  
    zerovalue
    
 
    eigenvectors with eigenvalues of an absolute value smaller than zerovalue will be excluded in eigenvector search
    
 
-  
    ExactEV
    
+  
    ExactEV
    
 
    Set ExactEV=TRUE to use exact expectations and variances rather than the expectation and variance of Moran's I from the previous iteration, default FALSE
    
 
-  
    symmetric
    
+  
    symmetric
    
 
    Should the spatial weights matrix be forced to symmetry, default TRUE
    
 
-  
    alpha
    
+  
    alpha
    
 
    if not NULL, used instead of the tol= argument as a stopping rule to choose all eigenvectors up to and including the one with a probability value exceeding alpha.
    
 
-  
    alternative
    
+  
    alternative
    
 
    a character string specifying the alternative hypothesis, must be one of greater, less or two.sided (default).
    
 
-  
    verbose
    
+  
    verbose
    
 
    default NULL, use global option value; if TRUE report eigenvectors selected
    
 
 
    
-    
    
-    
    Value
    
-    
-
-
    An SfResult object, with:
    
+    
    
+    
    Value
    
+    
    An SfResult object, with:
    
 
    selection
    
 
    a matrix summarising the selection of eigenvectors for inclusion, with columns:
    Step
    
 
    Step counter of the selection procedure
    
@@ -154,28 +129,28 @@ 
    Value
    
       
    gamma
    
 
    regression coefficient of selected eigenvector in fit
    
 
-    
+
 
    The first row is the value at the start of the search
    
 
   
    dataset
    
 
    a matrix of the selected eigenvectors in order of selection
    
 
 
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Tiefelsdorf M, Griffith DA. (2007) Semiparametric Filtering of Spatial Autocorrelation: The Eigenvector Approach. Environment and Planning A, 39 (5) 1193 - 1221.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Yongwan Chun, Michael Tiefelsdorf, Roger Bivand
    
     
    
-    
    
-    
    See also
    
-    
    lm, eigen, nb2listw, listw2U
    
+    
    
+    
    See also
    
+    
    lm, eigen, nb2listw, listw2U
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    require("sf", quietly=TRUE)
 columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
 #require("spdep", quietly=TRUE)
@@ -377,27 +352,23 @@ 
    Examples
    
 #> 
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/Wald1.Sarlm.html b/docs/reference/Wald1.Sarlm.html
new file mode 100644
index 0000000..72496f8
--- /dev/null
+++ b/docs/reference/Wald1.Sarlm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/anova.Sarlm.html b/docs/reference/anova.Sarlm.html
new file mode 100644
index 0000000..72496f8
--- /dev/null
+++ b/docs/reference/anova.Sarlm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/aple.html b/docs/reference/aple.html
index 85cf2e6..4f81f75 100644
--- a/docs/reference/aple.html
+++ b/docs/reference/aple.html
@@ -1,117 +1,92 @@
 
-Approximate profile-likelihood estimator (APLE) — aple • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Approximate profile-likelihood estimator (APLE)
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Approximate profile-likelihood estimator (APLE)
    
+
+      
    aple.Rd
    
     
    
 
-    
    
+    
    
     
    The Approximate profile-likelihood estimator (APLE) of the simultaneous autoregressive model's spatial dependence parameter was introduced in Li et al. (2007). It employs a correction term using the eigenvalues of the spatial weights matrix, and consequently should not be used for large numbers of observations. It also requires that the variable has a mean of zero, and it is assumed that it has been detrended. The spatial weights object is assumed to be row-standardised, that is using default style="W" in nb2listw.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    aple(x, listw, override_similarity_check=FALSE, useTrace=TRUE)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    x
    
+    
    
+    
    Arguments
    
+    
    
+
    x
    
 
    a zero-mean detrended continuous variable
    
 
-  
    listw
    
+  
    listw
    
 
    a listw object from for example spdep::nb2listw
    
 
-  
    override_similarity_check
    
+  
    override_similarity_check
    
 
    default FALSE, if TRUE - typically for row-standardised weights with asymmetric underlying general weights - similarity is not checked
    
 
-  
    useTrace
    
+  
    useTrace
    
 
    default TRUE, use trace of sparse matrix W %*% W (Li et al. (2010)), if FALSE, use crossproduct of eigenvalues of W as in Li et al. (2007)
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    This implementation has been checked with Hongfei Li's own implementation using her data; her help was very valuable.
    
     
    
-    
    
-    
    Value
    
-    
-
-
    A scalar APLE value.
    
+    
    
+    
    Value
    
+    
    A scalar APLE value.
    
     
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Li, H, Calder, C. A. and Cressie N. A. C. (2007) Beyond Moran's I: testing for spatial dependence based on the spatial autoregressive model. Geographical Analysis 39, 357-375; Li, H, Calder, C. A. and Cressie N. A. C. (2012) One-step estimation of spatial dependence parameters: Properties and extensions of the APLE statistic, Journal of Multivariate Analysis 105, 68-84.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    nb2listw, aple.mc, aple.plot
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    wheat <- st_read(system.file("shapes/wheat.gpkg", package="spData")[1], quiet=TRUE)
 library(spdep)
 #> 
@@ -124,6 +99,7 @@ 
    Examples
    
 #>     set.mcOption
 nbr1 <- spdep::poly2nb(wheat, queen=FALSE)
 nbrl <- spdep::nblag(nbr1, 2)
+#> Warning: lag 2 neighbour object has 2 sub-graphs
 nbr12 <- spdep::nblag_cumul(nbrl)
 cms0 <- with(as.data.frame(wheat), tapply(yield, c, median))
 cms1 <- c(model.matrix(~ factor(c) -1, data=wheat) %*% cms0)
@@ -163,27 +139,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/aple.mc.html b/docs/reference/aple.mc.html
index da43ccc..be89839 100644
--- a/docs/reference/aple.mc.html
+++ b/docs/reference/aple.mc.html
@@ -1,120 +1,96 @@
 
-Approximate profile-likelihood estimator (APLE) permutation test — aple.mc • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Approximate profile-likelihood estimator (APLE) permutation test
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Approximate profile-likelihood estimator (APLE) permutation test
    
+
+      
    aple.mc.Rd
    
     
    
 
-    
    
+    
    
     
    A permutation bootstrap test for the approximate profile-likelihood estimator (APLE).
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    aple.mc(x, listw, nsim, override_similarity_check=FALSE, useTrace=TRUE)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    x
    
+    
    
+    
    Arguments
    
+    
    
+
    x
    
 
    a zero-mean detrended continuous variable
    
 
-  
    listw
    
+  
    listw
    
 
    a listw object from for example spdep::nb2listw
    
 
-  
    nsim
    
+  
    nsim
    
 
    number of simulations
    
 
-  
    override_similarity_check
    
+  
    override_similarity_check
    
 
    default FALSE, if TRUE - typically for row-standardised weights with asymmetric underlying general weights - similarity is not checked
    
 
-  
    useTrace
    
+  
    useTrace
    
 
    default TRUE, use trace of sparse matrix W %*% W (Li et al. (2010)), if FALSE, use crossproduct of eigenvalues of W as in Li et al. (2007)
    
 
 
    
-    
    
-    
    Value
    
-    
-
-
    A boot object as returned by the boot function.
    
+    
    
+    
    Value
    
+    
    A boot object as returned by the boot function.
    
     
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Li, H, Calder, C. A. and Cressie N. A. C. (2007) Beyond Moran's I: testing for spatial dependence based on the spatial autoregressive model. Geographical Analysis 39, 357-375; Li, H, Calder, C. A. and Cressie N. A. C. (2012) One-step estimation of spatial dependence parameters: Properties and extensions of the APLE statistic, Journal of Multivariate Analysis 105, 68-84.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    aple, boot
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    # \dontrun{
 wheat <- st_read(system.file("shapes/wheat.gpkg", package="spData")[1], quiet=TRUE)
 nbr1 <- spdep::poly2nb(wheat, queen=FALSE)
 nbrl <- spdep::nblag(nbr1, 2)
+#> Warning: lag 2 neighbour object has 2 sub-graphs
 nbr12 <- spdep::nblag_cumul(nbrl)
 wheat_g <- wheat
 st_geometry(wheat_g) <- NULL
@@ -178,27 +154,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/aple.plot.html b/docs/reference/aple.plot.html
index 875f3a2..2cd3ac3 100644
--- a/docs/reference/aple.plot.html
+++ b/docs/reference/aple.plot.html
@@ -1,108 +1,83 @@
 
-Approximate profile-likelihood estimator (APLE) scatterplot — aple.plot • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Approximate profile-likelihood estimator (APLE) scatterplot
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Approximate profile-likelihood estimator (APLE) scatterplot
    
+
+      
    aple.plot.Rd
    
     
    
 
-    
    
+    
    
     
    A scatterplot decomposition of the approximate profile-likelihood estimator, and a local APLE based on the list of vectors returned by the scatterplot function.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    aple.plot(x, listw, override_similarity_check=FALSE, useTrace=TRUE, do.plot=TRUE, ...)
 localAple(x, listw, override_similarity_check=FALSE, useTrace=TRUE)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    x
    
+    
    
+    
    Arguments
    
+    
    
+
    x
    
 
    a zero-mean detrended continuous variable
    
 
-  
    listw
    
+  
    listw
    
 
    a listw object from for example spdep::nb2listw
    
 
-  
    override_similarity_check
    
+  
    override_similarity_check
    
 
    default FALSE, if TRUE - typically for row-standardised weights with asymmetric underlying general weights - similarity is not checked
    
 
-  
    useTrace
    
+  
    useTrace
    
 
    default TRUE, use trace of sparse matrix W %*% W (Li et al. (2010)), if FALSE, use crossproduct of eigenvalues of W as in Li et al. (2007)
    
 
-  
    do.plot
    
+  
    do.plot
    
 
    default TRUE: should a scatterplot be drawn
    
 
-  
    ...
    
+  
    ...
    
 
    other arguments to be passed to plot
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    The function solves a secondary eigenproblem of size n internally, so constructing the values for the scatterplot is quite compute and memory intensive, and is not suitable for very large n.
    
     
    
-    
    
-    
    Value
    
-    
-
-
    aple.plot returns list with components:
    
+    
    
+    
    Value
    
+    
    aple.plot returns list with components:
    
 
    X
    
 
    A vector as described in Li et al. (2007), p. 366.
    
 
@@ -112,25 +87,26 @@ 
    Value
    
 
 
    localAple returns a vector of local APLE values.
    
     
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Li, H, Calder, C. A. and Cressie N. A. C. (2007) Beyond Moran's I: testing for spatial dependence based on the spatial autoregressive model. Geographical Analysis 39, pp. 357-375; Li, H, Calder, C. A. and Cressie N. A. C. (2012) One-step estimation of spatial dependence parameters: Properties and extensions of the APLE statistic, Journal of Multivariate Analysis 105, 68-84.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    aple
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    # \dontrun{
 wheat <- st_read(system.file("shapes/wheat.gpkg", package="spData")[1], quiet=TRUE)
 nbr1 <- spdep::poly2nb(wheat, queen=FALSE)
 nbrl <- spdep::nblag(nbr1, 2)
+#> Warning: lag 2 neighbour object has 2 sub-graphs
 nbr12 <- spdep::nblag_cumul(nbrl)
 cms0 <- with(as.data.frame(wheat), tapply(yield, c, median))
 cms1 <- c(model.matrix(~ factor(c) -1, data=wheat) %*% cms0)
@@ -209,27 +185,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/as.data.frame.Sarlm.pred.html b/docs/reference/as.data.frame.Sarlm.pred.html
new file mode 100644
index 0000000..d484aaf
--- /dev/null
+++ b/docs/reference/as.data.frame.Sarlm.pred.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/as_dgRMatrix_listw.html b/docs/reference/as_dgRMatrix_listw.html
new file mode 100644
index 0000000..210cb07
--- /dev/null
+++ b/docs/reference/as_dgRMatrix_listw.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/as_dsCMatrix_I.html b/docs/reference/as_dsCMatrix_I.html
new file mode 100644
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--- /dev/null
+++ b/docs/reference/as_dsCMatrix_I.html
@@ -0,0 +1,8 @@
+
+  
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+    
+    
+  
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diff --git a/docs/reference/as_dsCMatrix_IrW.html b/docs/reference/as_dsCMatrix_IrW.html
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--- /dev/null
+++ b/docs/reference/as_dsCMatrix_IrW.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/as_dsTMatrix_listw.html b/docs/reference/as_dsTMatrix_listw.html
new file mode 100644
index 0000000..210cb07
--- /dev/null
+++ b/docs/reference/as_dsTMatrix_listw.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/bptest.Sarlm.html b/docs/reference/bptest.Sarlm.html
new file mode 100644
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--- /dev/null
+++ b/docs/reference/bptest.Sarlm.html
@@ -0,0 +1,8 @@
+
+  
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+    
+    
+  
+
+
diff --git a/docs/reference/can.be.simmed.html b/docs/reference/can.be.simmed.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/can.be.simmed.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/cheb_setup.html b/docs/reference/cheb_setup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/cheb_setup.html
@@ -0,0 +1,8 @@
+
+  
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+    
+    
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+
+
diff --git a/docs/reference/coef.Gmsar.html b/docs/reference/coef.Gmsar.html
new file mode 100644
index 0000000..0cf5fc8
--- /dev/null
+++ b/docs/reference/coef.Gmsar.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/coef.Lagmess.html b/docs/reference/coef.Lagmess.html
new file mode 100644
index 0000000..9b7573e
--- /dev/null
+++ b/docs/reference/coef.Lagmess.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/coef.Sarlm.html b/docs/reference/coef.Sarlm.html
new file mode 100644
index 0000000..4dbdc74
--- /dev/null
+++ b/docs/reference/coef.Sarlm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/coef.Spautolm.html b/docs/reference/coef.Spautolm.html
new file mode 100644
index 0000000..571745b
--- /dev/null
+++ b/docs/reference/coef.Spautolm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/coef.Stsls.html b/docs/reference/coef.Stsls.html
new file mode 100644
index 0000000..d4980c7
--- /dev/null
+++ b/docs/reference/coef.Stsls.html
@@ -0,0 +1,8 @@
+
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+    
+    
+    
+  
+
+
diff --git a/docs/reference/coerce,listw,CsparseMatrix-method.html b/docs/reference/coerce,listw,CsparseMatrix-method.html
new file mode 100644
index 0000000..210cb07
--- /dev/null
+++ b/docs/reference/coerce,listw,CsparseMatrix-method.html
@@ -0,0 +1,8 @@
+
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+    
+    
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+
+
diff --git a/docs/reference/coerce,listw,RsparseMatrix-method.html b/docs/reference/coerce,listw,RsparseMatrix-method.html
new file mode 100644
index 0000000..210cb07
--- /dev/null
+++ b/docs/reference/coerce,listw,RsparseMatrix-method.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/coerce,listw,symmetricMatrix-method.html b/docs/reference/coerce,listw,symmetricMatrix-method.html
new file mode 100644
index 0000000..210cb07
--- /dev/null
+++ b/docs/reference/coerce,listw,symmetricMatrix-method.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/create_WX.html b/docs/reference/create_WX.html
new file mode 100644
index 0000000..db024e0
--- /dev/null
+++ b/docs/reference/create_WX.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/deviance.Gmsar.html b/docs/reference/deviance.Gmsar.html
new file mode 100644
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--- /dev/null
+++ b/docs/reference/deviance.Gmsar.html
@@ -0,0 +1,8 @@
+
+  
+    
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+    
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+
diff --git a/docs/reference/deviance.Lagmess.html b/docs/reference/deviance.Lagmess.html
new file mode 100644
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--- /dev/null
+++ b/docs/reference/deviance.Lagmess.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/deviance.Sarlm.html b/docs/reference/deviance.Sarlm.html
new file mode 100644
index 0000000..4dbdc74
--- /dev/null
+++ b/docs/reference/deviance.Sarlm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/deviance.Spautolm.html b/docs/reference/deviance.Spautolm.html
new file mode 100644
index 0000000..571745b
--- /dev/null
+++ b/docs/reference/deviance.Spautolm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/deviance.Stsls.html b/docs/reference/deviance.Stsls.html
new file mode 100644
index 0000000..d4980c7
--- /dev/null
+++ b/docs/reference/deviance.Stsls.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
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+
+
diff --git a/docs/reference/do_ldet.html b/docs/reference/do_ldet.html
index 88a6497..e9c485b 100644
--- a/docs/reference/do_ldet.html
+++ b/docs/reference/do_ldet.html
@@ -1,74 +1,50 @@
 
-Spatial regression model Jacobian computations — do_ldet • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Spatial regression model Jacobian computations
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Spatial regression model Jacobian computations
    
+
+      
    do_ldet.Rd
    
     
    
 
-    
    
+    
    
     
    These functions are made available in the package namespace for other developers, and are not intended for users. They provide a shared infrastructure for setting up data for Jacobian computation, and then for caclulating the Jacobian, either exactly or approximately, in maximum likelihood fitting of spatial regression models. The techniques used are the exact eigenvalue, Cholesky decompositions (Matrix, spam), and LU ones, with Chebyshev and Monte Carlo approximations; moments use the methods due to Martin and Smirnov/Anselin.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    do_ldet(coef, env, which=1)
 jacobianSetup(method, env, con, pre_eig=NULL, trs=NULL, interval=NULL, which=1)
 cheb_setup(env, q=5, which=1)
@@ -91,86 +67,87 @@ 
    Spatial regression model Jacobian computations
    
 can.be.simmed(listw)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    coef
    
+    
    
+    
    Arguments
    
+    
    
+
    coef
    
 
    spatial coefficient value
    
 
-  
    env
    
+  
    env
    
 
    environment containing pre-computed objects, fixed after assignment in setup functions
    
 
-  
    which
    
+  
    which
    
 
    default 1; if 2, use second listw object
    
 
-  
    method
    
+  
    method
    
 
    string value, used by jacobianSetup to choose method
    
 
-  
    con
    
+  
    con
    
 
    control list passed from model fitting function and parsed in jacobianSetup to set environment variables for method-specific setup
    
 
-  
    pre_eig
    
+  
    pre_eig
    
 
    pre-computed eigenvalues of length n
    
 
-  
    q
    
+  
    q
    
 
    Chebyshev approximation order; default in calling spdep functions is 5, here it cannot be missing and does not have a default
    
 
-  
    p
    
+  
    p
    
 
    Monte Carlo approximation number of random normal variables; default calling spdep functions is 16, here it cannot be missing and does not have a default
    
 
-  
    m
    
+  
    m
    
 
    Monte Carlo approximation number of series terms; default in calling spdep functions is 30, here it cannot be missing and does not have a default; m serves the same purpose in the moments method
    
 
-  
    pivot
    
+  
    pivot
    
 
    default “MMD”, may also be “RCM” for Cholesky decompisition using spam
    
 
-  
    in_coef
    
+  
    in_coef
    
 
    fill-in initiation coefficient value, default 0.1
    
 
-  
    Imult
    
+  
    Imult
    
 
    see Cholesky; numeric scalar which defaults to zero. The matrix that is decomposed is A+m*I where m is the value of Imult and I is the identity matrix of order ncol(A). Default in calling spdep functions is 2, here it cannot be missing and does not have a default, but is rescaled for binary weights matrices in proportion to the maximim row sum in those calling functions
    
 
-  
    super
    
+  
    super
    
 
    see Cholesky; logical scalar indicating is a supernodal decomposition should be created.  The alternative is a simplicial decomposition. Default in calling spdep functions is FALSE for “Matrix_J” and as.logical(NA) for “Matrix”.  Setting it to NA leaves the choice to a CHOLMOD-internal heuristic
    
 
-  
    order
    
+  
    order
    
 
    default FALSE; used in LU_prepermutate, note warnings given for lu method
    
 
-  
    trs
    
+  
    trs
    
 
    A numeric vector of m traces, as from trW
    
 
-  
    type
    
+  
    type
    
 
    moments trace type, see trW
    
 
-  
    correct
    
+  
    correct
    
 
    default TRUE: use Smirnov correction term, see trW
    
 
-  
    trunc
    
+  
    trunc
    
 
    default TRUE: truncate Smirnov correction term, see trW
    
 
-  
    eq7
    
+  
    eq7
    
 
    default TRUE; use equation 7 in Smirnov and Anselin (2009), if FALSE no unit root correction
    
 
-  
    SE_method
    
+  
    SE_method
    
 
    default “LU”, alternatively “MC”; underlying lndet method to use for generating SE toolbox emulation grid
    
 
-  
    nrho
    
+  
    nrho
    
 
    default 200, number of lndet values in first stage SE toolbox emulation grid
    
 
-  
    interval
    
+  
    interval
    
 
    default c(-1,0.999) if interval argument NULL, bounds for SE toolbox emulation grid
    
 
-  
    interpn
    
+  
    interpn
    
 
    default 2000, number of lndet values to interpolate in second stage SE toolbox emulation grid
    
 
-  
    SElndet
    
+  
    SElndet
    
 
    default NULL, used to pass a pre-computed two-column matrix of coefficient values and corresponding interpolated lndet values
    
 
-  
    listw
    
+  
    listw
    
 
    a spatial weights object
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    Since environments are containers in the R workspace passed by reference rather than by value, they are useful for passing objects to functions called in numerical optimisation, here for the maximum likelihood estimation of spatial regression models. This technique can save a little time on each function call, balanced against the need to access the objects in the environment inside the function. The environment should contain a family string object either “SAR”, “CAR” or “SMA” (used in do_ldet to choose spatial moving average in spautolm, and these specific objects before calling the set-up functions:
    
 
    eigen
    
 
    Classical Ord eigenvalue computations - either:
    listw
    
@@ -182,11 +159,11 @@ 
    Details
    
     
    verbose
    
 
    logical scalar: legacy report print control, for historical reasons only
    
 
-  
+
 
    or:
    pre_eig
    
 
    pre-computed eigenvalues
    
 
-  
+
 
    and assigns to the environment:
    eig
    
 
    a vector of eigenvalues
    
 
@@ -196,7 +173,7 @@ 
    Details
    
     
    method
    
 
    string: “eigen”
    
 
-  
+
 
    
 
   
    Matrix
    
@@ -206,7 +183,7 @@ 
    Details
    
     
    can.sim
    
 
    logical scalar: can the spatial weights be made symmetric by similarity
    
 
-  
+
 
    and assigns to the environment:
    csrw
    
 
    sparse spatial weights matrix
    
 
@@ -222,7 +199,7 @@ 
    Details
    
     
    method
    
 
    string: “Matrix”
    
 
-  
+
 
    
 
   
    Matrix_J
    
@@ -235,7 +212,7 @@ 
    Details
    
     
    n
    
 
    number of spatial objects
    
 
-  
+
 
    and assigns to the environment:
    csrw
    
 
    sparse spatial weights matrix
    
 
@@ -248,7 +225,7 @@ 
    Details
    
     
    method
    
 
    string: “Matrix_J”
    
 
-  
+
 
    
 
   
    spam
    
@@ -261,7 +238,7 @@ 
    Details
    
     
    n
    
 
    number of spatial objects
    
 
-  
+
 
    and assigns to the environment:
    csrw
    
 
    sparse spatial weights matrix
    
 
@@ -269,12 +246,12 @@ 
    Details
    
 
    sparse identity matrix
    
 
     
    pivot
    
-
    string --- pivot method
    
+
    string — pivot method
    
 
     
    method
    
 
    string: “spam”
    
 
-  
+
 
    
 
   
    spam_update
    
@@ -287,7 +264,7 @@ 
    Details
    
     
    n
    
 
    number of spatial objects
    
 
-  
+
 
    and assigns to the environment:
    csrw
    
 
    sparse spatial weights matrix
    
 
@@ -300,7 +277,7 @@ 
    Details
    
     
    method
    
 
    string: “spam”
    
 
-  
+
 
    
 
   
    LU
    
@@ -310,7 +287,7 @@ 
    Details
    
     
    n
    
 
    number of spatial objects
    
 
-  
+
 
    and assigns to the environment:
    W
    
 
    sparse spatial weights matrix
    
 
@@ -320,7 +297,7 @@ 
    Details
    
     
    method
    
 
    string: “LU”
    
 
-  
+
 
    
 
   
    LU_prepermutate
    
@@ -330,7 +307,7 @@ 
    Details
    
     
    n
    
 
    number of spatial objects
    
 
-  
+
 
    and assigns to the environment:
    W
    
 
    sparse spatial weights matrix
    
 
@@ -346,14 +323,14 @@ 
    Details
    
     
    method
    
 
    string: “LU”
    
 
-  
+
 
    
 
   
    MC
    
 
    Monte Carlo approximation:
    listw
    
 
    A listw spatial weights object
    
 
-  
+
 
    and assigns to the environment:
    clx
    
 
    list of Monte Carlo approximation terms  (the first two simulated traces are replaced by their analytical equivalents)
    
 
@@ -363,14 +340,14 @@ 
    Details
    
     
    method
    
 
    string: “MC”
    
 
-  
+
 
    
 
   
    cheb
    
 
    Chebyshev approximation:
    listw
    
 
    A listw spatial weights object
    
 
-  
+
 
    and assigns to the environment:
    trT
    
 
    vector of Chebyshev approximation terms
    
 
@@ -380,7 +357,7 @@ 
    Details
    
     
    method
    
 
    string: “Chebyshev”
    
 
-  
+
 
    
 
   
    moments
    
@@ -390,7 +367,7 @@ 
    Details
    
     
    can.sim
    
 
    logical scalar: can the spatial weights be made symmetric by similarity
    
 
-  
+
 
    and assigns to the environment:
    trs
    
 
    vector of traces, possibly approximated
    
 
@@ -409,7 +386,7 @@ 
    Details
    
     
    method
    
 
    string: “moments”
    
 
-  
+
 
    
 
   
    SE_classic
    
@@ -419,7 +396,7 @@ 
    Details
    
     
    n
    
 
    number of spatial objects
    
 
-  
+
 
    and assigns to the environment:
    detval
    
 
    two column matrix of lndet grid values
    
 
@@ -429,7 +406,7 @@ 
    Details
    
     
    SE_method
    
 
    string: “LU” or “MC”
    
 
-  
+
 
    
 
   
    SE_whichMin
    
@@ -439,7 +416,7 @@ 
    Details
    
     
    n
    
 
    number of spatial objects
    
 
-  
+
 
    and assigns to the environment:
    detval
    
 
    two column matrix of lndet grid values
    
 
@@ -449,7 +426,7 @@ 
    Details
    
     
    SE_method
    
 
    string: “LU” or “MC”
    
 
-  
+
 
    
 
   
    SE_interp
    
@@ -459,7 +436,7 @@ 
    Details
    
     
    n
    
 
    number of spatial objects
    
 
-  
+
 
    and assigns to the environment:
    fit
    
 
    fitted spline object from which to predict lndet values
    
 
@@ -469,33 +446,33 @@ 
    Details
    
     
    SE_method
    
 
    string: “LU” or “MC”
    
 
-  
+
 
    
 
 
 
    Some set-up functions may also assign similar to the environment if the weights were made symmetric by similarity.
    
 
    Three set-up functions emulate the behaviour of the Spatial Econometrics toolbox (March 2010) maximum likelihood lndet grid performance. The toolbox lndet functions compute a smaller number of lndet values for a grid of coefficient values (spacing 0.01), and then interpolate to a finer grid of values (spacing 0.001). “SE_classic”, which is an implementation of the SE toolbox code, for example in f_sar.m, appears to have selected a row in the grid matrix one below the correct row when the candidate coefficient value was between 0.005 and 0.01-fuzz, always rounding the row index down. A possible alternative is to choose the index that is closest to the candidate coefficient value (“SE_whichMin”). Another alternative is to fit a spline model to the first stage coarser grid, and pass this fitted model to the log likelihood function to make a point prediction using the candidate coefficient value, rather than finding the grid index (“SE_interp”).
    
     
    
-    
    
-    
    Value
    
+    
    
+    
    Value
    
     
    do_ldet returns the value of the Jacobian for the calculation method recorded in the environment argument, and for the Monte Carlo approximation, returns a measure of the spread of the approximation as an “sd” attribute; the remaining functions modify the environment in place as a side effect and return nothing.
    
     
    
-    
    
-    
    References
    
-    
    LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 77--110.
    
+    
    
+    
    References
    
+    
    LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 77–110.
    
 
    Bivand, R. S., Hauke, J., and Kossowski, T. (2013). Computing the Jacobian in Gaussian spatial autoregressive models: An illustrated comparison of available methods. Geographical Analysis, 45(2), 150-179.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    spautolm, lagsarlm, errorsarlm, Cholesky
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    data(boston, package="spData")
 #require("spdep", quietly=TRUE)
 lw <- spdep::nb2listw(boston.soi)
@@ -597,27 +574,23 @@ 
    Examples
    
 rm(env)
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/eigen_pre_setup.html b/docs/reference/eigen_pre_setup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/eigen_pre_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/eigen_setup.html b/docs/reference/eigen_setup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/eigen_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/eigenw.html b/docs/reference/eigenw.html
index 5aa859f..3a759d4 100644
--- a/docs/reference/eigenw.html
+++ b/docs/reference/eigenw.html
@@ -1,149 +1,130 @@
 
-Spatial weights matrix eigenvalues — griffith_sone • spatialregSpatial weights matrix eigenvalues — griffith_sone • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Spatial weights matrix eigenvalues
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Spatial weights matrix eigenvalues
    
+
+      
    eigenw.Rd
    
     
    
 
-    
    
-    
    The eigenw function returns a numeric vector of eigenvalues of 
-the weights matrix generated from the spatial weights object listw. 
-The eigenvalues are used to speed the computation of the Jacobian in 
+    
    
+    
    The eigenw function returns a numeric vector of eigenvalues of
+the weights matrix generated from the spatial weights object listw.
+The eigenvalues are used to speed the computation of the Jacobian in
 spatial model estimation:
    
 
    $$\log(\det[I - \rho W]) = \sum_{i=1}^{n}\log(1 - \rho \lambda_i)$$
    
 
    where \(W\) is the n by n spatial weights matrix, and \(\lambda_i\) are the
 eigenvalues of \(W\).
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    eigenw(listw, quiet=NULL)
 griffith_sone(P, Q, type="rook")
 subgraph_eigenw(nb, glist=NULL, style="W", zero.policy=NULL, quiet=NULL)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    listw
    
+    
    
+    
    Arguments
    
+    
    
+
    listw
    
 
    a listw object created for example by nb2listw
    
 
-  
    quiet
    
+  
    quiet
    
 
    default NULL, use global !verbose option value; set to FALSE for short summary
    
 
-  
    P
    
+  
    P
    
 
    number of columns in the grid (number of units in a horizontal axis direction)
    
 
-  
    Q
    
+  
    Q
    
 
    number of rows in the grid (number of units in a vertical axis direction.)
    
 
-  
    type
    
+  
    type
    
 
    “rook” or “queen”
    
 
-  
    nb
    
+  
    nb
    
 
    an object of class nb
    
 
-  
    glist
    
+  
    glist
    
 
    list of general weights corresponding to neighbours
    
 
-  
    style
    
+  
    style
    
 
    style can take values “W”, “B”, “C”, “U”, “minmax” and “S”
    
 
-  
    zero.policy
    
+  
    zero.policy
    
 
    default NULL, use global option value; if FALSE stop with error for any empty neighbour sets, if TRUE permit the weights list to be formed with zero-length weights vectors
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    
 The griffith_sone function function may be used, following Ord and Gasim (for references see Griffith and Sone (1995)), to calculate analytical eigenvalues for binary rook or queen contiguous neighbours where the data are arranged as a regular P times Q grid. The subgraph_eigenw function may be used when there are multiple graph components, of which the largest may be handled as a dense matrix. Here the eigenvalues are computed for each subgraph in turn, and catenated to reconstruct the complete set. The functions may be used to provide pre-computed eigenvalues for spatial regression functions.
    
     
    
-    
    
-    
    Value
    
-    
-
-
    a numeric or complex vector of eigenvalues of the weights matrix generated from the spatial weights object.
    
+    
    
+    
    Value
    
+    
    a numeric or complex vector of eigenvalues of the weights matrix generated from the spatial weights object.
    
     
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 155;
 Ord, J. K. 1975 Estimation methods for models of spatial interaction, Journal
 of the American Statistical Association, 70, 120-126.; Griffith, D. A. and Sone, A. (1995). Trade-offs associated with normalizing constant computational simplifications for estimating spatial statistical models. Journal of Statistical Computation and Simulation, 51, 165-183.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    eigen
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    #require(spdep)
 data(oldcol, package="spdep")
 W.eig <- eigenw(spdep::nb2listw(COL.nb, style="W"))
@@ -158,6 +139,7 @@ 
    Examples
    
 # cases for intrinsically asymmetric weights
 crds <- cbind(COL.OLD$X, COL.OLD$Y)
 k3 <- spdep::knn2nb(spdep::knearneigh(crds, k=3))
+#> Warning: neighbour object has 2 sub-graphs
 spdep::is.symmetric.nb(k3)
 #> [1] FALSE
 k3eig <- eigenw(spdep::nb2listw(k3, style="W"))
@@ -169,7 +151,8 @@ 
    Examples
    
 Jc
 #> [1] -1.749705+0i
 # subgraphs
-nc <- spdep::n.comp.nb(k3)
+nc <- attr(k3, "ncomp")
+if (is.null(nc)) nc <- spdep::n.comp.nb(k3)
 nc$nc
 #> [1] 2
 table(nc$comp.id)
@@ -248,27 +231,23 @@ 
    Examples
    
 #> [1] -1  1
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/errorsarlm.html b/docs/reference/errorsarlm.html
new file mode 100644
index 0000000..4dbdc74
--- /dev/null
+++ b/docs/reference/errorsarlm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/fitted.Gmsar.html b/docs/reference/fitted.Gmsar.html
new file mode 100644
index 0000000..0cf5fc8
--- /dev/null
+++ b/docs/reference/fitted.Gmsar.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/fitted.Lagmess.html b/docs/reference/fitted.Lagmess.html
new file mode 100644
index 0000000..9b7573e
--- /dev/null
+++ b/docs/reference/fitted.Lagmess.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/fitted.Me_res.html b/docs/reference/fitted.Me_res.html
new file mode 100644
index 0000000..1732931
--- /dev/null
+++ b/docs/reference/fitted.Me_res.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/fitted.Sarlm.html b/docs/reference/fitted.Sarlm.html
new file mode 100644
index 0000000..4dbdc74
--- /dev/null
+++ b/docs/reference/fitted.Sarlm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/fitted.SfResult.html b/docs/reference/fitted.SfResult.html
new file mode 100644
index 0000000..46596b8
--- /dev/null
+++ b/docs/reference/fitted.SfResult.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/fitted.Spautolm.html b/docs/reference/fitted.Spautolm.html
new file mode 100644
index 0000000..571745b
--- /dev/null
+++ b/docs/reference/fitted.Spautolm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/get.ClusterOption.html b/docs/reference/get.ClusterOption.html
new file mode 100644
index 0000000..7cb0a7d
--- /dev/null
+++ b/docs/reference/get.ClusterOption.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/get.VerboseOption.html b/docs/reference/get.VerboseOption.html
new file mode 100644
index 0000000..c8246da
--- /dev/null
+++ b/docs/reference/get.VerboseOption.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/get.ZeroPolicyOption.html b/docs/reference/get.ZeroPolicyOption.html
new file mode 100644
index 0000000..c8246da
--- /dev/null
+++ b/docs/reference/get.ZeroPolicyOption.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/get.coresOption.html b/docs/reference/get.coresOption.html
new file mode 100644
index 0000000..7cb0a7d
--- /dev/null
+++ b/docs/reference/get.coresOption.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/get.mcOption.html b/docs/reference/get.mcOption.html
new file mode 100644
index 0000000..7cb0a7d
--- /dev/null
+++ b/docs/reference/get.mcOption.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/gstsls-1.png b/docs/reference/gstsls-1.png
index 9df8046..031c9b3 100644
Binary files a/docs/reference/gstsls-1.png and b/docs/reference/gstsls-1.png differ
diff --git a/docs/reference/gstsls.html b/docs/reference/gstsls.html
index f5c6f65..f32bb22 100644
--- a/docs/reference/gstsls.html
+++ b/docs/reference/gstsls.html
@@ -1,173 +1,152 @@
 
-Spatial simultaneous autoregressive SAC model estimation by GMM — gstsls • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Spatial simultaneous autoregressive SAC model estimation by GMM
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Spatial simultaneous autoregressive SAC model estimation by GMM
    
+
+      
    gstsls.Rd
    
     
    
 
-    
    
+    
    
     
    An implementation of Kelejian and Prucha's generalised moments estimator for the autoregressive parameter in a spatial model
   with a spatially lagged dependent variable.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    gstsls(formula, data = list(), listw, listw2 = NULL, na.action = na.fail, 
     zero.policy = attr(listw, "zero.policy"), pars=NULL, scaleU=FALSE, control = list(), 
-    verbose=NULL, method="nlminb", robust=FALSE, legacy=FALSE, W2X=TRUE) 
-# S3 method for Gmsar
+    verbose=NULL, method="nlminb", robust=FALSE, legacy=FALSE, W2X=TRUE, sig2n_k=FALSE) 
+# S3 method for class 'Gmsar'
 impacts(obj, ..., n = NULL, tr = NULL, R = NULL,
  listw = NULL, evalues=NULL, tol = 1e-06, empirical = FALSE, Q=NULL)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    formula
    
-
    a symbolic description of the model to be fit. The details 
+    
    
+    
    Arguments
    
+    
    
+
    formula
    
+
    a symbolic description of the model to be fit. The details
 of model specification are given for lm()
    
 
-  
    data
    
-
    an optional data frame containing the variables in the model. 
-By default the variables are taken from the environment which the function 
+  
    data
    
+
    an optional data frame containing the variables in the model.
+By default the variables are taken from the environment which the function
 is called.
    
 
-  
    listw
    
+  
    listw
    
 
    a listw object created for example by nb2listw
    
 
-  
    listw2
    
+  
    listw2
    
 
    a listw object created for example by nb2listw, if not given, set to the same spatial weights as the listw argument
    
 
-  
    na.action
    
+  
    na.action
    
 
    a function (default na.fail), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.
    
 
-  
    zero.policy
    
-
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without 
+  
    zero.policy
    
+
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without
 neighbours, if FALSE (default) assign NA - causing GMerrorsar() to terminate with an error
    
 
-  
    pars
    
-
    starting values for \(\lambda\) and \(\sigma^2\) for GMM optimisation, 
-  if missing (default), approximated from initial 2sls model as the autocorrelation coefficient corrected for weights style 
+  
    pars
    
+
    starting values for \(\lambda\) and \(\sigma^2\) for GMM optimisation,
+  if missing (default), approximated from initial 2sls model as the autocorrelation coefficient corrected for weights style
   and model sigma squared
    
 
-  
    scaleU
    
+  
    scaleU
    
 
    Default FALSE: scale the OLS residuals before computing the moment matrices; only used if the pars argument is missing
    
 
-  
    control
    
+  
    control
    
 
    A list of control parameters. See details in optim or nlminb
    
 
-  
    verbose
    
+  
    verbose
    
 
    default NULL, use global option value; if TRUE, reports function values during optimization.
    
 
-  
    method
    
+  
    method
    
 
    default nlminb, or optionally a method passed to optim to use an alternative optimizer
    
 
-  
    robust
    
+  
    robust
    
+
    see stsls
    
+
+  
    legacy
    
 
    see stsls
    
 
-  
    legacy
    
+  
    W2X
    
 
    see stsls
    
 
-  
    W2X
    
+ 
    sig2n_k
    
 
    see stsls
    
 
-  
    obj
    
+  
    obj
    
 
    A spatial regression object created by lagsarlm, lagmess or by lmSLX; in HPDinterval.LagImpact, a LagImpact object
    
 
-  
    ...
    
+  
    ...
    
 
    Arguments passed through to methods in the coda package
    
 
-  
    tr
    
+  
    tr
    
 
    A vector of traces of powers of the spatial weights matrix created using trW, for approximate impact measures; if not given, listw must be given for exact measures (for small to moderate spatial weights matrices); the traces must be for the same spatial weights as were used in fitting the spatial regression, and must be row-standardised
    
 
-  
    evalues
    
+  
    evalues
    
 
    vector of eigenvalues of spatial weights matrix for impacts calculations
    
 
-  
    R
    
+  
    R
    
 
    If given, simulations are used to compute distributions for the impact measures, returned as mcmc objects; the objects are used for convenience but are not output by an MCMC process
    
 
-  
    tol
    
+  
    tol
    
 
    Argument passed to mvrnorm: tolerance (relative to largest variance) for numerical lack of positive-definiteness in the coefficient covariance matrix
    
 
-  
    empirical
    
+  
    empirical
    
 
    Argument passed to mvrnorm (default FALSE): if true, the coefficients and their covariance matrix specify the empirical not population mean and covariance matrix
    
 
-  
    Q
    
+  
    Q
    
 
    default NULL, else an integer number of cumulative power series impacts to calculate if tr is given
    
 
-  
    n
    
+  
    n
    
 
    defaults to length(obj$residuals); in the method for Gmsar objects it may be used in panel settings to compute the impacts for cross-sectional weights only, suggested by Angela Parenti
    
 
 
 
    
-    
    
-    
    Details
    
-    
    When the control list is set with care, the function will converge to values close to the ML estimator 
+    
    
+    
    Details
    
+    
    When the control list is set with care, the function will converge to values close to the ML estimator
   without requiring computation of the Jacobian, the most resource-intensive part of ML estimation.
    
     
    
-    
    
-    
    Value
    
-    
-
-
    A list object of class Gmsar
    
+    
    
+    
    Value
    
+    
    A list object of class Gmsar
    
 
    lambda
    
 
    simultaneous autoregressive error coefficient
    
 
@@ -229,23 +208,23 @@ 
    Value
    
 
    (possibly) named vector of excluded or omitted observations if non-default na.action argument used
    
 
 
    
-    
    
-    
    References
    
-    
    Kelejian, H. H., and Prucha, I. R., 1999. A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. International Economic Review, 40, pp. 509--533; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York.
    
+    
    
+    
    References
    
+    
    Kelejian, H. H., and Prucha, I. R., 1999. A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. International Economic Review, 40, pp. 509–533; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York.
    
 
    Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. Journal of Statistical Software, 63(18), 1-36. doi:10.18637/jss.v063.i18
 .
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Gianfranco Piras and Roger Bivand
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    optim, nlminb, GMerrorsar, GMargminImage
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    #require("spdep", quietly=TRUE) 
 data(oldcol, package="spdep")
 COL.errW.GM <- gstsls(CRIME ~ INC + HOVAL, data=COL.OLD, spdep::nb2listw(COL.nb, style="W"))
@@ -262,13 +241,13 @@ 
    Examples
    
 #> Type: GM SARAR estimator
 #> Coefficients: (GM standard errors) 
 #>              Estimate Std. Error z value  Pr(>|z|)
-#> Rho_Wy       0.454171   0.185680  2.4460   0.01445
-#> (Intercept) 43.782818  10.923192  4.0082 6.117e-05
-#> INC         -0.994831   0.382774 -2.5990   0.00935
-#> HOVAL       -0.267076   0.091984 -2.9035   0.00369
+#> Rho_Wy       0.454171   0.177939  2.5524  0.010699
+#> (Intercept) 43.782818  10.467857  4.1826 2.882e-05
+#> INC         -0.994831   0.366818 -2.7121  0.006687
+#> HOVAL       -0.267076   0.088149 -3.0298  0.002447
 #> 
 #> Lambda: 0.016647
-#> Residual variance (sigma squared): 103.36, (sigma: 10.167)
+#> Residual variance (sigma squared): 94.921, (sigma: 9.7427)
 #> GM argmin sigma squared: 93.729
 #> Number of observations: 49 
 #> Number of parameters estimated: 6 
@@ -294,13 +273,13 @@ 
    Examples
    
 #> Type: GM SARAR estimator
 #> Coefficients: (GM standard errors) 
 #>              Estimate Std. Error z value  Pr(>|z|)
-#> Rho_Wy       0.454171   0.185680  2.4460   0.01445
-#> (Intercept) 43.782818  10.923192  4.0082 6.117e-05
-#> INC         -0.994831   0.382774 -2.5990   0.00935
-#> HOVAL       -0.267076   0.091984 -2.9035   0.00369
+#> Rho_Wy       0.454171   0.177939  2.5524  0.010699
+#> (Intercept) 43.782818  10.467857  4.1826 2.882e-05
+#> INC         -0.994831   0.366818 -2.7121  0.006687
+#> HOVAL       -0.267076   0.088149 -3.0298  0.002447
 #> 
 #> Lambda: 0.016647
-#> Residual variance (sigma squared): 103.36, (sigma: 10.167)
+#> Residual variance (sigma squared): 94.921, (sigma: 9.7427)
 #> (scaled) GM argmin sigma squared: 0.96653
 #> Number of observations: 49 
 #> Number of parameters estimated: 6 
@@ -315,27 +294,23 @@ 
    Examples
    
 #> HOVAL -0.2830618 -0.2062420 -0.4893038
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/impacts.Gmsar.html b/docs/reference/impacts.Gmsar.html
new file mode 100644
index 0000000..ecc4774
--- /dev/null
+++ b/docs/reference/impacts.Gmsar.html
@@ -0,0 +1,8 @@
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diff --git a/docs/reference/impacts.Lagmess.html b/docs/reference/impacts.Lagmess.html
new file mode 100644
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--- /dev/null
+++ b/docs/reference/impacts.Lagmess.html
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diff --git a/docs/reference/impacts.MCMC_sac_G.html b/docs/reference/impacts.MCMC_sac_G.html
new file mode 100644
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+++ b/docs/reference/impacts.MCMC_sac_G.html
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diff --git a/docs/reference/impacts.MCMC_sar_G.html b/docs/reference/impacts.MCMC_sar_G.html
new file mode 100644
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+++ b/docs/reference/impacts.MCMC_sar_G.html
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diff --git a/docs/reference/impacts.MCMC_sem_G.html b/docs/reference/impacts.MCMC_sem_G.html
new file mode 100644
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+++ b/docs/reference/impacts.MCMC_sem_G.html
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diff --git a/docs/reference/impacts.Sarlm.html b/docs/reference/impacts.Sarlm.html
new file mode 100644
index 0000000..72496f8
--- /dev/null
+++ b/docs/reference/impacts.Sarlm.html
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diff --git a/docs/reference/impacts.SlX.html b/docs/reference/impacts.SlX.html
new file mode 100644
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diff --git a/docs/reference/impacts.Stsls.html b/docs/reference/impacts.Stsls.html
new file mode 100644
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--- /dev/null
+++ b/docs/reference/impacts.Stsls.html
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diff --git a/docs/reference/impacts.html b/docs/reference/impacts.html
index 71cda4b..d8c5762 100644
--- a/docs/reference/impacts.html
+++ b/docs/reference/impacts.html
@@ -1,74 +1,50 @@
 
-Impacts in spatial lag models — impacts • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Impacts in spatial lag models
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Impacts in spatial lag models
    
+
+      
    impacts.Rd
    
     
    
 
-    
    
+    
    
     
    The calculation of impacts for spatial lag and spatial Durbin models is needed in order to interpret the regression coefficients correctly, because of the spillovers between the terms in these data generation processes (unlike the spatial error model). Methods for “SLX” and Bayesian fitted models are also provided, the former do not need MC simulations, while the latter pass through MCMC draws.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    #\method{impacts}{sarlm}(obj, \dots, tr, R = NULL, listw = NULL, evalues=NULL,
 # useHESS = NULL, tol = 1e-06, empirical = FALSE, Q=NULL)
 #\method{impacts}{lagmess}(obj, ..., R=NULL, listw=NULL, tol=1e-6,
@@ -77,105 +53,102 @@ 
    Impacts in spatial lag models
    
 #\method{impacts}{MCMC_sar_g}(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL)
 #\method{impacts}{MCMC_sem_g}(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL)
 #\method{impacts}{MCMC_sac_g}(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL)
-# S3 method for LagImpact
+# S3 method for class 'LagImpact'
 plot(x, ..., choice="direct", trace=FALSE, density=TRUE)
-# S3 method for LagImpact
+# S3 method for class 'LagImpact'
 print(x, ..., reportQ=NULL)
-# S3 method for LagImpact
+# S3 method for class 'LagImpact'
 summary(object, ..., zstats=FALSE, short=FALSE, reportQ=NULL)
 #\method{print}{WXImpact}(x, ...)
 #\method{summary}{WXImpact}(object, ..., adjust_k=(attr(object, "type") == "SDEM"))
-# S3 method for LagImpact
+# S3 method for class 'LagImpact'
 HPDinterval(obj, prob = 0.95, ..., choice="direct")
 intImpacts(rho, beta, P, n, mu, Sigma, irho, drop2beta, bnames, interval,
  type, tr, R, listw, evalues, tol, empirical, Q, icept, iicept, p, mess=FALSE,
  samples=NULL, zero_fill = NULL, dvars = NULL)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    obj
    
+    
    
+    
    Arguments
    
+    
    
+
    obj
    
 
    A spatial regression object created by lagsarlm
 or by lmSLX; in HPDinterval.LagImpact, a LagImpact object
    
 
-  
    ...
    
+  
    ...
    
 
    Arguments passed through to methods in the coda package
    
 
-  
    tr
    
+  
    tr
    
 
    A vector of traces of powers of the spatial weights matrix created using trW, for approximate impact measures; if not given, listw must be given for exact measures (for small to moderate spatial weights matrices); the traces must be for the same spatial weights as were used in fitting the spatial regression, and must be row-standardised
    
 
-  
    listw
    
+  
    listw
    
 
    If tr is not given, a spatial weights object as created by nb2listw; they must be the same spatial weights as were used in fitting the spatial regression, but do not have to be row-standardised
    
 
-  
    evalues
    
+  
    evalues
    
 
    vector of eigenvalues of spatial weights matrix for impacts calculations
    
 
-  
    n
    
+  
    n
    
 
    defaults to length(obj$residuals); in the method for gmsar objects it may be used in panel settings to compute the impacts for cross-sectional weights only, suggested by Angela Parenti
    
 
-  
    R
    
+  
    R
    
 
    If given, simulations are used to compute distributions for the impact measures, returned as mcmc objects; the objects are used for convenience but are not output by an MCMC process
    
 
-  
    useHESS
    
+  
    useHESS
    
 
    Use the Hessian approximation (if available) even if the asymptotic coefficient covariance matrix is available; used for comparing methods
    
 
-  
    tol
    
+  
    tol
    
 
    Argument passed to mvrnorm: tolerance (relative to largest variance) for numerical lack of positive-definiteness in the coefficient covariance matrix
    
 
-  
    empirical
    
+  
    empirical
    
 
    Argument passed to mvrnorm (default FALSE): if true, the coefficients and their covariance matrix specify the empirical not population mean and covariance matrix
    
 
-  
    Q
    
+  
    Q
    
 
    default NULL, else an integer number of cumulative power series impacts to calculate if tr is given
    
 
-  
    reportQ
    
+  
    reportQ
    
 
    default NULL; if TRUE and Q given as an argument to impacts, report impact components
    
 
-  
    x, object
    
+  
    x, object
    
 
    LagImpact objects created by impacts methods
    
 
-  
    zstats
    
+  
    zstats
    
 
    default FALSE, if TRUE, also return z-values and p-values for the impacts based on the simulations
    
 
-  
    short
    
+  
    short
    
 
    default FALSE, if TRUE passed to the print summary method to omit printing of the mcmc summaries
    
 
-  
    choice
    
+  
    choice
    
 
    One of three impacts: direct, indirect, or total
    
 
-  
    trace
    
+  
    trace
    
 
    Argument passed to plot.mcmc: plot trace plots
    
 
-  
    density
    
+  
    density
    
 
    Argument passed to plot.mcmc: plot density plots
    
 
-  
    prob
    
+  
    prob
    
 
    Argument passed to HPDinterval.mcmc: a numeric scalar in the interval (0,1) giving the target probability content of the intervals
    
 
-  
    adjust_k
    
+  
    adjust_k
    
 
    default TRUE if SDEM else FALSE, adjust internal OLS SDEM standard errors by dividing by n rather than (n-k) (default changed and bug fixed after 0.7-8; standard errors now ML in SDEM summary and impacts summary and identical - for SLX use FALSE)
    
 
-  
    rho, beta, P, mu, Sigma, irho, drop2beta, bnames,
-    interval, type, icept, iicept, p, mess, samples, zero_fill, dvars
    
+  
    rho, beta, P, mu, Sigma, irho, drop2beta, bnames,
+    interval, type, icept, iicept, p, mess, samples, zero_fill, dvars
    
 
    internal arguments shared inside impacts methods
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    If called without R being set, the method returns the direct, indirect and total impacts for the variables in the model, for the variables themselves in tha spatial lag model case, for the variables and their spatial lags in the spatial Durbin (mixed) model case. The spatial lag impact measures are computed using eq. 2.46 (LeSage and Pace, 2009, p. 38), either using the exact dense matrix (when listw is given), or traces of powers of the weights matrix (when tr is given). When the traces are created by powering sparse matrices, the exact and the trace methods should give very similar results, unless the number of powers used is very small, or the spatial coefficient is close to its bounds.
    
 
    If R is given, simulations will be used to create distributions for the impact measures, provided that the fitted model object contains a coefficient covariance matrix. The simulations are made using mvrnorm with the coefficients and their covariance matrix from the fitted model.
    
-
    The simulations are stored as mcmc objects as defined in the coda package; the objects are used for convenience but are not output by an MCMC process. The simulated values of the coefficients are checked to see that the spatial coefficient remains within its valid interval --- draws outside the interval are discarded.
    
+
    The simulations are stored as mcmc objects as defined in the coda package; the objects are used for convenience but are not output by an MCMC process. The simulated values of the coefficients are checked to see that the spatial coefficient remains within its valid interval — draws outside the interval are discarded.
    
 
    If a model is fitted with the “Durbin=” set to a formula subsetting the explanatory variables, the impacts object returned reports Durbin impacts for variables included in the formula and lag impacts for the other variables.
    
 
    When Q and tr are given, addition impact component results are provided for each step in the traces of powers of the weights matrix up to and including the Q'th power. This increases computing time because the output object is substantially increased in size in proportion to the size of Q.
    
 
    The method for gmsar objects is only for those of type SARAR output by gstsls, and assume that the spatial error coefficient is fixed, and thus omitted from the coefficients and covariance matrix used for simulation.
    
     
    
-    
    
-    
    Value
    
-    
-
-
    An object of class LagImpact.
    
-
-
+    
    
+    
    Value
    
+    
    An object of class LagImpact.
    
 
    If no simulation is carried out, the object returned is a list with:
    
 
    direct
    
 
    numeric vector
    
@@ -187,8 +160,6 @@ 
    Value
    
 
    numeric vector
    
 
 
    and a matching Qres list attribute if Q was given.
    
-
-
 
    If simulation is carried out, the object returned is a list with:
    
 
    res
    
 
    a list with three components as for the non-simulation case, with a matching Qres list attribute if Q was given
    
@@ -197,23 +168,23 @@ 
    Value
    
 
    a list with three mcmc matrices, for the direct, indirect and total impacts with a matching Qmcmc list attribute if Q was given
    
 
 
    
-    
    
-    
    References
    
-    
    LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 33--42, 114--115; LeSage J and MM Fischer (2008) Spatial growth regressions: model specification, estimation and interpretation. Spatial Economic Analysis 3 (3), pp. 275--304.
    
+    
    
+    
    References
    
+    
    LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 33–42, 114–115; LeSage J and MM Fischer (2008) Spatial growth regressions: model specification, estimation and interpretation. Spatial Economic Analysis 3 (3), pp. 275–304.
    
 
    Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. Journal of Statistical Software, 63(18), 1-36. doi:10.18637/jss.v063.i18
 .
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    trW, lagsarlm, nb2listw, mvrnorm, plot.mcmc, summary.mcmc, HPDinterval
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    require("sf", quietly=TRUE)
 columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
 #require("spdep", quietly=TRUE)
@@ -861,27 +832,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/index.html b/docs/reference/index.html
index 0ce5590..64da49e 100644
--- a/docs/reference/index.html
+++ b/docs/reference/index.html
@@ -1,197 +1,226 @@
 
-Function reference • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-      
    Reference
    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Package index
    
     
    
 
-    
-      
-        
-      
-        
-      
-        
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-        
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-        
-      
-        
-      
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-        
-      
-        
-      
    
-          
    All functions 
    
-          
    
-        
    
-          
    GMerrorsar() summary(<Gmsar>) GMargminImage() 
    
-        
    Spatial simultaneous autoregressive error model estimation by GMM
    
-          
    MCMCsamp() 
    
-        
    MCMC sample from fitted spatial regression
    
-          
    ME() 
    
-        
    Moran eigenvector GLM filtering
    
-          
    lagsarlm() errorsarlm() sacsarlm() summary(<Sarlm>) print(<Sarlm>) print(<summary.Sarlm>) residuals(<Sarlm>) deviance(<Sarlm>) coef(<Sarlm>) vcov(<Sarlm>) fitted(<Sarlm>) 
    
-        
    Spatial simultaneous autoregressive model estimation by maximum likelihood
    
-          
    spBreg_lag() spBreg_sac() spBreg_err() impacts(<MCMC_sar_G>) impacts(<MCMC_sem_G>) impacts(<MCMC_sac_G>) 
    
-        
    Bayesian MCMC spatial simultaneous autoregressive model estimation
    
-          
    lmSLX() print(<SlX>) summary(<SlX>) print(<summary.SlX>) impacts(<SlX>) print(<WXimpact>) summary(<WXimpact>) predict(<SlX>) create_WX() 
    
-        
    Spatial Durbin linear (SLX, spatially lagged X) model
    
-          
    SpatialFiltering() 
    
-        
    Semi-parametric spatial filtering
    
-          
    aple() 
    
-        
    Approximate profile-likelihood estimator (APLE)
    
-          
    aple.mc() 
    
-        
    Approximate profile-likelihood estimator (APLE) permutation test
    
-          
    aple.plot() localAple() 
    
-        
    Approximate profile-likelihood estimator (APLE) scatterplot
    
-          
    do_ldet() jacobianSetup() cheb_setup() mcdet_setup() eigen_setup() eigen_pre_setup() spam_setup() spam_update_setup() Matrix_setup() Matrix_J_setup() LU_setup() LU_prepermutate_setup() moments_setup() SE_classic_setup() SE_whichMin_setup() SE_interp_setup() can.be.simmed() 
    
-        
    Spatial regression model Jacobian computations
    
-          
    eigenw() griffith_sone() subgraph_eigenw() 
    
-        
    Spatial weights matrix eigenvalues
    
-          
    gstsls() impacts(<Gmsar>) 
    
-        
    Spatial simultaneous autoregressive SAC model estimation by GMM
    
-          
    plot(<LagImpact>) print(<LagImpact>) summary(<LagImpact>) HPDinterval(<LagImpact>) intImpacts() 
    
-        
    Impacts in spatial lag models
    
-          
    invIrM() invIrW() 
    
-        
    Compute SAR generating operator
    
-          
    lagmess() 
    
-        
    Matrix exponential spatial lag model
    
-          
    lextrB() lextrW() lextrS() l_max() 
    
-        
    Find extreme eigenvalues of binary symmetric spatial weights
    
-          
    predict(<Sarlm>) print(<Sarlm.pred>) as.data.frame(<Sarlm.pred>) 
    
-        
    Prediction for spatial simultaneous autoregressive linear model objects
    
-          
    LR.Sarlm() logLik(<Sarlm>) LR1.Sarlm() Wald1.Sarlm() Hausman.test(<Sarlm>) anova(<Sarlm>) bptest.Sarlm() impacts(<Sarlm>) 
    
-        
    Likelihood ratio test
    
-          
    set.mcOption() get.mcOption() set.coresOption() get.coresOption() set.ClusterOption() get.ClusterOption() 
    
-        
    Options for parallel support
    
-          
    set.VerboseOption() get.VerboseOption() set.ZeroPolicyOption() get.ZeroPolicyOption() 
    
-        
    Control checking of spatial object IDs
    
-          
    similar.listw() 
    
-        
    Create symmetric similar weights lists
    
-          
    as.spam.listw() listw2U_spam() listw2U_Matrix() as_dgRMatrix_listw() as_dsTMatrix_listw() as_dsCMatrix_I() as_dsCMatrix_IrW() Jacobian_W() powerWeights() 
    
-        
    Spatial neighbour sparse representation
    
-          
    spautolm() summary(<Spautolm>) 
    
-        
    Spatial conditional and simultaneous autoregression model estimation
    
-          
    stsls() impacts(<Stsls>) 
    
-        
    Generalized spatial two stage least squares
    
-          
    trW() mom_calc() mom_calc_int2() 
    
-        
    Spatial weights matrix powers traces
    
-
-  
-
    
+    
    
+      
    All functions
    
+
+
+
+
+    
    
+
+
+
+
+      
    
+
+          GMerrorsar() summary(<Gmsar>) GMargminImage()
+
+        
    
+        
    Spatial simultaneous autoregressive error model estimation by GMM
    
+      
    
+
+          MCMCsamp()
+
+        
    
+        
    MCMC sample from fitted spatial regression
    
+      
    
+
+          ME()
+
+        
    
+        
    Moran eigenvector GLM filtering
    
+      
    
+
+          lagsarlm() errorsarlm() sacsarlm() summary(<Sarlm>) print(<Sarlm>) print(<summary.Sarlm>) residuals(<Sarlm>) deviance(<Sarlm>) coef(<Sarlm>) vcov(<Sarlm>) fitted(<Sarlm>)
+
+        
    
+        
    Spatial simultaneous autoregressive model estimation by maximum likelihood
    
+      
    
+
+          spBreg_lag() spBreg_sac() spBreg_err() impacts(<MCMC_sar_G>) impacts(<MCMC_sem_G>) impacts(<MCMC_sac_G>)
+
+        
    
+        
    Bayesian MCMC spatial simultaneous autoregressive model estimation
    
+      
    
+
+          lmSLX() print(<SlX>) summary(<SlX>) print(<summary.SlX>) impacts(<SlX>) print(<WXimpact>) summary(<WXimpact>) predict(<SlX>) create_WX()
+
+        
    
+        
    Spatial Durbin linear (SLX, spatially lagged X) model
    
+      
    
+
+          SpatialFiltering()
+
+        
    
+        
    Semi-parametric spatial filtering
    
+      
    
+
+          aple()
+
+        
    
+        
    Approximate profile-likelihood estimator (APLE)
    
+      
    
+
+          aple.mc()
 
+        
    
+        
    Approximate profile-likelihood estimator (APLE) permutation test
    
+      
    
 
-      
    
+        
    Approximate profile-likelihood estimator (APLE) scatterplot
    
+      
    
+
+          do_ldet() jacobianSetup() cheb_setup() mcdet_setup() eigen_setup() eigen_pre_setup() spam_setup() spam_update_setup() Matrix_setup() Matrix_J_setup() LU_setup() LU_prepermutate_setup() moments_setup() SE_classic_setup() SE_whichMin_setup() SE_interp_setup() can.be.simmed()
+
+        
    
+        
    Spatial regression model Jacobian computations
    
+      
    
+
+          eigenw() griffith_sone() subgraph_eigenw()
+
+        
    
+        
    Spatial weights matrix eigenvalues
    
+      
    
+
+          gstsls() impacts(<Gmsar>)
+
+        
    
+        
    Spatial simultaneous autoregressive SAC model estimation by GMM
    
+      
    
+
+          plot(<LagImpact>) print(<LagImpact>) summary(<LagImpact>) HPDinterval(<LagImpact>) intImpacts()
+
+        
    
+        
    Impacts in spatial lag models
    
+      
    
+
+          invIrM() invIrW()
+
+        
    
+        
    Compute SAR generating operator
    
+      
    
+
+          lagmess()
+
+        
    
+        
    Matrix exponential spatial lag model
    
+      
    
+
+          lextrB() lextrW() lextrS() l_max()
+
+        
    
+        
    Find extreme eigenvalues of binary symmetric spatial weights
    
+      
    
+
+          predict(<Sarlm>) print(<Sarlm.pred>) as.data.frame(<Sarlm.pred>)
+
+        
    
+        
    Prediction for spatial simultaneous autoregressive linear model objects
    
+      
    
+
+          LR.Sarlm() logLik(<Sarlm>) LR1.Sarlm() Wald1.Sarlm() Hausman.test(<Sarlm>) anova(<Sarlm>) bptest.Sarlm() impacts(<Sarlm>)
+
+        
    
+        
    Likelihood ratio test
    
+      
    
+
+          set.mcOption() get.mcOption() set.coresOption() get.coresOption() set.ClusterOption() get.ClusterOption()
+
+        
    
+        
    Options for parallel support
    
+      
    
+
+          set.VerboseOption() get.VerboseOption() set.ZeroPolicyOption() get.ZeroPolicyOption()
+
+        
    
+        
    Control checking of spatial object IDs
    
+      
    
+
+          similar.listw()
+
+        
    
+        
    Create symmetric similar weights lists
    
+      
    
+
+          as.spam.listw() listw2U_spam() listw2U_Matrix() as_dgRMatrix_listw() as_dsTMatrix_listw() as_dsCMatrix_I() as_dsCMatrix_IrW() Jacobian_W() powerWeights()
+
+        
    
+        
    Spatial neighbour sparse representation
    
+      
    
+
+          spautolm() summary(<Spautolm>)
+
+        
    
+        
    Spatial conditional and simultaneous autoregression model estimation
    
+      
    
+
+          stsls() impacts(<Stsls>)
+
+        
    
+        
    Generalized spatial two stage least squares
    
+      
    
+
+          trW() mom_calc() mom_calc_int2()
+
+        
    
+        
    Spatial weights matrix powers traces
    
+      
    
+  
    
+
+
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/intImpacts.html b/docs/reference/intImpacts.html
new file mode 100644
index 0000000..8259488
--- /dev/null
+++ b/docs/reference/intImpacts.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/invIrM-1.png b/docs/reference/invIrM-1.png
index 9bd2900..33c61db 100644
Binary files a/docs/reference/invIrM-1.png and b/docs/reference/invIrM-1.png differ
diff --git a/docs/reference/invIrM.html b/docs/reference/invIrM.html
index 7743f53..52956df 100644
--- a/docs/reference/invIrM.html
+++ b/docs/reference/invIrM.html
@@ -1,134 +1,109 @@
 
-Compute SAR generating operator — invIrM • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Compute SAR generating operator
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Compute SAR generating operator
    
+
+      
    invIrM.Rd
    
     
    
 
-    
    
+    
    
     
    Computes the matrix used for generating simultaneous autoregressive random variables, for a given value of rho, a neighbours list object or a matrix, a chosen coding scheme style, and optionally a list of general weights corresponding to neighbours.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    invIrM(neighbours, rho, glist=NULL, style="W", method="solve",
  feasible=NULL)
 invIrW(x, rho, method="solve", feasible=NULL)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    neighbours
    
+    
    
+    
    Arguments
    
+    
    
+
    neighbours
    
 
    an object of class nb
    
 
-  
    rho
    
+  
    rho
    
 
    autoregressive parameter
    
 
-  
    glist
    
+  
    glist
    
 
    list of general weights corresponding to neighbours
    
 
-  
    style
    
+  
    style
    
 
    style can take values W, B, C, and S
    
 
-  
    method
    
+  
    method
    
 
    default solve, can also take value chol
    
 
-  
    feasible
    
+  
    feasible
    
 
    if NULL, the given value of rho is checked to see if it lies within its feasible range, if TRUE, the test is not conducted
    
 
-  
    x
    
-
    either a listw object from for example nb2listw, or a square spatial weights matrix, optionally a sparse matrix
    
+  
    x
    
+
    either a listw object from for example nb2listw or a square spatial weights matrix, optionally a sparse matrix
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    The invIrW function generates the full weights matrix V, checks that rho lies in its feasible range between 1/min(eigen(V)) and 1/max(eigen(V)), and returns the nxn inverted matrix $$(I - \rho V)^{-1}$$. With method=“chol” (only for a listw object), Cholesky decomposition is used, thanks to contributed code by Markus Reder and Werner Mueller.
    
 
    Note that, in some situations in simulation, it may matter that the random vector from rnorm or similar will not be exactly N(0, 1), and it will also contain random amounts of spatial autocorrelection itself, which will mix with the spatial autocorrelection injected by the process operator $$(I - \rho V)^{-1}$$. In addition, it will not follow the stipulated distribution exactly either, so that several steps may be needed to scale the random vector, to remove artefacts coming from its deviance from distributional parameters, and to remove random spatial autocorrelation - see the examples below. Thanks to Rune Østergaard Pedersen for bring up this question.
    
 
    The powerWeights function uses power series summation to cumulate the product $$(I - \rho V)^{-1} \%*\% X$$ from $$(I + \rho V + (\rho V)^2 + \dots) \%*\% X$$, which can be done by storing only sparse V and several matrices of the same dimensions as X. This makes it possible to handle larger spatial weights matrices, but is sensitive to the power weights order and the tolerance arguments when the spatial coefficient is close to its bounds, leading to incorrect estimates of the implied inverse matrix.
    
     
    
-    
    
-    
    Value
    
-    
-
-
    An nxn matrix with a "call" attribute; the powerWeights function returns a matrix of the same dimensions as X which has been multipled by the power series equivalent of the dense matrix $$(I - \rho V)^{-1}$$.
    
+    
    
+    
    Value
    
+    
    An nxn matrix with a "call" attribute; the powerWeights function returns a matrix of the same dimensions as X which has been multipled by the power series equivalent of the dense matrix $$(I - \rho V)^{-1}$$.
    
     
    
-    
    
-    
    Note
    
+    
    
+    
    Note
    
     
    Before version 0.6-10, powerWeights only worked correctly for positive rho, with differences from true values increasing as rho approached -1, and exploding between -1 and the true negative bound.
    
     
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Tiefelsdorf, M., Griffith, D. A., Boots, B. 1999 A variance-stabilizing coding scheme for spatial link matrices, Environment and Planning A, 31, pp. 165-180; Tiefelsdorf, M. 2000 Modelling spatial processes, Lecture notes in earth sciences, Springer, p. 76; Haining, R. 1990 Spatial data analysis in the social and environmental sciences, Cambridge University Press, p. 117; Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 152; Reder, M. and Mueller, W. (2007) An Improvement of the invIrM Routine of the Geostatistical R-package spdep by Cholesky Inversion, Statistical Projects, LV No: 238.205, SS 2006, Department of Applied Statistics, Johannes Kepler University, Linz
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    nb2listw
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    library(spdep)
 nb7rt <- cell2nb(7, 7, torus=TRUE)
 lw <- nb2listw(nb7rt, style="W")
@@ -178,10 +153,10 @@ 
    Examples
    
 x <- matrix(rnorm(length(nb7rt)), ncol=1)
 system.time(e <- invIrM(nb7rt, rho=0.9, method="chol", feasible=TRUE) %*% x)
 #>    user  system elapsed 
-#>   0.003   0.000   0.003 
+#>   0.003   0.000   0.002 
 system.time(e <- invIrM(nb7rt, rho=0.9, method="chol", feasible=NULL) %*% x)
 #>    user  system elapsed 
-#>   0.003   0.000   0.003 
+#>   0.002   0.000   0.002 
 system.time(e <- invIrM(nb7rt, rho=0.9, method="solve", feasible=TRUE) %*% x)
 #>    user  system elapsed 
 #>   0.001   0.000   0.001 
@@ -191,27 +166,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/invIrW.html b/docs/reference/invIrW.html
new file mode 100644
index 0000000..c42a90a
--- /dev/null
+++ b/docs/reference/invIrW.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/jacobianSetup.html b/docs/reference/jacobianSetup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/jacobianSetup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/l_max.html b/docs/reference/l_max.html
new file mode 100644
index 0000000..b73a068
--- /dev/null
+++ b/docs/reference/l_max.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/lagmess.html b/docs/reference/lagmess.html
index 91d14fd..c2bfd31 100644
--- a/docs/reference/lagmess.html
+++ b/docs/reference/lagmess.html
@@ -1,132 +1,107 @@
 
-Matrix exponential spatial lag model — lagmess • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Matrix exponential spatial lag model
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Matrix exponential spatial lag model
    
+
+      
    lagmess.Rd
    
     
    
 
-    
    
+    
    
     
    The function fits a matrix exponential spatial lag model, using optim to find the value of alpha, the spatial coefficient.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    lagmess(formula, data = list(), listw, zero.policy = NULL, na.action = na.fail,
  q = 10, start = -2.5, control=list(), method="BFGS", verbose=NULL,
  use_expm=FALSE)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    formula
    
-
    a symbolic description of the model to be fit. The details 
+    
    
+    
    Arguments
    
+    
    
+
    formula
    
+
    a symbolic description of the model to be fit. The details
 of model specification are given for lm()
    
 
-  
    data
    
-
    an optional data frame containing the variables in the model. 
-By default the variables are taken from the environment which the function 
+  
    data
    
+
    an optional data frame containing the variables in the model.
+By default the variables are taken from the environment which the function
 is called.
    
 
-  
    listw
    
+  
    listw
    
 
    a listw object created for example by spdep::nb2listw()
    
 
-  
    zero.policy
    
-
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without 
+  
    zero.policy
    
+
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without
 neighbours, if FALSE assign NA - causing lagmess() to terminate with an error
    
 
-  
    na.action
    
+  
    na.action
    
 
    a function (default options("na.action")), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.
    
 
-  
    q
    
+  
    q
    
 
    default 10; number of powers of the spatial weights to use
    
 
-  
    start
    
+  
    start
    
 
    starting value for numerical optimization, should be a small negative number
    
 
-  
    control
    
+  
    control
    
 
    control parameters passed to optim
    
 
-  
    method
    
+  
    method
    
 
    default BFGS, method passed to optim
    
 
-  
    verbose
    
+  
    verbose
    
 
    default NULL, use global option value; if TRUE report function values during optimization
    
 
-  
    use_expm
    
+  
    use_expm
    
 
    default FALSE; if TRUE use expm::expAtv instead of a truncated power series of W
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    The underlying spatial lag model:
    
 
    $$y = \rho W y + X \beta + \varepsilon$$
    
 
    where \(\rho\) is the spatial parameter may be fitted by maximum likelihood. In that case, the log likelihood function includes the logarithm of cumbersome Jacobian term \(|I - \rho W|\). If we rewrite the model as:
    
 
    $$S y = X \beta + \varepsilon$$
    
 
    we see that in the ML case \(S y = (I - \rho W) y\). If W is row-stochastic, S may be expressed as a linear combination of row-stochastic matrices. By pre-computing the matrix \([y, Wy, W^2y, ..., W^{q-1}y]\), the term \(S y (\alpha)\) can readily be found by numerical optimization using the matrix exponential approach. \(\alpha\) and \(\rho\) are related as \(\rho = 1 - \exp{\alpha}\), conditional on the number of matrix power terms taken q.
    
     
    
-    
    
-    
    Value
    
-    
-
-
    The function returns an object of class Lagmess with components:
    
+    
    
+    
    Value
    
+    
    The function returns an object of class Lagmess with components:
    
 
    lmobj
    
 
    the lm object returned after fitting alpha
    
 
@@ -155,21 +130,21 @@ 
    Value
    
 
    the log likelihood of the aspatial model for the same data
    
 
 
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    J. P. LeSage and R. K. Pace (2007) A matrix exponential specification. Journal of Econometrics, 140, 190-214; J. P. LeSage and R. K. Pace (2009) Introduction to Spatial Econometrics. CRC Press, Chapter 9.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no and Eric Blankmeyer
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    lagsarlm, optim
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    #require(spdep, quietly=TRUE)
 data(baltimore, package="spData")
 baltimore$AGE <- ifelse(baltimore$AGE < 1, 1, baltimore$AGE)
@@ -445,27 +420,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/lagsarlm.html b/docs/reference/lagsarlm.html
new file mode 100644
index 0000000..4dbdc74
--- /dev/null
+++ b/docs/reference/lagsarlm.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/lextrB.html b/docs/reference/lextrB.html
index 61d999b..7119521 100644
--- a/docs/reference/lextrB.html
+++ b/docs/reference/lextrB.html
@@ -1,95 +1,72 @@
 
-Find extreme eigenvalues of binary symmetric spatial weights — lextrB • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Find extreme eigenvalues of binary symmetric spatial weights
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Find extreme eigenvalues of binary symmetric spatial weights
    
+
+      
    lextrB.Rd
    
     
    
 
-    
    
+    
    
     
    The functions find extreme eigenvalues of binary symmetric spatial weights, when these form planar graphs; general weights are not permiited. l_max finds the largest eigenvalue using Rayleigh quotient methods of any “listw” object. lextrB first calls l_max, and uses its output to find the smallest eigenvalue in addition for binary symmetric spatial weights. lextrW extends these to find the smallest eigenvalue for intrinsically symmetric row-standardized binary weights matrices (transformed to symmetric through similarity internally). lextrS does the same for variance-stabilized (“S” style) intrinsically symmetric binary weights matrices (transformed to symmetric through similarity internally).
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    lextrB(lw, zero.policy = TRUE, control = list())
 lextrW(lw, zero.policy=TRUE, control=list())
 lextrS(lw, zero.policy=TRUE, control=list())
 l_max(lw, zero.policy=TRUE, control=list())
    
     
    
 
-    
    
-    
    Arguments
    
-    
    lw
    
+    
    
+    
    Arguments
    
+    
    
+
    lw
    
 
    a binary symmetric listw object from, for example, nb2listw with style “B” for lextrB, style “W” for lextrW and style “S” for lextrS; for l_max, the object may be asymmetric and does not have to be binary
    
 
-  
    zero.policy
    
+  
    zero.policy
    
 
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA
    
 
-  
    control
    
+  
    control
    
 
    a list of control arguments
    
 
 
    
-    
    
-    
    Control arguments
    
-    
+    
    
+    
    Control arguments
    
+
 
    trace
    
 
    report values in while loops, default NULL assuming FALSE; logical
    
 
@@ -104,27 +81,25 @@ 
    Control arguments
    
 
 
 
    
-    
    
-    
    Value
    
-    
-
-
    The functions return approximations to the extreme eigenvalues with the eigenvectors returned as attributes of this object.
    
+    
    
+    
    Value
    
+    
    The functions return approximations to the extreme eigenvalues with the eigenvectors returned as attributes of this object.
    
     
    
-    
    
-    
    References
    
-    
    Griffith, D. A. (2004). Extreme eigenfunctions of adjacency matrices for planar graphs employed in spatial analyses. Linear Algebra and its Applications, 388:201--219.
    
+    
    
+    
    References
    
+    
    Griffith, D. A. (2004). Extreme eigenfunctions of adjacency matrices for planar graphs employed in spatial analyses. Linear Algebra and its Applications, 388:201–219.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand, Yongwan Chun, Daniel Griffith
    
     
    
-    
    
-    
    Note
    
+    
    
+    
    Note
    
     
    It may be necessary to modify control arguments if warnings about lack of convergence are seen.
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    data(boston, package="spData")
 #require(spdep, quietly=TRUE)
 ab.listb <- spdep::nb2listw(boston.soi, style="B")
@@ -193,27 +168,23 @@ 
    Examples
    
 #> [1] 1.110373
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/lextrS.html b/docs/reference/lextrS.html
new file mode 100644
index 0000000..b73a068
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diff --git a/docs/reference/lextrW.html b/docs/reference/lextrW.html
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+  
+    
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diff --git a/docs/reference/listw2U_Matrix.html b/docs/reference/listw2U_Matrix.html
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diff --git a/docs/reference/listw2U_spam.html b/docs/reference/listw2U_spam.html
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diff --git a/docs/reference/localAple.html b/docs/reference/localAple.html
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diff --git a/docs/reference/logLik.Lagmess.html b/docs/reference/logLik.Lagmess.html
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diff --git a/docs/reference/logLik.Sarlm.html b/docs/reference/logLik.Sarlm.html
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diff --git a/docs/reference/logLik.Spautolm.html b/docs/reference/logLik.Spautolm.html
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diff --git a/docs/reference/mcdet_setup.html b/docs/reference/mcdet_setup.html
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diff --git a/docs/reference/mom_calc.html b/docs/reference/mom_calc.html
new file mode 100644
index 0000000..93c1d83
--- /dev/null
+++ b/docs/reference/mom_calc.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
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diff --git a/docs/reference/mom_calc_int2.html b/docs/reference/mom_calc_int2.html
new file mode 100644
index 0000000..93c1d83
--- /dev/null
+++ b/docs/reference/mom_calc_int2.html
@@ -0,0 +1,8 @@
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+  
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+    
+  
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diff --git a/docs/reference/moments_setup.html b/docs/reference/moments_setup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/moments_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/plot.LagImpact.html b/docs/reference/plot.LagImpact.html
new file mode 100644
index 0000000..8259488
--- /dev/null
+++ b/docs/reference/plot.LagImpact.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/powerWeights.html b/docs/reference/powerWeights.html
new file mode 100644
index 0000000..210cb07
--- /dev/null
+++ b/docs/reference/powerWeights.html
@@ -0,0 +1,8 @@
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+  
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+    
+  
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diff --git a/docs/reference/predict.SlX.html b/docs/reference/predict.SlX.html
new file mode 100644
index 0000000..db024e0
--- /dev/null
+++ b/docs/reference/predict.SlX.html
@@ -0,0 +1,8 @@
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+  
+    
+    
+    
+  
+
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diff --git a/docs/reference/predict.sarlm.html b/docs/reference/predict.sarlm.html
index 913d59f..cdfa0b4 100644
--- a/docs/reference/predict.sarlm.html
+++ b/docs/reference/predict.sarlm.html
@@ -1,145 +1,122 @@
 
-Prediction for spatial simultaneous autoregressive linear model objects — predict.Sarlm • spatialregPrediction for spatial simultaneous autoregressive linear model objects — predict.Sarlm • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Prediction for spatial simultaneous autoregressive linear model objects
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Prediction for spatial simultaneous autoregressive linear model objects
    
+
+      
    predict.sarlm.Rd
    
     
    
 
-    
    
+    
    
     
    predict.Sarlm() calculates predictions as far as is at present possible for for spatial simultaneous autoregressive linear
 model objects, using Haining's terminology for decomposition into
-trend, signal, and noise, or other types of predictors --- see references.
    
+trend, signal, and noise, or other types of predictors — see references.
    
     
    
 
-    
    
-    
    # S3 method for Sarlm
+    
    
+    
    Usage
    
+    
    # S3 method for class 'Sarlm'
 predict(object, newdata = NULL, listw = NULL, pred.type = "TS", all.data = FALSE,
  zero.policy = NULL, legacy = TRUE, legacy.mixed = FALSE, power = NULL, order = 250,
  tol = .Machine$double.eps^(3/5), spChk = NULL, ...)
 #\method{predict}{SLX}(object, newdata, listw, zero.policy=NULL, ...)
-# S3 method for Sarlm.pred
+# S3 method for class 'Sarlm.pred'
 print(x, ...)
-# S3 method for Sarlm.pred
+# S3 method for class 'Sarlm.pred'
 as.data.frame(x, ...)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    object
    
-
    Sarlm object returned by lagsarlm, 
+    
    
+    
    Arguments
    
+    
    
+
    object
    
+
    Sarlm object returned by lagsarlm,
 errorsarlm or sacsarlm, the method for SLX objects takes the output of lmSLX
    
 
-  
    newdata
    
-
    data frame in which to predict --- if NULL, predictions are
+  
    newdata
    
+
    data frame in which to predict — if NULL, predictions are
 for the data on which the model was fitted. Should have row names corresponding to region.id. If row names are exactly the same than the ones used for training, it uses in-sample predictors for forecast.  See ‘Details’
    
 
-  
    listw
    
+  
    listw
    
 
    a listw object created for example by nb2listw. In the out-of-sample prediction case (ie. if newdata is not NULL), if legacy.mixed=FALSE or if pred.type!="TS", it should include both in-sample and out-of-sample spatial units. In this case, if regions of the listw are not in the correct order, they are reordered.  See ‘Details’
    
 
-  
    pred.type
    
-
    predictor type --- default “TS”, use decomposition into  
+  
    pred.type
    
+
    predictor type — default “TS”, use decomposition into
 trend, signal, and noise ; other types available depending on newdata. If newdata=NULL (in-sample prediction), “TS”, “trend”, “TC” and “BP” are available. If newdata is not NULL and its row names are the same than the data used to fit the model (forecast case), “TS”, “trend” and “TC” are available. In other cases (out-of-sample prediction), “TS”, “trend”, “KP1”, “KP2”, “KP3”, “KP4”, “KP5”, “TC”, “BP”, “BPW”, “BPN”, “TS1”, “TC1”, “BP1”, “BPW1” and “BPN1” are available.  See ‘Details’ and references
    
 
-  
    all.data
    
+  
    all.data
    
 
    (only applies to pred.type="TC" and newdata is not NULL) default FALSE: return predictions only for newdata units, if TRUE return predictions for all data units.  See ‘Details’
    
 
-  
    zero.policy
    
-
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without 
-neighbours, if FALSE (default) assign NA - causing the function to 
+  
    zero.policy
    
+
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without
+neighbours, if FALSE (default) assign NA - causing the function to
 terminate with an error
    
 
-  
    legacy
    
+  
    legacy
    
 
    (only applies to lag and Durbin (mixed) models for pred.type="TS") default TRUE: use ad-hoc predictor, if FALSE use DGP-based predictor
    
 
-  
    legacy.mixed
    
+  
    legacy.mixed
    
 
    (only applies to mixed models if newdata is not NULL) default FALSE: compute lagged variables from both in-sample and out-of-sample units with \([W X]_O\) and \([W X]_S\) where X=cbind(Xs, Xo), if TRUE compute lagged variables independantly between in-sample and out-of-sample units with \(W_{OO} X_O\) and \(W_{SS} X_S\)
    
 
-  
    power
    
+  
    power
    
 
    (only applies to lag and Durbin (mixed) models for “TS”, “KP1”, “KP2”, “KP3”, “TC”, “TC1”, “BP”, “BP1”, “BPN”, “BPN1”, “BPW” and “BPW1” types) use powerWeights, if default NULL, set FALSE if object$method is “eigen”, otherwise TRUE
    
 
-  
    order
    
+  
    order
    
 
    power series maximum limit if power is TRUE
    
 
-  
    tol
    
+  
    tol
    
 
    tolerance for convergence of power series if power is TRUE
    
 
-  
    spChk
    
+  
    spChk
    
 
    should the row names of data frames be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use get.spChkOption()
    
 
-  
    x
    
+  
    x
    
 
    the object to be printed
    
 
-
    
-
-
-
    
-
    ...
    
+
    
+
    
+
    ...
    
 
    further arguments passed through
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    The function supports three types of prediction.  In-sample prediction is the computation of predictors on the data used to fit the model (newdata=NULL).  Prevision, also called forecast, is the computation of some predictors (“trend”, in-sample “TC” and out-of-sample “TS”) on the same spatial units than the ones used to fit the model, but with different observations of the variables in the model (row names of newdata should have the same row names than the data frame used to fit the model).  And out-of-sample prediction is the computation of predictors on other spatial units than the ones used to fit the model (newdata has different row names).  For extensive definitions, see Goulard et al. (2017). 
    
 
    pred.type of predictors are available according to the model of object an to the type of prediction.  In the two following tables, “yes” means that the predictor can be used with the model, “no” means that predict.Sarlm() will stop with an error, and “yes*” means that the predictor is not designed for the specified model, but it can be used with predict.Sarlm().  In the last case, be careful with the computation of a inappropriate predictor.
    
 
    In-sample predictors by models
    
@@ -150,21 +127,21 @@ 
    Details
    
 
    In the following, the trend is the non-spatial smooth, the signal is the
 spatial smooth, and the noise is the residual.  The fit returned by pred.type="TS" is the
 sum of the trend and the signal.
    
-
    When pred.type="TS", the function approaches prediction first by dividing invocations between 
-those with or without newdata.  When no newdata is present, the response 
+
    When pred.type="TS", the function approaches prediction first by dividing invocations between
+those with or without newdata.  When no newdata is present, the response
 variable may be reconstructed as the sum of the trend, the signal, and the
 noise (residuals).  Since the values of the response variable are known,
 their spatial lags are used to calculate signal components (Cressie 1993, p. 564).  For the error
-model, trend = \(X \beta\), and signal = \(\lambda W y - 
+model, trend = \(X \beta\), and signal = \(\lambda W y -
 \lambda W X \beta\). For the lag and mixed
 models, trend = \(X \beta\), and signal = \(\rho W y\).
    
 
    This approach differs from the design choices made in other software, for
 example GeoDa, which does not use observations of the response variable,
 and corresponds to the newdata situation described below.
    
-
    When however newdata is used for prediction, no observations of the response 
+
    When however newdata is used for prediction, no observations of the response
 variable being predicted are available.  Consequently, while the trend
 components are the same, the signal cannot take full account of the spatial
-smooth.  In the error model and Durbin error model, the signal is set to zero, since the spatial smooth is expressed in terms of the error: 
+smooth.  In the error model and Durbin error model, the signal is set to zero, since the spatial smooth is expressed in terms of the error:
 \((I - \lambda W)^{-1} \varepsilon\).
    
 
    In the lag model, the signal can be expressed in the following way (for legacy=TRUE):
    
 
    $$(I - \rho W) y = X \beta + \varepsilon$$
@@ -178,7 +155,7 @@ 
    Details
    
 
    and the signal is found as the difference between prediction and trend. The numerical results for the legacy and DGP methods are identical.
    
 
    
 setting the error term to zero.  This also means that predictions of the
-signal component for lag and mixed models require the inversion of an 
+signal component for lag and mixed models require the inversion of an
 n-by-n matrix.
    
 
    Because the outcomes of the spatial smooth on the error term are
 unobservable, this means that the signal values for newdata are
@@ -190,32 +167,30 @@ 
    Details
    
 
    listw should be provided except if newdata=NULL and pred.type= include “TS”, “trend”, or if newdata is not NULL, pred.type="trend" and object is not a mixed model.  
    
 
    all.data is useful when some out-of-sample predictors return different predictions for in-sample units, than the same predictor type computed only on in-sample data.
    
     
    
-    
    
-    
    Value
    
-    
    
-
    predict.Sarlm() returns a vector of predictions with three attribute 
+    
    
+    
    Value
    
+    
    predict.Sarlm() returns a vector of predictions with three attribute
 vectors of trend, signal (only for pred.type="TS") and region.id values and two other attributes
 of pred.type and call with class Sarlm.pred.
    
-
    
 
    print.Sarlm.pred() is a print function for this class, printing and
 returning a data frame with columns: "fit", "trend" and "signal" (when available) and with region.id as row names.
    
     
    
-    
    
-    
    References
    
-    
    Haining, R. 1990 Spatial data analysis in the social and environmental sciences, Cambridge: Cambridge University Press, p. 258; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York; Michel Goulard, Thibault Laurent & Christine Thomas-Agnan, 2017 About predictions in spatial autoregressive models: optimal and almost optimal strategies,  Spatial Economic Analysis Volume 12, Issue 2--3, 304--325 doi:10.1080/17421772.2017.1300679
-, ; Kelejian, H. H. and Prucha, I. R. 2007 The relative efficiencies of various predictors in spatial econometric models containing spatial lags, Regional Science and Urban Economics, Volume 37, Issue 3, 363--374; Bivand, R. 2002 Spatial econometrics functions in R: Classes and methods, Journal of Geographical Systems, Volume 4, No. 4, 405--421
    
+    
    
+    
    References
    
+    
    Haining, R. 1990 Spatial data analysis in the social and environmental sciences, Cambridge: Cambridge University Press, p. 258; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York; Michel Goulard, Thibault Laurent & Christine Thomas-Agnan, 2017 About predictions in spatial autoregressive models: optimal and almost optimal strategies,  Spatial Economic Analysis Volume 12, Issue 2–3, 304–325 doi:10.1080/17421772.2017.1300679
+, ; Kelejian, H. H. and Prucha, I. R. 2007 The relative efficiencies of various predictors in spatial econometric models containing spatial lags, Regional Science and Urban Economics, Volume 37, Issue 3, 363–374; Bivand, R. 2002 Spatial econometrics functions in R: Classes and methods, Journal of Geographical Systems, Volume 4, No. 4, 405–421
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no and Martin Gubri
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    errorsarlm, lagsarlm, sacsarlm
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    data(oldcol, package="spdep")
 lw <- spdep::nb2listw(COL.nb)
 COL.lag.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, lw)
@@ -386,27 +361,23 @@ 
    Examples
    
 #> [1] TRUE
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/print.Gmsar.html b/docs/reference/print.Gmsar.html
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diff --git a/docs/reference/print.LagImpact.html b/docs/reference/print.LagImpact.html
new file mode 100644
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diff --git a/docs/reference/print.Me_res.html b/docs/reference/print.Me_res.html
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diff --git a/docs/reference/print.Sarlm.html b/docs/reference/print.Sarlm.html
new file mode 100644
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--- /dev/null
+++ b/docs/reference/print.Sarlm.html
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diff --git a/docs/reference/print.Sarlm.pred.html b/docs/reference/print.Sarlm.pred.html
new file mode 100644
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+++ b/docs/reference/print.Sarlm.pred.html
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diff --git a/docs/reference/print.SfResult.html b/docs/reference/print.SfResult.html
new file mode 100644
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diff --git a/docs/reference/print.SlX.html b/docs/reference/print.SlX.html
new file mode 100644
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diff --git a/docs/reference/print.Spautolm.html b/docs/reference/print.Spautolm.html
new file mode 100644
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diff --git a/docs/reference/print.Stsls.html b/docs/reference/print.Stsls.html
new file mode 100644
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diff --git a/docs/reference/print.WXimpact.html b/docs/reference/print.WXimpact.html
new file mode 100644
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diff --git a/docs/reference/print.summary.Gmsar.html b/docs/reference/print.summary.Gmsar.html
new file mode 100644
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diff --git a/docs/reference/print.summary.LagImpact.html b/docs/reference/print.summary.LagImpact.html
new file mode 100644
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diff --git a/docs/reference/print.summary.Spautolm.html b/docs/reference/print.summary.Spautolm.html
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diff --git a/docs/reference/print.summary.Stsls.html b/docs/reference/print.summary.Stsls.html
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diff --git a/docs/reference/print.summary.WXimpact.html b/docs/reference/print.summary.WXimpact.html
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diff --git a/docs/reference/residuals.Gmsar.html b/docs/reference/residuals.Gmsar.html
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diff --git a/docs/reference/residuals.Lagmess.html b/docs/reference/residuals.Lagmess.html
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diff --git a/docs/reference/residuals.Sarlm.html b/docs/reference/residuals.Sarlm.html
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diff --git a/docs/reference/residuals.Spautolm.html b/docs/reference/residuals.Spautolm.html
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diff --git a/docs/reference/residuals.Stsls.html b/docs/reference/residuals.Stsls.html
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diff --git a/docs/reference/sacsarlm.html b/docs/reference/sacsarlm.html
new file mode 100644
index 0000000..4dbdc74
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diff --git a/docs/reference/sarlm_tests.html b/docs/reference/sarlm_tests.html
index acfeb84..2bf9ed3 100644
--- a/docs/reference/sarlm_tests.html
+++ b/docs/reference/sarlm_tests.html
@@ -1,143 +1,118 @@
 
-Likelihood ratio test — LR.Sarlm • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Likelihood ratio test
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Likelihood ratio test
    
+
+      
    sarlm_tests.Rd
    
     
    
 
-    
    
+    
    
     
    The LR.Sarlm() function provides a likelihood ratio test for objects for which a logLik() function exists for their class, or for objects of class logLik. LR1.Sarlm() and Wald1.Sarlm() are used internally in summary.Sarlm(), but may be accessed directly; they report the values respectively of LR and Wald tests for the absence of spatial dependence in spatial lag or error models. The spatial Hausman test is available for models fitted with errorSarlm and GMerrorsar.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    LR.Sarlm(x, y)
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 logLik(object, ...)
 LR1.Sarlm(object)
 Wald1.Sarlm(object)
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 Hausman.test(object, ..., tol=NULL)
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 anova(object, ...)
 bptest.Sarlm(object, varformula=NULL, studentize = TRUE, data=list())
-# S3 method for Sarlm
+# S3 method for class 'Sarlm'
 impacts(obj, ..., tr, R = NULL, listw = NULL, evalues=NULL,
  useHESS = NULL, tol = 1e-06, empirical = FALSE, Q=NULL)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    x
    
+    
    
+    
    Arguments
    
+    
    
+
    x
    
 
    a logLik object or an object for which a logLik() function exists
    
 
-  
    y
    
+  
    y
    
 
    a logLik object or an object for which a logLik() function exists
    
 
-  
    object, obj
    
+  
    object, obj
    
 
    a Sarlm object
    
 
-  
    ...
    
+  
    ...
    
 
    further arguments passed to or from other methods
    
 
 
    
-
    varformula
    
+
    varformula
    
 
    a formula describing only the potential explanatory variables for the variance (no dependent variable needed). By default the same explanatory variables are taken as in the main regression model
    
 
-  
    studentize
    
+  
    studentize
    
 
    logical. If set to TRUE Koenker's studentized
    version of the test statistic will be used.
    
 
-  
    data
    
+  
    data
    
 
    an optional data frame containing the variables in the varformula
    
-  
    tr
    
+  
    tr
    
 
    A vector of traces of powers of the spatial weights matrix created using trW, for approximate impact measures; if not given, listw must be given for exact measures (for small to moderate spatial weights matrices); the traces must be for the same spatial weights as were used in fitting the spatial regression, and must be row-standardised
    
 
-  
    listw
    
+  
    listw
    
 
    If tr is not given, a spatial weights object as created by nb2listw; they must be the same spatial weights as were used in fitting the spatial regression, but do not have to be row-standardised
    
 
-  
    evalues
    
+  
    evalues
    
 
    vector of eigenvalues of spatial weights matrix for impacts calculations
    
 
-  
    R
    
+  
    R
    
 
    If given, simulations are used to compute distributions for the impact measures, returned as mcmc objects; the objects are used for convenience but are not output by an MCMC process
    
 
-  
    useHESS
    
+  
    useHESS
    
 
    Use the Hessian approximation (if available) even if the asymptotic coefficient covariance matrix is available; used for comparing methods
    
 
-  
    tol
    
+  
    tol
    
 
    Argument passed to mvrnorm and solve: tolerance (relative to largest variance) for numerical lack of positive-definiteness in the coefficient covariance matrix
    
 
-  
    empirical
    
+  
    empirical
    
 
    Argument passed to mvrnorm (default FALSE): if true, the coefficients and their covariance matrix specify the empirical not population mean and covariance matrix
    
 
-  
    Q
    
+  
    Q
    
 
    default NULL, else an integer number of cumulative power series impacts to calculate if tr is given
    
 
 
    
-    
    
-    
    Value
    
-    
-
-
    The tests return objects of class htest with:
    
+    
    
+    
    Value
    
+    
    The tests return objects of class htest with:
    
 
    statistic
    
 
    value of statistic
    
 
@@ -154,38 +129,35 @@ 
    Value
    
 
    description of test method
    
 
 
-  
    logLik.Sarlm() returns an object of class logLik
    
-
    
-
    LR1.Sarlm, Hausman.Sarlm and Wald1.Sarlm returm objects of class htest
    
-
-
+  
    logLik.Sarlm() returns an object of class logLik
+  LR1.Sarlm, Hausman.Sarlm and Wald1.Sarlm returm objects of class htest
    
     
    
-    
    
-    
    Note
    
+    
    
+    
    Note
    
     
    The numbers of degrees of freedom returned by logLik.Sarlm() include nuisance parameters, that is the number of regression coefficients, plus sigma, plus spatial parameter esitmate(s).
    
     
    
-    
    
-    
    References
    
-    
    LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 61--63; Pace RK and LeSage J (2008) A spatial Hausman test. Economics Letters 101, 282--284.
+    
    
+    
    References
    
+    
    LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 61–63; Pace RK and LeSage J (2008) A spatial Hausman test. Economics Letters 101, 282–284.
 T.S. Breusch & A.R. Pagan (1979),
 A Simple Test for Heteroscedasticity and Random Coefficient Variation.
-Econometrica 47, 1287--1294
    
+Econometrica 47, 1287–1294
    
 
    W. Krämer & H. Sonnberger (1986),
 The Linear Regression Model under Test. Heidelberg: Physica.
    
 
    L. Anselin (1988) Spatial econometrics: methods and models.
-Dordrecht: Kluwer, pp. 121--122.
    
+Dordrecht: Kluwer, pp. 121–122.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no, bptest: Torsten Hothorn and Achim Zeileis, modified by Roger Bivand
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    logLik.lm, anova.Sarlm
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    require("sf", quietly=TRUE)
 columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
 #require("spdep", quietly=TRUE)
@@ -241,27 +213,23 @@ 
    Examples
    
 #> 
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/set.ClusterOption.html b/docs/reference/set.ClusterOption.html
new file mode 100644
index 0000000..7cb0a7d
--- /dev/null
+++ b/docs/reference/set.ClusterOption.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/set.VerboseOption.html b/docs/reference/set.VerboseOption.html
new file mode 100644
index 0000000..c8246da
--- /dev/null
+++ b/docs/reference/set.VerboseOption.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/set.coresOption.html b/docs/reference/set.coresOption.html
new file mode 100644
index 0000000..7cb0a7d
--- /dev/null
+++ b/docs/reference/set.coresOption.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/set.mcOption.html b/docs/reference/set.mcOption.html
index 6a2542b..2df6fec 100644
--- a/docs/reference/set.mcOption.html
+++ b/docs/reference/set.mcOption.html
@@ -1,74 +1,50 @@
 
-Options for parallel support — set.mcOption • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Options for parallel support
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Options for parallel support
    
+
+      
    set.mcOption.Rd
    
     
    
 
-    
    
+    
    
     
    Provides support for the use of parallel computation in the parallel package.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    set.mcOption(value)
 get.mcOption()
 set.coresOption(value)
@@ -77,36 +53,35 @@ 
    Options for parallel support
    
 get.ClusterOption()
    
     
    
 
-    
    
-    
    Arguments
    
-    
    value
    
+    
    
+    
    Arguments
    
+    
    
+
    value
    
 
    valid replacement value
    
 
-  
    cl
    
+  
    cl
    
 
    a cluster object created by makeCluster in parallel
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    Options in the spatialreg package are held in an environment local to the package namespace and not exported. Option values are set and retrieved with pairs of access functions, get and set. The mc option is set by default to FALSE on Windows systems, as they cannot fork the R session; by default it is TRUE on other systems, but may be set FALSE. If mc is FALSE, the Cluster option is used: if mc is FALSE and the Cluster option is NULL no parallel computing is done, or the Cluster option is passed a “cluster” object created by the parallel or snow package for access without being passed as an argument. The cores option is set to NULL by default, and can be used to store the number of cores to use as an integer. If cores is NULL, facilities from the parallel package will not be used.
    
     
    
-    
    
-    
    Value
    
-    
-
-
    The option access functions return their current settings, the assignment functions usually return the previous value of the option.
    
+    
    
+    
    Value
    
+    
    The option access functions return their current settings, the assignment functions usually return the previous value of the option.
    
     
    
-    
    
-    
    Note
    
+    
    
+    
    Note
    
     
    An extended example is shown in the documentation of mom_calc, including treatment of seeding of RNG for multicore/cluster.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    ls(envir=spatialreg:::.spatialregOptions)
 #> [1] "cluster"      "cores"        "mc"           "rlecuyerSeed" "verbose"     
 #> [6] "zeroPolicy"  
@@ -173,27 +148,23 @@ 
    Examples
    
 #> 
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/set.spChkOption.html b/docs/reference/set.spChkOption.html
index d6acbd4..80c202a 100644
--- a/docs/reference/set.spChkOption.html
+++ b/docs/reference/set.spChkOption.html
@@ -1,74 +1,50 @@
 
-Control checking of spatial object IDs — set.ZeroPolicyOption • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Control checking of spatial object IDs
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Control checking of spatial object IDs
    
+
+      
    set.spChkOption.Rd
    
     
    
 
-    
    
+    
    
     
    Provides support for checking the mutual integrity of spatial neighbour weights and spatial data; similar mechanisms are used for passing global verbose and zero.policy options, and for providing access to a running cluster for embarrassingly parallel tasks.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    set.VerboseOption(check)
 get.VerboseOption()
 set.ZeroPolicyOption(check)
@@ -77,55 +53,51 @@ 
    Control checking of spatial object IDs
    
 #get.listw_is_CsparseMatrix_Option()
    
     
    
 
-    
    
-    
    Arguments
    
-    
    check
    
+    
    
+    
    Arguments
    
+    
    
+
    check
    
 
    a logical value, TRUE or FALSE
    
 
 
    
-    
    
-    
    Details
    
-    
    Analysis functions will have an spChk argument by default set to NULL, and will call get.spChkOption() to get the global spatial option for whether to check or not --- this is initialised to FALSE, and consequently should not break anything. It can be changed to TRUE using set.spChkOption(TRUE), or the spChk argument can be assigned in analysis functions. spNamedVec() is provided to ensure that rownames are passed on to single columns taken from two-dimensional arrays and data frames.
    
+    
    
+    
    Details
    
+    
    Analysis functions will have an spChk argument by default set to NULL, and will call get.spChkOption() to get the global spatial option for whether to check or not — this is initialised to FALSE, and consequently should not break anything. It can be changed to TRUE using set.spChkOption(TRUE), or the spChk argument can be assigned in analysis functions. spNamedVec() is provided to ensure that rownames are passed on to single columns taken from two-dimensional arrays and data frames.
    
     
    
-    
    
-    
    Value
    
-    
    
-
    set.spChkOption() returns the old logical value, get.spChkOption() returns the current logical value, and chkIDs() returns a logical value for the test lack of difference. spNamedVec() returns the selected column with the names set to the row names of the object from which it has been extracted.
    
+    
    
+    
    Value
    
+    
    set.spChkOption() returns the old logical value, get.spChkOption() returns the current logical value, and chkIDs() returns a logical value for the test lack of difference. spNamedVec() returns the selected column with the names set to the row names of the object from which it has been extracted.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    get.VerboseOption()
 #> [1] FALSE
 get.ZeroPolicyOption()
 #> [1] FALSE
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/similar.listw.html b/docs/reference/similar.listw.html
index 00b2a35..826b8d2 100644
--- a/docs/reference/similar.listw.html
+++ b/docs/reference/similar.listw.html
@@ -1,104 +1,79 @@
 
-Create symmetric similar weights lists — similar.listw • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Create symmetric similar weights lists
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Create symmetric similar weights lists
    
+
+      
    similar.listw.Rd
    
     
    
 
-    
    
+    
    
     
    From Ord's 1975 paper, it is known that the Jacobian for SAR models may be found by "symmetrizing" by similarity (the eigenvalues of similar matrices are identical, so the Jacobian is too). This applies only to styles "W" and "S" with underlying symmetric binary neighbour relations or symmetric general neighbour relations (so no k-nearest neighbour relations). The function is invoked automatically within the SAR fitting functions, to call eigen on a symmetric matrix for the default eigen method, or to make it possible to use the Matrix method on weights that can be "symmetrized" in this way.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    similar.listw(listw)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    listw
    
+    
    
+    
    Arguments
    
+    
    
+
    listw
    
 
    a listw object created for example by spdep::nb2listw
    
 
 
    
-    
    
-    
    Value
    
-    
-
-
    a listw object
    
+    
    
+    
    Value
    
+    
    a listw object
    
     
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Ord, J. K. 1975 Estimation methods for models of spatial interaction, Journal of the American Statistical Association, 70, 120-126
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    lagsarlm, errorsarlm
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    #require("spdep", quietly=TRUE)
 data(oldcol, package="spdep")
 COL.W <- spdep::nb2listw(COL.nb, style="W")
@@ -120,27 +95,23 @@ 
    Examples
    
 #> [1] -1.602757
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/spBreg_err.html b/docs/reference/spBreg_err.html
new file mode 100644
index 0000000..4866abf
--- /dev/null
+++ b/docs/reference/spBreg_err.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/spBreg_sac.html b/docs/reference/spBreg_sac.html
new file mode 100644
index 0000000..4866abf
--- /dev/null
+++ b/docs/reference/spBreg_sac.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/spam_setup.html b/docs/reference/spam_setup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/spam_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/spam_update_setup.html b/docs/reference/spam_update_setup.html
new file mode 100644
index 0000000..ae0235d
--- /dev/null
+++ b/docs/reference/spam_update_setup.html
@@ -0,0 +1,8 @@
+
+  
+    
+    
+    
+  
+
+
diff --git a/docs/reference/sparse_mat.html b/docs/reference/sparse_mat.html
index 8a6ea12..6bbd28a 100644
--- a/docs/reference/sparse_mat.html
+++ b/docs/reference/sparse_mat.html
@@ -1,74 +1,50 @@
 
-Spatial neighbour sparse representation — as.spam.listw • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Spatial neighbour sparse representation
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Spatial neighbour sparse representation
    
+
+      
    sparse_mat.Rd
    
     
    
 
-    
    
+    
    
     
    Interface between Matrix class objects and weights lists. The as.spam.listw method converts a "listw" object to a sparse matrix as defined in the spam package.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    as.spam.listw(listw)
 listw2U_spam(lw)
 listw2U_Matrix(lw)
@@ -80,41 +56,42 @@ 
    Spatial neighbour sparse representation
    
 powerWeights(W, rho, order=250, X, tol=.Machine$double.eps^(3/5))
    
     
    
 
-    
    
-    
    Arguments
    
-    
    listw, lw
    
+    
    
+    
    Arguments
    
+    
    
+
    listw, lw
    
 
    a listw object from for example nb2listw
    
 
-  
    W
    
+  
    W
    
 
    a dsTMatrix object created using as_dsTMatrix_listw from a symmetric listw object
    
 
-  
    rho
    
+  
    rho
    
 
    spatial regression coefficient
    
 
-  
    n
    
+  
    n
    
 
    length of diagonal for identity matrix
    
 
-  
    order
    
+  
    order
    
 
    Power series maximum limit
    
 
-  
    X
    
+  
    X
    
 
    A numerical matrix
    
 
-  
    tol
    
+  
    tol
    
 
    Tolerance for convergence of power series
    
 
 
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    nb2listw
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    # \dontrun{
 require(sf, quietly=TRUE)
 columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
@@ -125,7 +102,7 @@ 
    Examples
    
   col.sp <- as.spam.listw(col.listw)
   str(col.sp)
 }
-#> Spam version 2.10-0 (2023-10-23) is loaded.
+#> Spam version 2.11-0 (2024-10-03) is loaded.
 #> Type 'help( Spam)' or 'demo( spam)' for a short introduction 
 #> and overview of this package.
 #> Help for individual functions is also obtained by adding the
@@ -180,11 +157,11 @@ 
    Examples
    
 W <- as(lw, "CsparseMatrix")
 system.time(e <- invIrM(nb7rt, rho=0.98, method="solve", feasible=NULL) %*% x)
 #>    user  system elapsed 
-#>   0.003   0.000   0.002 
+#>   0.002   0.000   0.003 
 system.time(ee <- powerWeights(W, rho=0.98, X=x))
 #> Warning: not converged within order iterations
 #>    user  system elapsed 
-#>   0.170   0.007   0.178 
+#>   0.173   0.006   0.180 
 str(attr(ee, "internal"))
 #> List of 5
 #>  $ series: num [1:250] 0.287 0.234 0.201 0.178 0.16 ...
@@ -197,10 +174,10 @@ 
    Examples
    
 # \dontrun{
 system.time(ee <- powerWeights(W, rho=0.9, X=x))
 #>    user  system elapsed 
-#>   0.129   0.006   0.135 
+#>   0.130   0.002   0.133 
 system.time(ee <- powerWeights(W, rho=0.98, order=1000, X=x))
 #>    user  system elapsed 
-#>   0.795   0.009   0.807 
+#>   0.662   0.011   0.675 
 all.equal(e, as(ee, "matrix"), check.attributes=FALSE)
 #> [1] TRUE
 nb60rt <- spdep::cell2nb(60, 60, torus=TRUE)
@@ -222,27 +199,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/spautolm.html b/docs/reference/spautolm.html
index 9b01ce1..1ae6676 100644
--- a/docs/reference/spautolm.html
+++ b/docs/reference/spautolm.html
@@ -1,158 +1,135 @@
 
-Spatial conditional and simultaneous autoregression model estimation — spautolm • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Spatial conditional and simultaneous autoregression model estimation
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Spatial conditional and simultaneous autoregression model estimation
    
+
+      
    spautolm.Rd
    
     
    
 
-    
    
+    
    
     
    Function taking family and weights arguments for spatial autoregression model estimation by Maximum Likelihood, using dense matrix methods, not suited to large data sets with thousands of observations. With one of the sparse matrix methods, larger numbers of observations can be handled, but the interval= argument should be set. The implementation is GLS using the single spatial coefficient value, here termed lambda, found by line search using optimize to maximise the log likelihood.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    spautolm(formula, data = list(), listw, weights,
  na.action, family = "SAR", method="eigen", verbose = NULL, trs=NULL,
  interval=NULL, zero.policy = NULL, tol.solve=.Machine$double.eps,
  llprof=NULL, control=list())
-# S3 method for Spautolm
+# S3 method for class 'Spautolm'
 summary(object, correlation = FALSE, adj.se=FALSE,
  Nagelkerke=FALSE, ...)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    formula
    
-
    a symbolic description of the model to be fit. The details 
+    
    
+    
    Arguments
    
+    
    
+
    formula
    
+
    a symbolic description of the model to be fit. The details
 of model specification are given for lm()
    
 
-  
    data
    
-
    an optional data frame containing the variables in the model. 
-By default the variables are taken from the environment which the function 
+  
    data
    
+
    an optional data frame containing the variables in the model.
+By default the variables are taken from the environment which the function
 is called.
    
 
-  
    listw
    
+  
    listw
    
 
    a listw object created for example by nb2listw
    
 
-  
    weights
    
+  
    weights
    
 
    an optional vector of weights to be used in the fitting process
    
 
-  
    na.action
    
+  
    na.action
    
 
    a function (default options("na.action")), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the weights list will be subsetted to remove NAs in the data. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.
    
 
-  
    family
    
+  
    family
    
 
    character string: either "SAR" or "CAR" for simultaneous or conditional autoregressions; "SMA" for spatial moving average added thanks to Jielai Ma - "SMA" is only implemented for method="eigen" because it necessarily involves dense matrices
    
 
-  
    method
    
+  
    method
    
 
    character string: default "eigen" for use of dense matrices, "Matrix_J" for sparse matrices (restricted to spatial weights symmetric or similar to symmetric) using methods in the Matrix package; “Matrix” provides updating Cholesky decomposition methods. Values of method may also include "LU", which provides an alternative sparse matrix decomposition approach, and the "Chebyshev" and Monte Carlo "MC" approximate log-determinant methods.
    
 
-  
    verbose
    
+  
    verbose
    
 
    default NULL, use global option value; if TRUE, reports function values during optimization.
    
 
-  
    trs
    
+  
    trs
    
 
    default NULL, if given, a vector of powered spatial weights matrix traces output by trW; when given, used in some Jacobian methods
    
 
-  
    interval
    
+  
    interval
    
 
    search interval for autoregressive parameter when not using method="eigen"; default is c(-1,0.999), optimize will reset NA/NaN to a bound and gives a warning when the interval is poorly set; method="Matrix" will attempt to search for an appropriate interval, if find_interval=TRUE (fails on some platforms)
    
 
-  
    zero.policy
    
-
    default NULL, use global option value; Include list of no-neighbour observations in output if TRUE --- otherwise zero.policy is handled within the listw argument
    
+  
    zero.policy
    
+
    default NULL, use global option value; Include list of no-neighbour observations in output if TRUE — otherwise zero.policy is handled within the listw argument
    
 
-  
    tol.solve
    
+  
    tol.solve
    
 
    the tolerance for detecting linear dependencies in the columns of matrices to be inverted - passed to solve() (default=double precision machine tolerance). Errors in solve() may constitute indications of poorly scaled variables: if the variables have scales differing much from the autoregressive coefficient, the values in this matrix may be very different in scale, and inverting such a matrix is analytically possible by definition, but numerically unstable; rescaling the RHS variables alleviates this better than setting tol.solve to a very small value
    
 
-  
    llprof
    
+  
    llprof
    
 
    default NULL, can either be an integer, to divide the feasible range into llprof points, or a sequence of spatial coefficient values, at which to evaluate the likelihood function
    
 
- 
    control
    
+ 
    control
    
 
    list of extra control arguments - see section below
    
 
-  
    object
    
+  
    object
    
 
    Spautolm object from spautolm
    
 
-  
    correlation
    
+  
    correlation
    
 
    logical; if 'TRUE', the correlation matrix of the estimated parameters is returned and printed (default=FALSE)
    
 
-  
    adj.se
    
+  
    adj.se
    
 
    if TRUE, adjust the coefficient standard errors for the number of fitted coefficients
    
 
-  
    Nagelkerke
    
+  
    Nagelkerke
    
 
    if TRUE, the Nagelkerke pseudo R-squared is reported
    
 
-  
    ...
    
+  
    ...
    
 
    further arguments passed to or from other methods
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    This implementation is based on lm.gls and errorsarlm. In particular, the function does not (yet) prevent asymmetric spatial weights being used with "CAR" family models. It appears that both numerical issues (convergence in particular) and uncertainties about the exact spatial weights matrix used make it difficult to reproduce Cressie and Chan's 1989 results, also given in Cressie 1993.
    
-
    Note that the fitted() function for the output object assumes that the response 
+
    Note that the fitted() function for the output object assumes that the response
 variable may be reconstructed as the sum of the trend, the signal, and the
 noise (residuals). Since the values of the response variable are known,
-their spatial lags are used to calculate signal components (Cressie 1993, p. 564). This differs from other software, including GeoDa, which does not use knowledge of the response 
+their spatial lags are used to calculate signal components (Cressie 1993, p. 564). This differs from other software, including GeoDa, which does not use knowledge of the response
 variable in making predictions for the fitting data.
    
     
    
-    
    
-    
    Control arguments
    
-    
+    
    
+    
    Control arguments
    
+
 
    tol.opt:
    
 
    the desired accuracy of the optimization - passed to optimize() (default=.Machine$double.eps^(2/3))
    
 
@@ -215,11 +192,9 @@ 
    Control arguments
    
 
 
 
    
-    
    
-    
    Value
    
-    
-
-
    A list object of class Spautolm:
    
+    
    
+    
    Value
    
+    
    A list object of class Spautolm:
    
 
    fit
    
 
    a list, with items:
    coefficients
    
 
    ML coefficient estimates
    
@@ -245,7 +220,7 @@ 
    Value
    
     
    residuals
    
 
    difference between observed and fitted values
    
 
-  
+
 
    
 
   
    lambda
    
@@ -306,27 +281,27 @@ 
    Value
    
 
    weights used in model fitting
    
 
 
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion;
 Ord, J. K. 1975 Estimation methods for models of spatial interaction,
 Journal of the American Statistical Association, 70, 120-126; Waller, L. A., Gotway, C. A. 2004 Applied spatial statistics for public health, Wiley, Hoboken, NJ, 325-380; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York, 548-568; Ripley, B. D. 1981 Spatial statistics, Wiley, New York, 88-95; LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    Note
    
+    
    
+    
    Note
    
     
    The standard errors given in Waller and Gotway (2004) are adjusted for the numbers of parameters estimated, and may be reproduced by using the additional argument adj.se=TRUE in the summary method. In addition, the function returns fitted values and residuals as given by Cressie (1993) p. 564.
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    optimize, errorsarlm, do_ldet
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    require("sf", quietly=TRUE)
 nydata <- st_read(system.file("shapes/NY8_bna_utm18.gpkg", package="spData")[1], quiet=TRUE)
 # \dontrun{
@@ -422,7 +397,7 @@ 
    Examples
    
  data=nydata, listw=listw_NY, family="SAR", method="eigen",
  control=list(pre_eig=eigs)))
 #>    user  system elapsed 
-#>   0.195   0.001   0.196 
+#>     0.2     0.0     0.2 
 res <- summary(esar1f)
 print(res)
 #> 
@@ -467,7 +442,7 @@ 
    Examples
    
 system.time(esar1M <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
  data=nydata, listw=listw_NY, family="SAR", method="Matrix"))
 #>    user  system elapsed 
-#>   0.228   0.000   0.229 
+#>   0.227   0.000   0.227 
 summary(esar1M)
 #> 
 #> Call: 
@@ -498,7 +473,7 @@ 
    Examples
    
  data=nydata, listw=listw_NY, family="SAR", method="Matrix",
  control=list(super=TRUE)))
 #>    user  system elapsed 
-#>   0.201   0.000   0.204 
+#>   0.203   0.000   0.204 
 summary(esar1M)
 #> 
 #> Call: 
@@ -558,7 +533,7 @@ 
    Examples
    
 system.time(esar1wM <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
  data=nydata, listw=listw_NY, weights=POP8, family="SAR", method="Matrix"))
 #>    user  system elapsed 
-#>   0.218   0.000   0.219 
+#>    0.22    0.00    0.22 
 summary(esar1wM)
 #> 
 #> Call: 
@@ -675,7 +650,7 @@ 
    Examples
    
 system.time(ecar1M <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
  data=nydata, listw=listw_NY, family="CAR", method="Matrix"))
 #>    user  system elapsed 
-#>   0.245   0.000   0.247 
+#>   0.311   0.000   0.313 
 summary(ecar1M)
 #> 
 #> Call: 
@@ -737,7 +712,7 @@ 
    Examples
    
 system.time(ecar1wM <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
  data=nydata, listw=listw_NY, weights=POP8, family="CAR", method="Matrix"))
 #>    user  system elapsed 
-#>   0.256   0.000   0.259 
+#>   0.260   0.000   0.262 
 summary(ecar1wM)
 #> 
 #> Call: 
@@ -773,6 +748,7 @@ 
    Examples
    
 lm_nc <- lm(ft.SID74 ~ 1)
 sids.nhbr30 <- spdep::dnearneigh(cbind(nc.sids$east, nc.sids$north), 0, 30,
  row.names=row.names(nc.sids))
+#> Warning: neighbour object has 3 sub-graphs
 sids.nhbr30.dist <- spdep::nbdists(sids.nhbr30, cbind(nc.sids$east, nc.sids$north))
 sids.nhbr <- spdep::listw2sn(spdep::nb2listw(sids.nhbr30,
  glist=sids.nhbr30.dist, style="B", zero.policy=TRUE))
@@ -794,63 +770,63 @@ 
    Examples
    
 #> [1] "Anson"
 mdata.4 <- mdata[-outl,]
 W <- spdep::listw2mat(sids.nhbr.listw)
-#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
+#> Error: object 'sids.nhbr.listw' not found
 W.4 <- W[-outl, -outl]
-#> Error in eval(expr, envir, enclos): object 'W' not found
+#> Error: object 'W' not found
 sids.nhbr.listw.4 <- spdep::mat2listw(W.4)
-#> Error in eval(expr, envir, enclos): object 'W.4' not found
+#> Error: object 'W.4' not found
 esarI <- errorsarlm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw,
  zero.policy=TRUE)
-#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
+#> Error: object 'sids.nhbr.listw' not found
 summary(esarI)
 #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarI' not found
 esarIa <- spautolm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw,
  family="SAR")
-#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
+#> Error: object 'sids.nhbr.listw' not found
 summary(esarIa)
 #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIa' not found
 esarIV <- errorsarlm(ft.SID74 ~ ft.NWBIR74, data=mdata, listw=sids.nhbr.listw,
  zero.policy=TRUE)
-#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
+#> Error: object 'sids.nhbr.listw' not found
 summary(esarIV)
 #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIV' not found
 esarIVa <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata, listw=sids.nhbr.listw,
  family="SAR")
-#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
+#> Error: object 'sids.nhbr.listw' not found
 summary(esarIVa)
 #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIVa' not found
 esarIaw <- spautolm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw,
  weights=BIR74, family="SAR")
-#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
+#> Error: object 'sids.nhbr.listw' not found
 summary(esarIaw)
 #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIaw' not found
 esarIIaw <- spautolm(ft.SID74 ~ both - 1, data=mdata, listw=sids.nhbr.listw,
  weights=BIR74, family="SAR")
-#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
+#> Error: object 'sids.nhbr.listw' not found
 summary(esarIIaw)
 #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIIaw' not found
 esarIVaw <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata,
  listw=sids.nhbr.listw, weights=BIR74, family="SAR")
-#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
+#> Error: object 'sids.nhbr.listw' not found
 summary(esarIVaw)
 #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIVaw' not found
 ecarIaw <- spautolm(ft.SID74 ~ 1, data=mdata.4, listw=sids.nhbr.listw.4,
  weights=BIR74, family="CAR")
-#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw.4' not found
+#> Error: object 'sids.nhbr.listw.4' not found
 summary(ecarIaw)
 #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'ecarIaw' not found
 ecarIIaw <- spautolm(ft.SID74 ~ both - 1, data=mdata.4,
  listw=sids.nhbr.listw.4, weights=BIR74, family="CAR")
-#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw.4' not found
+#> Error: object 'sids.nhbr.listw.4' not found
 summary(ecarIIaw)
 #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'ecarIIaw' not found
 ecarIVaw <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata.4,
  listw=sids.nhbr.listw.4, weights=BIR74, family="CAR")
-#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw.4' not found
+#> Error: object 'sids.nhbr.listw.4' not found
 summary(ecarIVaw)
 #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'ecarIVaw' not found
 nc.sids$fitIV <- append(fitted.values(ecarIVaw), NA, outl-1)
-#> Error in eval(expr, envir, enclos): object 'ecarIVaw' not found
+#> Error: object 'ecarIVaw' not found
 plot(nc.sids[,"fitIV"], nbreaks=12) # Cressie 1993, p. 565
 #> Error in `[.data.frame`(x, i, j, drop = drop): undefined columns selected
 # }
@@ -957,27 +933,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/stsls.html b/docs/reference/stsls.html
index f5ec277..829c831 100644
--- a/docs/reference/stsls.html
+++ b/docs/reference/stsls.html
@@ -1,150 +1,133 @@
 
-Generalized spatial two stage least squares — stsls • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Generalized spatial two stage least squares
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Generalized spatial two stage least squares
    
+
+      
    stsls.Rd
    
     
    
 
-    
    
+    
    
     
    The function fits a spatial lag model by two stage least squares, with the option of adjusting the results for heteroskedasticity.
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    stsls(formula, data = list(), listw, zero.policy = NULL,
- na.action = na.fail, robust = FALSE, HC=NULL, legacy=FALSE, W2X = TRUE)
-# S3 method for Stsls
+ na.action = na.fail, robust = FALSE, HC=NULL, legacy=FALSE, W2X = TRUE,
+ sig2n_k=TRUE, adjust.n=FALSE)
+# S3 method for class 'Stsls'
 impacts(obj, ..., tr, R = NULL, listw = NULL, evalues=NULL,
  tol = 1e-06, empirical = FALSE, Q=NULL)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    formula
    
-
    a symbolic description of the model to be fit. The details 
+    
    
+    
    Arguments
    
+    
    
+
    formula
    
+
    a symbolic description of the model to be fit. The details
 of model specification are given for lm()
    
 
-  
    data
    
-
    an optional data frame containing the variables in the model. 
-By default the variables are taken from the environment which the function 
+  
    data
    
+
    an optional data frame containing the variables in the model.
+By default the variables are taken from the environment which the function
 is called.
    
 
-  
    listw
    
+  
    listw
    
 
    a listw object created for example by nb2listw
    
 
-  
    zero.policy
    
-
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without 
+  
    zero.policy
    
+
    default NULL, use global option value; if TRUE assign zero to the lagged value of zones without
 neighbours, if FALSE (default) assign NA - causing lagsarlm() to terminate with an error
    
 
-  
    na.action
    
+  
    na.action
    
 
    a function (default na.fail), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.
    
 
-  
    robust
    
+  
    robust
    
 
    default FALSE, if TRUE, apply a heteroskedasticity correction to the coefficients covariances
    
 
-  
    HC
    
+  
    HC
    
 
    default NULL, if robust is TRUE, assigned “HC0”, may take values “HC0” or “HC1” for White estimates or MacKinnon-White estimates respectively
    
 
- 
    legacy
    
-
    the argument chooses between two implementations of the robustness correction: default FALSE - use the estimate of Omega only in the White consistent estimator of the variance-covariance matrix, if TRUE, use the original implementation which runs a GLS using the estimate of Omega, and yields different coefficient estimates as well - see example below
    
+ 
    legacy
    
+
    the argument chooses between two implementations of the robustness correction: default FALSE - use the estimate of Omega only in the White consistent estimator of the variance-covariance matrix, if TRUE, use the original implementation which runs a GLS using the estimate of Omega, overrides sig2n_k, and yields different coefficient estimates as well - see example below
    
+
+ 
    W2X
    
+
    default TRUE, if FALSE only WX are used as instruments in the spatial two stage least squares; until release 0.4-60, only WX were used - see example below; Python spreg::GM_Lag is default FALSE
    
 
- 
    W2X
    
-
    default TRUE, if FALSE only WX are used as instruments in the spatial two stage least squares; until release 0.4-60, only WX were used - see example below
    
+ 
    sig2n_k
    
+
    default TRUE - use n-k to calculate sigma^2, if FALSE use n; Python spreg::GM_Lag is default FALSE
    
 
-  
    obj
    
+ 
    adjust.n
    
+
    default FALSE, used in creating spatial weights constants for the Anselin-Kelejian (1997) test
    
+
+  
    obj
    
 
    A spatial regression object created by lagsarlm, lagmess or by lmSLX; in HPDinterval.LagImpact, a LagImpact object
    
 
-  
    ...
    
+  
    ...
    
 
    Arguments passed through to methods in the coda package
    
 
-  
    tr
    
+  
    tr
    
 
    A vector of traces of powers of the spatial weights matrix created using trW, for approximate impact measures; if not given, listw must be given for exact measures (for small to moderate spatial weights matrices); the traces must be for the same spatial weights as were used in fitting the spatial regression, and must be row-standardised
    
 
-  
    evalues
    
+  
    evalues
    
 
    vector of eigenvalues of spatial weights matrix for impacts calculations
    
 
-  
    R
    
+  
    R
    
 
    If given, simulations are used to compute distributions for the impact measures, returned as mcmc objects; the objects are used for convenience but are not output by an MCMC process
    
 
-  
    tol
    
+  
    tol
    
 
    Argument passed to mvrnorm: tolerance (relative to largest variance) for numerical lack of positive-definiteness in the coefficient covariance matrix
    
 
-  
    empirical
    
+  
    empirical
    
 
    Argument passed to mvrnorm (default FALSE): if true, the coefficients and their covariance matrix specify the empirical not population mean and covariance matrix
    
 
-  
    Q
    
+  
    Q
    
 
    default NULL, else an integer number of cumulative power series impacts to calculate if tr is given
    
 
 
    
-    
    
-    
    Details
    
+    
    
+    
    Details
    
     
    The fitting implementation fits a spatial lag model:
    
 
    $$y = \rho W y + X \beta + \varepsilon$$
    
 
    by using spatially lagged X variables as instruments for the spatially lagged dependent variable.
    
+
    From version 1.3-6, the general Anselin-Kelejian (1997) test for residual spatial autocorrelation is added.
    
     
    
-    
    
-    
    Value
    
-    
-
-
    an object of class "Stsls" containing:
    
+    
    
+    
    Value
    
+    
    an object of class "Stsls" containing:
    
 
    coefficients
    
 
    coefficient estimates
    
 
@@ -161,26 +144,29 @@ 
    Value
    
 
    degrees of freedom
    
 
 
    
-    
    
-    
    References
    
+    
    
+    
    References
    
     
    Kelejian, H.H. and I.R. Prucha (1998). A generalized spatial two
 stage least squares procedure for estimating a spatial autoregressive
 model with autoregressive disturbances. Journal of Real Estate
-Finance and Economics 17, 99-121.
    
+Finance and Economics 17, 99-121. doi:10.1023/A:1007707430416
+.
    
+
    Anselin, L., & Kelejian, H. H. (1997). Testing for Spatial Error Autocorrelation in the Presence of Endogenous Regressors. International Regional Science Review, 20(1-2), 153-182. doi:10.1177/016001769702000109
+.
    
 
    Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. Journal of Statistical Software, 63(18), 1-36. doi:10.18637/jss.v063.i18
 .
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Luc Anselin, Gianfranco Piras and Roger Bivand
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    lagsarlm
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    data(oldcol, package="spdep")
 #require(spdep, quietly=TRUE)
 lw <- spdep::nb2listw(COL.nb)
@@ -237,12 +223,14 @@ 
    Examples
    
 #> HOVAL       -0.265489   0.091852 -2.8904  0.003847
 #> 
 #> Residual variance (sigma squared): 103.44, (sigma: 10.171)
+#> Anselin-Kelejian (1997) test for residual autocorrelation
+#> test value: 0.043401, p-value: 0.83497
 #> 
 #> Correlation of Coefficients:
-#>      [,1]  [,2]  [,3] 
-#> [1,] -0.92            
-#> [2,]  0.63 -0.76      
-#> [3,]  0.04 -0.16 -0.36
+#>             Rho   (Intercept) INC  
+#> (Intercept) -0.92                  
+#> INC          0.63 -0.76            
+#> HOVAL        0.04 -0.16       -0.36
 #> 
 coef(x)
 #>               Estimate  Std. Error   t value     Pr(>|t|)
@@ -324,12 +312,41 @@ 
    Examples
    
 #> HOVAL       -0.265681   0.091954 -2.8893  0.003861
 #> 
 #> Residual variance (sigma squared): 103.67, (sigma: 10.182)
+#> Anselin-Kelejian (1997) test for residual autocorrelation
+#> test value: 0.058156, p-value: 0.80943
 #> 
 #> Correlation of Coefficients:
-#>      [,1]  [,2]  [,3] 
-#> [1,] -0.93            
-#> [2,]  0.64 -0.77      
-#> [3,]  0.04 -0.16 -0.36
+#>             Rho   (Intercept) INC  
+#> (Intercept) -0.93                  
+#> INC          0.64 -0.77            
+#> HOVAL        0.04 -0.16       -0.36
+#> 
+COL.lag.stslsWn <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, lw, W2X=FALSE, sig2n_k=FALSE)
+summary(COL.lag.stslsWn, correlation=TRUE)
+#> 
+#> Call:stsls(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = lw, 
+#>     W2X = FALSE, sig2n_k = FALSE)
+#> 
+#> Residuals:
+#>        Min         1Q     Median         3Q        Max 
+#> -37.785778  -5.442414  -0.052649   6.170104  23.039123 
+#> 
+#> Coefficients: 
+#>              Estimate Std. Error t value  Pr(>|t|)
+#> Rho          0.444202   0.181257  2.4507  0.014259
+#> (Intercept) 44.359512  10.691995  4.1489 3.341e-05
+#> INC         -1.014319   0.371318 -2.7317  0.006301
+#> HOVAL       -0.265681   0.088121 -3.0150  0.002570
+#> 
+#> Residual variance (sigma squared): 95.203, (sigma: 9.7572)
+#> Anselin-Kelejian (1997) test for residual autocorrelation
+#> test value: 0.058156, p-value: 0.80943
+#> 
+#> Correlation of Coefficients:
+#>             Rho   (Intercept) INC  
+#> (Intercept) -0.93                  
+#> INC          0.64 -0.77            
+#> HOVAL        0.04 -0.16       -0.36
 #> 
 COL.lag.stslsR <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, lw,
 robust=TRUE, W2X=FALSE)
@@ -350,12 +367,14 @@ 
    Examples
    
 #> HOVAL       -0.26568        0.17353 -1.5311  0.125752
 #> 
 #> Residual variance (sigma squared): 103.67, (sigma: 10.182)
+#> Anselin-Kelejian (1997) test for residual autocorrelation
+#> test value: 0.056852, p-value: 0.81154
 #> 
 #> Correlation of Coefficients:
-#>      [,1]  [,2]  [,3] 
-#> [1,] -0.90            
-#> [2,]  0.15 -0.28      
-#> [3,]  0.24 -0.24 -0.83
+#>             Rho   (Intercept) INC  
+#> (Intercept) -0.90                  
+#> INC          0.15 -0.28            
+#> HOVAL        0.24 -0.24       -0.83
 #> 
 COL.lag.stslsRl <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, lw,
 robust=TRUE, legacy=TRUE, W2X=FALSE)
@@ -376,6 +395,8 @@ 
    Examples
    
 #> HOVAL       -0.25047        0.17333 -1.4450  0.148461
 #> 
 #> Asymptotic robust residual variance: 96.446, (sigma: 9.8207)
+#> Anselin-Kelejian (1997) test for residual autocorrelation
+#> test value: 0.10254, p-value: 0.7488
 #> 
 #> Correlation of Coefficients:
 #>             Rho   (Intercept) INC  
@@ -416,30 +437,28 @@ 
    Examples
    
 #> log(LSTAT)  -2.3984e-01  2.2470e-02 -10.6740 < 2.2e-16
 #> 
 #> Residual variance (sigma squared): 0.020054, (sigma: 0.14161)
+#> Anselin-Kelejian (1997) test for residual autocorrelation
+#> test value: 4.3942, p-value: 0.036062
 #> 
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/subgraph_eigenw.html b/docs/reference/subgraph_eigenw.html
new file mode 100644
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diff --git a/docs/reference/summary.Gmsar.html b/docs/reference/summary.Gmsar.html
new file mode 100644
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diff --git a/docs/reference/summary.LagImpact.html b/docs/reference/summary.LagImpact.html
new file mode 100644
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diff --git a/docs/reference/summary.Lagmess.html b/docs/reference/summary.Lagmess.html
new file mode 100644
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diff --git a/docs/reference/summary.Sarlm.html b/docs/reference/summary.Sarlm.html
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diff --git a/docs/reference/summary.SlX.html b/docs/reference/summary.SlX.html
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diff --git a/docs/reference/summary.Spautolm.html b/docs/reference/summary.Spautolm.html
new file mode 100644
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diff --git a/docs/reference/summary.Stsls.html b/docs/reference/summary.Stsls.html
new file mode 100644
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diff --git a/docs/reference/summary.WXimpact.html b/docs/reference/summary.WXimpact.html
new file mode 100644
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diff --git a/docs/reference/trW.html b/docs/reference/trW.html
index 7914052..46fd0c4 100644
--- a/docs/reference/trW.html
+++ b/docs/reference/trW.html
@@ -1,137 +1,112 @@
 
-Spatial weights matrix powers traces — trW • spatialreg
-    
-
-    
    
-      
    
-  
    
-    
    
-    
    Spatial weights matrix powers traces
    
-    
-    
+
  • Changelog
    • 
+      
      • 
+
      • 
+      
    
+
+
+  
    
+
    
+
    
+  
    
+
+      
    Spatial weights matrix powers traces
    
+
+      
    trW.Rd
    
     
    
 
-    
    
+    
    
     
    The function is used to prepare a vector of traces of powers of a spatial weights matrix
    
     
    
 
-    
    
+    
    
+    
    Usage
    
     
    trW(W=NULL, m = 30, p = 16, type = "mult", listw=NULL, momentsSymmetry=TRUE)
 mom_calc(lw, m)
 mom_calc_int2(is, m, nb, weights, Card)
    
     
    
 
-    
    
-    
    Arguments
    
-    
    W
    
+    
    
+    
    Arguments
    
+    
    
+
    W
    
 
    A spatial weights matrix in CsparseMatrix form
    
 
-  
    m
    
+  
    m
    
 
    The number of powers; must be an even number for ‘type’=“moments” (default changed from 100 to 30 (2010-11-17))
    
 
-  
    p
    
+  
    p
    
 
    The number of samples used in Monte Carlo simulation of the traces if type is MC (default changed from 50 to 16 (2010-11-17))
    
 
-  
    type
    
+  
    type
    
 
    Either “mult” (default) for powering a sparse matrix (with moderate or larger N, the matrix becomes dense, and may lead to swapping), or “MC” for Monte Carlo simulation of the traces (the first two simulated traces are replaced by their analytical equivalents), or “moments” to use the looping space saving algorithm proposed by Smirnov and Anselin (2009) - for “moments”, W must be symmetric, for row-standardised weights through a similarity transformation
    
 
-  
    listw, lw
    
+  
    listw, lw
    
 
    a listw object, which should either be fully symmetric, or be constructed as similar to symmetric from intrinsically symmetric neighbours using similar.listw, used with ‘type’=“moments”
    
 
-  
    momentsSymmetry
    
+  
    momentsSymmetry
    
 
    default TRUE; assert Smirnov/Anselin symmetry assumption
    
 
-  
    is
    
+  
    is
    
 
    (used internally only in mom_calc_int2 for ‘type’=“moments” on a cluster)
    
 
-  
    nb
    
+  
    nb
    
 
    (used internally only in mom_calc_int2 for ‘type’=“moments” on a cluster)
    
 
-  
    weights
    
+  
    weights
    
 
    (used internally only in mom_calc_int2 for ‘type’=“moments” on a cluster)
    
 
-  
    Card
    
+  
    Card
    
 
    (used internally only in mom_calc_int2 for ‘type’=“moments” on a cluster)
    
 
 
    
-    
    
-    
    Value
    
-    
-
-
    A numeric vector of m traces, with “timings” and “type” attributes; the ‘type’=“MC” also returns the standard deviation of the p-vector V divided by the square root of p as a measure of spread for the trace estimates.
    
+    
    
+    
    Value
    
+    
    A numeric vector of m traces, with “timings” and “type” attributes; the ‘type’=“MC” also returns the standard deviation of the p-vector V divided by the square root of p as a measure of spread for the trace estimates.
    
     
    
-    
    
-    
    Note
    
+    
    
+    
    Note
    
     
    mom_calc and mom_calc_int2 are for internal use only
    
     
    
-    
    
-    
    References
    
-    
    LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 96--105; Smirnov O and L Anselin (2009) An O(N) parallel method of computing the Log-Jacobian of the variable transformation for models with spatial interaction on a lattice. Computational Statistics and Data Analysis 53 (2009) 2983--2984.
    
+    
    
+    
    References
    
+    
    LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 96–105; Smirnov O and L Anselin (2009) An O(N) parallel method of computing the Log-Jacobian of the variable transformation for models with spatial interaction on a lattice. Computational Statistics and Data Analysis 53 (2009) 2983–2984.
    
     
    
-    
    
-    
    Author
    
+    
    
+    
    Author
    
     
    Roger Bivand Roger.Bivand@nhh.no
    
     
    
-    
    
-    
    See also
    
+    
    
+    
    See also
    
     
    as_dgRMatrix_listw, nb2listw
    
     
    
 
-    
    
-    
    Examples
    
+    
    
+    
    Examples
    
     
    require("sf", quietly=TRUE) 
 columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
 #require(spdep, quietly=TRUE)
@@ -140,21 +115,21 @@ 
    Examples
    
 W <- as(listw, "CsparseMatrix")
 system.time(trMat <- trW(W, type="mult"))
 #>    user  system elapsed 
-#>   0.003   0.000   0.003 
+#>   0.002   0.000   0.002 
 str(trMat)
 #>  num [1:30] 0 10.91 3.65 5.62 3.66 ...
-#>  - attr(*, "timings")= Named num [1:2] 0.003 0.003
+#>  - attr(*, "timings")= Named num [1:2] 0.002 0.002
 #>   ..- attr(*, "names")= chr [1:2] "user.self" "elapsed"
 #>  - attr(*, "type")= chr "mult"
 #>  - attr(*, "n")= int 49
 set.seed(1100)
 system.time(trMC <- trW(W, type="MC"))
 #>    user  system elapsed 
-#>   0.005   0.000   0.006 
+#>   0.005   0.000   0.005 
 str(trMC)
 #>  num [1:30] 0 10.91 3.69 5.36 3.64 ...
 #>  - attr(*, "sd")= num [1:30] NA NA 0.598 0.495 0.489 ...
-#>  - attr(*, "timings")= Named num [1:2] 0.005 0.006
+#>  - attr(*, "timings")= Named num [1:2] 0.005 0.005
 #>   ..- attr(*, "names")= chr [1:2] "user.self" "elapsed"
 #>  - attr(*, "type")= chr "MC"
 #>  - attr(*, "n")= int 49
@@ -180,10 +155,10 @@ 
    Examples
    
 #> [1] TRUE
 system.time(trMat <- trW(W, m=24, type="mult"))
 #>    user  system elapsed 
-#>   0.002   0.000   0.003 
+#>   0.003   0.000   0.003 
 str(trMat)
 #>  num [1:24] 0 10.91 3.65 5.62 3.66 ...
-#>  - attr(*, "timings")= Named num [1:2] 0.002 0.003
+#>  - attr(*, "timings")= Named num [1:2] 0.003 0.003
 #>   ..- attr(*, "names")= chr [1:2] "user.self" "elapsed"
 #>  - attr(*, "type")= chr "mult"
 #>  - attr(*, "n")= int 49
@@ -206,10 +181,10 @@ 
    Examples
    
 listwS <- similar.listw(listw)
 system.time(trmom <- trW(listw=listwS, m=24, type="moments"))
 #>    user  system elapsed 
-#>   0.109   0.000   0.110 
+#>   0.116   0.000   0.117 
 str(trmom)
 #>  num [1:24] 0 124.2 32.7 63.7 33.2 ...
-#>  - attr(*, "timings")= Named num [1:2] 0.109 0.109
+#>  - attr(*, "timings")= Named num [1:2] 0.116 0.117
 #>   ..- attr(*, "names")= chr [1:2] "user.self" "elapsed"
 #>  - attr(*, "type")= chr "moments"
 #>  - attr(*, "n")= int 506
@@ -225,7 +200,7 @@ 
    Examples
    
 }
 system.time(trmomp <- trW(listw=listwS, m=24, type="moments"))
 #>    user  system elapsed 
-#>   0.107   0.000   0.108 
+#>   0.119   0.000   0.119 
 if(!get.mcOption()) {
   set.ClusterOption(NULL)
   stopCluster(cl)
@@ -236,27 +211,23 @@ 
    Examples
    
 # }
 
    
     
    
-  
    
-  
-
    
+  
    
 
 
-      
    
-  
    Developed by Roger Bivand, Gianfranco Piras.
    
+    
    
+  
    Developed by Roger Bivand, Gianfranco Piras.
    
 
    
 
-
    
-  
    Site built with pkgdown 2.0.9.
    
+
    
+  
    Site built with pkgdown 2.1.1.
    
 
    
 
-      
    
+    
    
+
 
-  
 
 
-  
 
   
 
diff --git a/docs/reference/vcov.Sarlm.html b/docs/reference/vcov.Sarlm.html
new file mode 100644
index 0000000..4dbdc74
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diff --git a/docs/search.json b/docs/search.json
new file mode 100644
index 0000000..bd21e7b
--- /dev/null
+++ b/docs/search.json
@@ -0,0 +1 @@
+[{"path":"https://r-spatial.github.io/spatialreg/articles/SpatialFiltering.html","id":"introduction-1","dir":"Articles","previous_headings":"","what":"Introduction 1","title":"Moran Eigenvectors","text":"Moran eigenvector approach (Dray, Legendre, Peres-Neto 2006; Griffith Peres-Neto 2006) involved spatial patterns represented maps eigenvectors; choosing suitable orthogonal patterns adding linear generalised linear model, spatial dependence present residuals can moved model. uses brute force search set eigenvectors matrix 𝐌𝐖𝐌\\mathbf{M W M}, $$\\mathbf{M} = \\mathbf{} - \\mathbf{X}(\\mathbf{X}^{\\rm T} \\mathbf{X})^{-1}\\mathbf{X}^{\\rm T}$$ symmetric idempotent projection matrix 𝐖\\mathbf{W} spatial weights. spatial lag form SpatialFiltering GLM form , 𝐗\\mathbf{X} nn-vector ones, intercept . general form, SpatialFiltering chooses subset nn eigenvectors reduce residual spatial autocorrelation error model covariates. lag form adds covariates assessment eigenvectors choose, use constructing eigenvectors. SpatialFiltering implemented contributed Yongwan Chun Michael Tiefelsdorf, presented Tiefelsdorf Griffith (2007); based Matlab code Pedro Peres-Neto discussed Dray, Legendre, Peres-Neto (2006) Griffith Peres-Neto (2006). Since SpatialFiltering approach allow weights used, see residual autocorrelation original linear model absorbed, ‘whitened’ inclusion selected eigenvectors model, covariate coefficients change little. addition eigenvectors – representing independent spatial pattern – relieves residual autocorrelation, otherwise makes changes substantive coefficient values. function also searches eigenvectors spatial lag variant underlying model, GLM framework. criterion permutation bootstrap test Moran’s II regression residuals, case, limited remaining spatial autocorrelation, set α=0.5\\alpha = 0.5. Even generous stopping rule, eigenvectors chosen; combined contribution just improves fit GLM model.  Figure fig:geigen2fig:geigen2 shows spatial patterns chosen match small amount spatial autocorrelation remaining model. Poisson regressions, closeness TCE sites highly significant. Since, however, many TCE sites also close densely populated urban areas possible presence point-source non-point-source pollution, premature take results simply face value. , however, potentially useful contrast cities Binghamton south study area several sites vicinity, Syracuse north without TCE sites data set.","code":"library(spdep) require(\"sf\", quietly=TRUE) if (packageVersion(\"spData\") >= \"2.3.2\") {     NY8 <- sf::st_read(system.file(\"shapes/NY8_utm18.gpkg\", package=\"spData\")) } else {     NY8 <- sf::st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\"))     sf::st_crs(NY8) <- \"EPSG:32618\"     NY8$Cases <- NY8$TRACTCAS } ## Reading layer `NY8_utm18' from data source  ##   `/home/rsb/lib/r_libs/spData/shapes/NY8_utm18.gpkg' using driver `GPKG' ## Simple feature collection with 281 features and 17 fields ## Geometry type: POLYGON ## Dimension:     XY ## Bounding box:  xmin: 358241.9 ymin: 4649755 xmax: 480393.1 ymax: 4808545 ## Projected CRS: WGS 84 / UTM zone 18N NY_nb <- read.gal(system.file(\"weights/NY_nb.gal\", package=\"spData\"), override.id=TRUE) library(spatialreg) nySFE <- SpatialFiltering(Z~PEXPOSURE+PCTAGE65P+PCTOWNHOME, data=NY8, nb=NY_nb, style=\"W\", verbose=FALSE) nylmSFE <- lm(Z~PEXPOSURE+PCTAGE65P+PCTOWNHOME+fitted(nySFE), data=NY8) summary(nylmSFE) ##  ## Call: ## lm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME + fitted(nySFE),  ##     data = NY8) ##  ## Residuals: ##     Min      1Q  Median      3Q     Max  ## -1.5184 -0.3523 -0.0105  0.3221  3.1964  ##  ## Coefficients: ##                    Estimate Std. Error t value Pr(>|t|)     ## (Intercept)        -0.51728    0.14606  -3.542 0.000469 *** ## PEXPOSURE           0.04884    0.03230   1.512 0.131717     ## PCTAGE65P           3.95089    0.55776   7.083 1.25e-11 *** ## PCTOWNHOME         -0.56004    0.15688  -3.570 0.000423 *** ## fitted(nySFE)vec13 -2.09397    0.60534  -3.459 0.000630 *** ## fitted(nySFE)vec44 -2.24003    0.60534  -3.700 0.000261 *** ## fitted(nySFE)vec6   1.02979    0.60534   1.701 0.090072 .   ## fitted(nySFE)vec38  1.29282    0.60534   2.136 0.033613 *   ## fitted(nySFE)vec20  1.10064    0.60534   1.818 0.070150 .   ## fitted(nySFE)vec14 -1.05105    0.60534  -1.736 0.083662 .   ## fitted(nySFE)vec75  1.90600    0.60534   3.149 0.001826 **  ## fitted(nySFE)vec21 -1.06331    0.60534  -1.757 0.080138 .   ## fitted(nySFE)vec36  1.17861    0.60534   1.947 0.052578 .   ## fitted(nySFE)vec61 -1.08582    0.60534  -1.794 0.073986 .   ## --- ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ##  ## Residual standard error: 0.6053 on 267 degrees of freedom ## Multiple R-squared:  0.3401, Adjusted R-squared:  0.308  ## F-statistic: 10.58 on 13 and 267 DF,  p-value: < 2.2e-16 nylm <- lm(Z~PEXPOSURE+PCTAGE65P+PCTOWNHOME, data=NY8) anova(nylm, nylmSFE) ## Analysis of Variance Table ##  ## Model 1: Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME ## Model 2: Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME + fitted(nySFE) ##   Res.Df     RSS Df Sum of Sq      F    Pr(>F)     ## 1    277 119.619                                   ## 2    267  97.837 10    21.782 5.9444 3.988e-08 *** ## --- ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 NYlistwW <- nb2listw(NY_nb, style = \"W\") set.seed(111) nyME <- ME(Cases~PEXPOSURE+PCTAGE65P+PCTOWNHOME, data=NY8, offset=log(POP8), family=\"poisson\", listw=NYlistwW, alpha=0.46) nyME ##   Eigenvector ZI pr(ZI) ## 0          NA NA   0.31 ## 1          24 NA   0.44 ## 2         223 NA   0.42 ## 3         206 NA   0.43 ## 4         169 NA   0.48 NY8$eigen_1 <- fitted(nyME)[,1] NY8$eigen_2 <- fitted(nyME)[,2] #gry <- brewer.pal(9, \"Greys\")[-1] plot(NY8[,c(\"eigen_1\", \"eigen_2\")]) nyglmME <- glm(Cases~PEXPOSURE+PCTAGE65P+PCTOWNHOME+offset(log(POP8))+fitted(nyME), data=NY8, family=\"poisson\") summary(nyglmME) ##  ## Call: ## glm(formula = Cases ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME + offset(log(POP8)) +  ##     fitted(nyME), family = \"poisson\", data = NY8) ##  ## Coefficients: ##                    Estimate Std. Error z value Pr(>|z|)     ## (Intercept)        -8.13431    0.18388 -44.237  < 2e-16 *** ## PEXPOSURE           0.14136    0.03134   4.511 6.45e-06 *** ## PCTAGE65P           4.16875    0.60149   6.931 4.19e-12 *** ## PCTOWNHOME         -0.39290    0.19222  -2.044  0.04096 *   ## fitted(nyME)vec24   1.62658    0.72243   2.252  0.02435 *   ## fitted(nyME)vec223  0.92941    0.70391   1.320  0.18671     ## fitted(nyME)vec206 -0.11559    0.68987  -0.168  0.86693     ## fitted(nyME)vec169 -1.82674    0.68142  -2.681  0.00735 **  ## --- ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ##  ## (Dispersion parameter for poisson family taken to be 1) ##  ##     Null deviance: 428.25  on 280  degrees of freedom ## Residual deviance: 340.08  on 273  degrees of freedom ## AIC: Inf ##  ## Number of Fisher Scoring iterations: 5 nyGLMp <- glm(Cases~PEXPOSURE+PCTAGE65P+PCTOWNHOME+offset(log(POP8)), data=NY8,family=\"poisson\") anova(nyGLMp, nyglmME, test=\"Chisq\") ## Analysis of Deviance Table ##  ## Model 1: Cases ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME + offset(log(POP8)) ## Model 2: Cases ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME + offset(log(POP8)) +  ##     fitted(nyME) ##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)   ## 1       277     353.35                        ## 2       273     340.08  4   13.269  0.01003 * ## --- ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"Spatial weights objects as sparse matrices and graphs","text":"Since spdep package created, spatial weights objects constructed lists three components attributes, old-style class listw objects. first component listw object nb object, list n integer vectors, least character vector region.id attribute n unique values (like row.names data.frame object); n number spatial entities. Component list contains integer identifiers neighbours sorted vector duplication values 1:n; neighbours, component vector length 1 value 0L. nb object may contain attribute indicating whether symmetric , whether neighbour j implies j neighbour . neighbour definitions symmetric construction, contiguities distance thresholds, others asymmetric, k-nearest neighbours. nb object redundantly stores -j j-links. second component listw object list n numeric vectors, length corresponding non-zero vectors nbobject. give values spatial weights -j neighbour pair. often case neighbours symmetric construction, weights , example weights row-standardised dividing row input weights count neighbours cardinality neighbour set . nb2listwfunction, also possible pass general weights, inverse distances, shares boundary lengths . third component listw object records style weights character code, \"B\" binary weights taking values zero one (one recorded), \"W\" row-standardised weights, . order subset listw objects, knowledge style may necessary obvious similar way sparse matrices stored, either row - like listw object, column. key insight storing zero values unnecessary, need store row column locations non-zero values. Early , Netlib library used provide limited support spdep sparse matrices, followed functionality SparseM, spam, Matrix. spdep spatialreg versions 1.2, vignette accompanying functionality moved spatialreg.","code":""},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"spatialreg-depends-on-matrix","dir":"Articles","previous_headings":"Introduction","what":"spatialreg depends on Matrix","title":"Spatial weights objects as sparse matrices and graphs","text":"Since Matrix recommended package, functionality increasingly used time, become one two packages spatialreg depends. reported loading:","code":"library(spatialreg) ## Loading required package: spData ## Loading required package: Matrix ## Loading required package: sf ## Linking to GEOS 3.13.0, GDAL 3.10.0, PROJ 9.5.0; sf_use_s2() is TRUE"},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"getting-some-data","dir":"Articles","previous_headings":"Introduction","what":"Getting some data","title":"Spatial weights objects as sparse matrices and graphs","text":"legacy Columbus OH data set 49 spatial entities, polygons, defined boundaries policing districts city. spatialreg imports spdep turn depends sf.","code":"dothis <- TRUE if (!suppressPackageStartupMessages(require(sf, quietly=TRUE))) {   message(\"install the sf package\")   dothis <- FALSE } if (dothis) {   sf_extSoftVersion() } ##           GEOS           GDAL         proj.4 GDAL_with_GEOS     USE_PROJ_H  ##       \"3.13.0\"       \"3.10.0\"        \"9.5.0\"         \"true\"         \"true\"  ##           PROJ  ##        \"9.5.0\" library(sf) columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1]) ## Reading layer `columbus' from data source  ##   `/home/rsb/lib/r_libs/spData/shapes/columbus.gpkg' using driver `GPKG' ## Simple feature collection with 49 features and 20 fields ## Geometry type: POLYGON ## Dimension:     XY ## Bounding box:  xmin: 5.874907 ymin: 10.78863 xmax: 11.28742 ymax: 14.74245 ## Projected CRS: Undefined Cartesian SRS with unknown unit row.names(columbus)[1:10] ##  [1] \"1\"  \"2\"  \"3\"  \"4\"  \"5\"  \"6\"  \"7\"  \"8\"  \"9\"  \"10\""},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"finding-contiguous-neighbours-and-droppping-links","dir":"Articles","previous_headings":"Introduction","what":"Finding contiguous neighbours and droppping links","title":"Spatial weights objects as sparse matrices and graphs","text":"Contiguous neighbours often used polygonal spatial entities, poly2nb function defaulting queen criterion - entities neighbours share boundary point. see entity IDs copied across nb object: order make object complicated, let us drop neighbour links 21st entity (noting print method reports ID entity neighbours, number 1:n), plot resulting map neighbours:","code":"nb_q <- spdep::poly2nb(columbus) nb_q ## Neighbour list object: ## Number of regions: 49  ## Number of nonzero links: 236  ## Percentage nonzero weights: 9.829238  ## Average number of links: 4.816327 attr(nb_q, \"region.id\")[1:10] ##  [1] \"1\"  \"2\"  \"3\"  \"4\"  \"5\"  \"6\"  \"7\"  \"8\"  \"9\"  \"10\" spdep::is.symmetric.nb(nb_q) ## [1] TRUE col2 <- spdep::droplinks(nb_q, 21) ## Warning in spdep::droplinks(nb_q, 21): some observations have no neighbours ## Warning in spdep::droplinks(nb_q, 21): neighbour object has 3 sub-graphs nb_q[[21]] ## [1] 24 30 34 col2[[21]] ## [1] 0 col2 ## Neighbour list object: ## Number of regions: 49  ## Number of nonzero links: 230  ## Percentage nonzero weights: 9.579342  ## Average number of links: 4.693878  ## 1 region with no links: ## 21 ## 3 disjoint connected subgraphs spdep::is.symmetric.nb(col2) ## [1] TRUE coords <- st_coordinates(st_centroid(st_geometry(columbus))) plot(nb_q, coords, col=\"grey\") plot(col2, coords, add=TRUE)"},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"using-sparse-matrices-to-represent-spatial-weights","dir":"Articles","previous_headings":"","what":"Using sparse matrices to represent spatial weights","title":"Spatial weights objects as sparse matrices and graphs","text":"present listw objects can coerced objects classes defined Matrix. style lost coercion, may possible reconstruct spatial weights sparse matrix representation preserve . start symmetric binary weights, first creating spatial weights object, signalling one entity neighbours zero.policy argument (default false). matrix graph representations -neighbour entities obvious.","code":"nb_B <- spdep::nb2listw(col2, style=\"B\", zero.policy=TRUE) nb_B$style ## [1] \"B\""},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"symmetric-sparse-matrices","dir":"Articles","previous_headings":"Using sparse matrices to represent spatial weights","what":"Symmetric sparse matrices","title":"Spatial weights objects as sparse matrices and graphs","text":"spdep provides coercion methods listw \"symmetricMatrix\", \"RsparseMatrix\" \"CsparseMatrix\" classes defined Matrix. \"RsparseMatrix\" representation similar listw, row-based, used less frequently operations sparse matrices. entity IDs passed using sparse matrix row column names present. believe listw object can represented symmetric matrix, storing triangle rather -j j-weights. coercion method check whether symmetry present proceeding: Let us now try retreive list neighbours symmetric sparse matrix. present, coerce one Matrix internal representation another order get \"dgCMatrix\" format used inside mat2listw, coerce \"dgTMatrix\" \"dsTMatrix\". style retreived automatically, set \"M\" indicate conversion matrix. neighbour links retreived correctly, IDs:","code":"library(spatialreg) library(Matrix) B <- as(nb_B, \"CsparseMatrix\") all(B == t(B)) ## [1] TRUE str(B) ## Formal class 'dgCMatrix' [package \"Matrix\"] with 6 slots ##   ..@ i       : int [1:230] 1 2 0 2 3 0 1 3 4 1 ... ##   ..@ p       : int [1:50] 0 2 5 9 13 21 23 27 33 41 ... ##   ..@ Dim     : int [1:2] 49 49 ##   ..@ Dimnames:List of 2 ##   .. ..$ : chr [1:49] \"1\" \"2\" \"3\" \"4\" ... ##   .. ..$ : chr [1:49] \"1\" \"2\" \"3\" \"4\" ... ##   ..@ x       : num [1:230] 1 1 1 1 1 1 1 1 1 1 ... ##   ..@ factors : list() rownames(B)[1:10] ##  [1] \"1\"  \"2\"  \"3\"  \"4\"  \"5\"  \"6\"  \"7\"  \"8\"  \"9\"  \"10\" nb_B1 <- spdep::mat2listw(as(as(B, \"TsparseMatrix\"), \"CsparseMatrix\"),     style=\"B\", zero.policy=TRUE) ## Warning in sn2listw(df, style = style, zero.policy = zero.policy, from_mat2listw = TRUE): no-neighbour observations found, set zero.policy to TRUE; ## this warning will soon become an error ## Warning in sn2listw(df, style = style, zero.policy = zero.policy, ## from_mat2listw = TRUE): neighbour object has 3 sub-graphs ## Warning in spdep::mat2listw(as(as(B, \"TsparseMatrix\"), \"CsparseMatrix\"), : ## neighbour object has 3 sub-graphs nb_B1$style ## [1] \"B\" all.equal(nb_B1$neighbours, col2, check.attributes=FALSE) ## [1] TRUE all.equal(attr(nb_B1$neighbours, \"region.id\"), attr(nb_B$neighbours, \"region.id\")) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"log-determinants-symmetric-weights-used-in-spatial-regression","dir":"Articles","previous_headings":"Using sparse matrices to represent spatial weights","what":"Log determinants (symmetric weights) used in spatial regression","title":"Spatial weights objects as sparse matrices and graphs","text":"initial reason implementing support sparse weights matrices spdep permit calculation log determinant term spatial regressions larger data sets. Using eigenvalue approach example spatialreg::eigenw limited need operate dense matrices memory solve eigenproblem: n large, may become impractical /time-consuming, permit rapid calculation values log determinant differing values spatial coefficient ρ\\rho. Matrix package provides many determinant methods, \"dsCMatrix\" resulting subtracting \"dsCMatrix\", product scalar \"dsTMatrix\", \"ddiMatrix\". value log determinant follows, calling sparse Cholesky decomposition internally suitable input matrices. computation sparse Cholesky decomposition value spatial coefficient ρ\\rho may avoided updating pre-computed object; approach provides fast accurate log determinants larger (large) data sets:","code":"rho <- 0.1 do_spatialreg <- FALSE if (requireNamespace(\"spatialreg\", quietly=TRUE)) do_spatialreg <- TRUE if (do_spatialreg) sum(log(1 - rho * spatialreg::eigenw(nb_B))) ## [1] -1.44787 n <- nrow(B) I <- Diagonal(n) class(I - rho * B) ## [1] \"dgCMatrix\" ## attr(,\"package\") ## [1] \"Matrix\" c(determinant(I - rho * B, logarithm=TRUE)$modulus) ## [1] -1.44787 nW <- -B nChol <- Cholesky(nW, Imult=8) n * log(rho) + (2 * c(determinant(update(nChol, nW, 1/rho), sqrt=TRUE)$modulus)) ## [1] 15.40218"},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"asymmetric-sparse-matrices","dir":"Articles","previous_headings":"Using sparse matrices to represent spatial weights","what":"Asymmetric sparse matrices","title":"Spatial weights objects as sparse matrices and graphs","text":"use row-standardisation leads asymmetry even underlying neighbours symmetric, unless entities matching numbers neighbours (example regular grid torus): lag method listw objects often used create spatially lagged values, returns values vector given product sparse general matrix input numeric vector. Note setting zero.policy TRUE, spatial lag entity 21, neighbours, zero construction:","code":"nb_W <- spdep::nb2listw(col2, style=\"W\", zero.policy=TRUE) W <- as(nb_W, \"CsparseMatrix\") str(W) ## Formal class 'dgCMatrix' [package \"Matrix\"] with 6 slots ##   ..@ i       : int [1:230] 1 2 0 2 3 0 1 3 4 1 ... ##   ..@ p       : int [1:50] 0 2 5 9 13 21 23 27 33 41 ... ##   ..@ Dim     : int [1:2] 49 49 ##   ..@ Dimnames:List of 2 ##   .. ..$ : chr [1:49] \"1\" \"2\" \"3\" \"4\" ... ##   .. ..$ : chr [1:49] \"1\" \"2\" \"3\" \"4\" ... ##   ..@ x       : num [1:230] 0.333 0.25 0.5 0.25 0.25 ... ##   ..@ factors : list() all(W == t(W)) ## [1] FALSE set.seed(1) x <- runif(n) r1 <- as.numeric(W %*% x) r2 <- lag(nb_W, x, zero.policy=TRUE) all.equal(r1, r2, check.attributes=FALSE) ## [1] TRUE plot(x, r1, ylim=c(0,1)) c(x[21], r1[21]) ## [1] 0.9347052 0.0000000"},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"log-determinants-asymmetric-weights-used-in-spatial-regression","dir":"Articles","previous_headings":"Using sparse matrices to represent spatial weights","what":"Log determinants (asymmetric weights) used in spatial regression","title":"Spatial weights objects as sparse matrices and graphs","text":"Calculating log determinant asymmetric weights (symmetric neighbours symmetry induced non-constant numbers neighbours) may carried using eigenvalues , result may complex vector (, discussed ). appropriate determinant method \"dgCMatrix\" objects uses LU decomposition internally: can show internal workings method :","code":"rho <- 0.5 sum(log(1 - rho * eigenw(nb_W))) ## [1] -1.594376 class(I - rho * W) ## [1] \"dgCMatrix\" ## attr(,\"package\") ## [1] \"Matrix\" c(determinant(I - rho * W, logarithm=TRUE)$modulus) ## [1] -1.594376 LU <- lu(I - rho * W) sum(log(abs(diag(slot(LU, \"U\"))))) ## [1] -1.594376"},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"log-determinants-symmetric-by-similarity","dir":"Articles","previous_headings":"Using sparse matrices to represent spatial weights","what":"Log determinants: symmetric by similarity","title":"Spatial weights objects as sparse matrices and graphs","text":"nb2listw function stores components can employed transform asymmetric weights matrix symmetry similarity, permitting log determinant computed using less costly numerical methods. \"W\" style used cardinalities neighbour sets (row sums) introduce row standardisation, stored attribute: first restore row-standarised matrix binary form (must symmetric), can pre- post-multiply square roots inverted neighbour counts, yielding symmetric matrix appropriate properties: can seen, division square root zero entity 21 problem row dW zero. transformation similarity permits use numerical methods sparse symmetric matrices (equivalently eigenvalues dense matrices). Note transformation available intrinsically asymmetric neighbours, intrinsically asymmetric general weights.","code":"d <- attr(nb_W$weights, \"comp\")$d all.equal(d, spdep::card(col2)) ## [1] TRUE dW <- Diagonal(n, d) %*% W all(dW == t(dW)) ## [1] TRUE isd <- Diagonal(n, 1/sqrt(d)) isd[21,21] ## [1] Inf Ws <- as(isd %*% dW %*% isd, \"symmetricMatrix\") rowSums(Ws)[21] ## [1] 0 class(Ws) ## [1] \"dsCMatrix\" ## attr(,\"package\") ## [1] \"Matrix\" c(determinant(I - rho * Ws, logarithm=TRUE)$modulus) ## [1] -1.594376"},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"using-eigs-in-rspectra-for-finding-some-eigenvalues","dir":"Articles","previous_headings":"Using sparse matrices to represent spatial weights","what":"Using eigs in RSpectra for finding some eigenvalues","title":"Spatial weights objects as sparse matrices and graphs","text":"spatial regression, domain spatial coefficient given inverse maximum minimum eigenvalues. n moderate, eigenvalues anyway, interval line search available without extra effort. n somewhat larger, use may made eigs function RSpectra: case, results trivial small k. Using row-standardisation nice feature setting upper bound unity, graph methods finding whether lower bound -1.","code":"1/range(spatialreg::eigenw(nb_B)) ## [1] -0.3212551  0.1638329 if (!require(\"RSpectra\", quietly=TRUE)) dothis <- FALSE 1/c(eigs(B, k=1, which=\"SR\")$values, eigs(B, k=1, which=\"LR\")$values) ## [1] -0.3212551  0.1638329 1/range(eigenw(nb_W)) ## [1] -1.544645  1.000000 1/Re(c(eigs(W, k=1, which=\"SR\")$values, eigs(W, k=1, which=\"LR\")$values)) ## [1] -1.544645  1.000000"},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"converting-from-symmetric-adjacency-matrix-to-graph","dir":"Articles","previous_headings":"Using igraph for spatial weights as graphs","what":"Converting from symmetric adjacency matrix to graph","title":"Spatial weights objects as sparse matrices and graphs","text":"First ’ll see get sparse matrices graphs. mode symmetric matrix \"undirected\" definition:","code":"class(B) ## [1] \"dgCMatrix\" ## attr(,\"package\") ## [1] \"Matrix\" object.size(B) ## 10824 bytes if (!require(\"igraph\", quietly=FALSE)) dothis <- FALSE ## Loading required package: igraph ##  ## Attaching package: 'igraph' ## The following objects are masked from 'package:stats': ##  ##     decompose, spectrum ## The following object is masked from 'package:base': ##  ##     union g1 <- graph_from_adjacency_matrix(B, mode=\"undirected\") class(g1) ## [1] \"igraph\" object.size(g1) ## 6544 bytes"},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"converting-from-graph-to-symmetric-adjacency-matrix","dir":"Articles","previous_headings":"Using igraph for spatial weights as graphs","what":"Converting from graph to symmetric adjacency matrix","title":"Spatial weights objects as sparse matrices and graphs","text":"can also convert graph back matrix, note as_adjacency_matrix chooses particular class sparse matrix returned, conversion process typically leads many matrices fewer graph types, back fewer matrix types:","code":"# Matrix 1.4-2 vulnerability work-around ow <- options(\"warn\")$warn options(\"warn\"=2L) B1 <- try(as_adjacency_matrix(g1), silent=TRUE) if (!inherits(B1, \"try-error\")) print(class(B1)) ## [1] \"dgCMatrix\" ## attr(,\"package\") ## [1] \"Matrix\" if (!inherits(B1, \"try-error\")) print(object.size(B1)) ## 10824 bytes if (!inherits(B1, \"try-error\")) print(all.equal(B, as(B1, \"CsparseMatrix\"))) ## [1] TRUE options(\"warn\"=ow)"},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"graph-components-in-spdep","dir":"Articles","previous_headings":"Using igraph for spatial weights as graphs","what":"Graph components in spdep","title":"Spatial weights objects as sparse matrices and graphs","text":"simple example using igraph existing spdep function Nicholas Lewin-Koh’s n.comp.nb early days package. useful know whether nb object divided separate subgraphs, entities members subgraph.","code":"res <- spdep::n.comp.nb(col2) table(res$comp.id) ##  ##  1  2  3  ## 42  1  6"},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"graph-components-in-igraph","dir":"Articles","previous_headings":"Using igraph for spatial weights as graphs","what":"Graph components in igraph","title":"Spatial weights objects as sparse matrices and graphs","text":"result can obtained using clusters function igraph: holds row-standardised variant:","code":"c1 <- components(g1) c1$no == res$nc ## [1] TRUE all.equal(c1$membership, res$comp.id) ## [1] \"names for target but not for current\" all.equal(c1$csize, c(table(res$comp.id)), check.attributes=FALSE) ## [1] TRUE W <- as(spdep::nb2listw(col2, style=\"W\", zero.policy=TRUE), \"CsparseMatrix\") g1W <- graph_from_adjacency_matrix(W, mode=\"directed\", weighted=\"W\") c1W <- components(g1W) all.equal(c1W$membership, res$comp.id) ## [1] \"names for target but not for current\""},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"shortest-paths-in-weights-matrices-igraph","dir":"Articles","previous_headings":"Using igraph for spatial weights as graphs","what":"Shortest paths in weights matrices: igraph","title":"Spatial weights objects as sparse matrices and graphs","text":"Finding shortest paths spatial entities across given graph way express closeness. graph connected, possible traverse graph edges node , longest shortest path useful measure. igraph, .connected function tells us tells us graph connected, know figure . diameter measure diameter largest component subgraph. Note generates n x n matrix:","code":"is_connected(g1) ## [1] FALSE dg1 <- diameter(g1) dg1 ## [1] 7 sp_mat <- distances(g1) str(sp_mat) ##  num [1:49, 1:49] 0 1 1 2 2 3 4 3 3 4 ... ##  - attr(*, \"dimnames\")=List of 2 ##   ..$ : chr [1:49] \"1\" \"2\" \"3\" \"4\" ... ##   ..$ : chr [1:49] \"1\" \"2\" \"3\" \"4\" ..."},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"shortest-paths-in-weights-matrices-spdep","dir":"Articles","previous_headings":"Using igraph for spatial weights as graphs","what":"Shortest paths in weights matrices: spdep","title":"Spatial weights objects as sparse matrices and graphs","text":"spdep, using nblag maximum number lag orders - diameter, unknown advance (largest lag order number links greater zero), run problem represent missing neighbour information. insert zero weights matrix connection using zero.policy=TRUE, generate zero shortest path. create matrix matches one produced shortest.paths, need set non-structural zeros infinity (length path unconnected nodes), re-instate structural zeros diagonal:","code":"nbl10 <- spdep::nblag(col2, maxlag=10) ## Warning in spdep::nblag(col2, maxlag = 10): lag 1 neighbour object has 3 ## sub-graphs ## Warning in spdep::nblag(col2, maxlag = 10): lag 2 neighbour object has 4 ## sub-graphs ## Warning in spdep::nblag(col2, maxlag = 10): lag 3 neighbour object has 8 ## sub-graphs ## Warning in spdep::nblag(col2, maxlag = 10): lag 4 neighbour object has 8 ## sub-graphs ## Warning in spdep::nblag(col2, maxlag = 10): lag 5 neighbour object has 14 ## sub-graphs ## Warning in spdep::nblag(col2, maxlag = 10): lag 6 neighbour object has 29 ## sub-graphs ## Warning in spdep::nblag(col2, maxlag = 10): lag 7 neighbour object has 43 ## sub-graphs ## Warning in spdep::nblag(col2, maxlag = 10): lag 8 neighbour object has 49 ## sub-graphs ## Warning in spdep::nblag(col2, maxlag = 10): lag 9 neighbour object has 49 ## sub-graphs ## Warning in spdep::nblag(col2, maxlag = 10): lag 10 neighbour object has 49 ## sub-graphs vals <- sapply(nbl10, function(x) sum(spdep::card(x))) zero <- which(vals == 0) zero[1]-1 ## [1] 7 lmat <- lapply(nbl10[1:(zero[1]-1)], spdep::nb2mat, style=\"B\", zero.policy=TRUE) mat <- matrix(0, n, n) for (i in seq(along=lmat)) mat = mat + i*lmat[[i]] mat[mat==0] <- Inf diag(mat) <- 0 all.equal(mat, sp_mat, check.attributes=FALSE) ## [1] TRUE"},{"path":"https://r-spatial.github.io/spatialreg/articles/nb_igraph.html","id":"smirnovanselin-2009-cyclical-matrices","dir":"Articles","previous_headings":"Using igraph for spatial weights as graphs","what":"Smirnov/Anselin (2009) cyclical matrices","title":"Spatial weights objects as sparse matrices and graphs","text":"Another area graph representation might prove useful trying establish domain spatial coefficient spatial weights row-standardised. case construction know maximum eigenvalue 1. multiple blocks, graph components, numbers nodes per block greater 1, maximum eigenvalue 1. remaining problems numbers zero eigenvalues (least singleton graph components), whether non-singleton component fulfills condition termed Smirnov Anselin (2009) cyclical matrix, minimum eigenvalue -1. term cyclical appears used many different ways, clear use Smirnov Anselin (2009, pp. 2984-2985) indicates meaning used find relevant graph function. definition used block matrix (subgraph) cyclical : “every location, every pair neighbours connected.” , w[,j] w[,k] greater zero, w[j,k] must zero meet condition. internal function find_q1_q2 returns number non-singleton components, number meet condition. block/subgraph testing condition meets w[j,k] > 0, point breaks. Smirnov Anselin (2009) state rook neighbours regular grid meet condition: One block/graph component found, one meets cyclical matrix condition, also shown domain: apply spatial weights using , two non-singleton components, neither meeting cyclical matrix condition: construction, two-node connected graph components also meet condition, eigenvalues sum zero, maximum unity, minimum must -1.","code":"nb_r <- spdep::cell2nb(7, 7, type=\"rook\") nb_rW <- spdep::nb2listw(nb_r, style=\"W\") spdep:::find_q1_q2(nb_rW) ## [1] 1 1 1/range(Re(eigenw(similar.listw(nb_rW)))) ## [1] -1  1 spdep:::find_q1_q2(nb_W) ## [1] 2 0 1/range(Re(eigenw(similar.listw(nb_W)))) ## [1] -1.544645  1.000000"},{"path":"https://r-spatial.github.io/spatialreg/articles/sids_models.html","id":"introduction","dir":"Articles","previous_headings":"","what":"Introduction","title":"North Carolina SIDS data set (models)","text":"data set presented first Symons, Grimson, Yuan (1983), analysed reference spatial nature data Cressie Read (1985), expanded Cressie Chan (1989), used detail Cressie (1991). 100 counties North Carolina, includes counts numbers live births (also non-white live births) numbers sudden infant deaths, July 1, 1974 June 30, 1978 July 1, 1979 June 30, 1984 periods. Cressie Read (1985), listing county neighbours based shared boundaries (contiguity) given, Cressie Chan (1989), Cressie (1991, 386–89), different listing based criterion distance county seats, cutoff 30 miles. county seat location coordinates given miles local (unknown) coordinate reference system. data also used exemplify range functions spatial statistics module user’s manual (Kaluzny et al. 1996).","code":""},{"path":"https://r-spatial.github.io/spatialreg/articles/sids_models.html","id":"getting-the-data-into-r","dir":"Articles","previous_headings":"","what":"Getting the data into R","title":"North Carolina SIDS data set (models)","text":"using spdep spatialreg packages, version: spdep, version 1.3-7.1, 2024-10-13, sf package tmap package. data sources referred documented help page nc.sids data set spData. actual data, included shapefile county boundaries North Carolina made available maptools package 1. data known geographical coordinates (longitude-latitude decimal degrees) assumed use NAD27 datum. now examine data set reproduced Cressie collaborators, included spData (formerly spdep), add neighbour relationships used Cressie Chan (1989) background map graph shown Figure :","code":"library(spdep) nc <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) #st_crs(nc) <- \"+proj=longlat +datum=NAD27\" row.names(nc) <- as.character(nc$FIPSNO) nc$ft.SID74 <- sqrt(1000)*(sqrt(nc$SID74/nc$BIR74) + sqrt((nc$SID74+1)/nc$BIR74)) nc$both <- factor(paste(nc$L_id, nc$M_id, sep=\":\")) ## [1] TRUE gal_file <- system.file(\"weights/ncCC89.gal\", package=\"spData\")[1] ncCC89 <- read.gal(gal_file, region.id=nc$FIPSNO)"},{"path":"https://r-spatial.github.io/spatialreg/articles/sids_models.html","id":"car-model-fitting","dir":"Articles","previous_headings":"Getting the data into R","what":"CAR model fitting","title":"North Carolina SIDS data set (models)","text":"now try replicate three four models fitted (Cressie Chan 1989) transformed rates variable. first thing try replicate 30 mile distance county seats neighbours, almost works. try reconstruct three four models fit, concluding can get quite close, number questions raised along way. Building weights much complicated, use combination distance-metric population--risk based weights, can get quite close (see also Kaluzny et al. 1996): first model () null model just intercept, second (II) includes 12 parcels contiguous counties 4 east-west 4 north-south bands, fourth (IV) includes transformed non-white birth-rate: Cressie identifies Anson county outlier, drops analysis. weights constructed complicated way, subsetted dropping row column weights matrix: appears numerical issues (convergence particular) uncertainties exact spatial weights matrix used make difficult reproduce results Cressie Chan (1989), also given Cressie (1991). now try replicate null weighted CAR model (Cressie intercept 2.838, θ̂\\hat{\\theta} 0.833, k=1): spatial parcels model seems work, Cressie’s θ̂\\hat{\\theta} 0.710, failure numerical Hessian used calculate standard error spatial coefficient: Finally, non-white model repeats Cressie’s finding much variance transformed SIDS rate 1974–8 can accounted transformed non-white birth variable (Cressie intercept 1.644, b̂\\hat{b} 0.0346, θ̂\\hat{\\theta} 0.640 — significant), estimate spatial coefficient close :  final figure shows value log likelihood function null model ():","code":"sids.nhbr30.dist <- nbdists(ncCC89, cbind(nc$east, nc$north)) sids.nhbr <- listw2sn(nb2listw(ncCC89, glist=sids.nhbr30.dist, style=\"B\", zero.policy=TRUE)) dij <- sids.nhbr[,3] n <- nc$BIR74 el1 <- min(dij)/dij el2 <- sqrt(n[sids.nhbr$to]/n[sids.nhbr$from]) sids.nhbr$weights <- el1*el2 if (packageVersion(\"spdep\") >= \"1.3.1\") {   sids.nhbr.listw <- sn2listw(sids.nhbr, style=\"B\", zero.policy=TRUE) } else {   sids.nhbr.listw <- sn2listw(sids.nhbr) } nc$ft.NWBIR74 <- sqrt(1000)*(sqrt(nc$NWBIR74/nc$BIR74) + sqrt((nc$NWBIR74+1)/nc$BIR74)) lm_nc <- lm(ft.SID74 ~ 1, data=nc) outl <- which.max(rstandard(lm_nc)) as.character(nc$NAME[outl]) ## [1] \"Anson\" W <- listw2mat(sids.nhbr.listw) W.4 <- W[-outl, -outl] sids.nhbr.listw.4 <- mat2listw(W.4) nc2 <- nc[!(1:length(nc$CNTY_ID) %in% outl),] library(spatialreg) ecarIaw <- spautolm(ft.SID74 ~ 1, data=nc2, listw=sids.nhbr.listw.4, weights=BIR74, family=\"CAR\") summary(ecarIaw) ##  ## Call: spautolm(formula = ft.SID74 ~ 1, data = nc2, listw = sids.nhbr.listw.4,  ##     weights = BIR74, family = \"CAR\") ##  ## Residuals: ##       Min        1Q    Median        3Q       Max  ## -2.010292 -0.639658 -0.062209  0.443549  2.018065  ##  ## Coefficients:  ##             Estimate Std. Error z value  Pr(>|z|) ## (Intercept) 2.945323   0.095135  30.959 < 2.2e-16 ##  ## Lambda: 0.86814 LR test value: 22.83 p-value: 1.7701e-06  ## Numerical Hessian standard error of lambda: 0.04838  ##  ## Log likelihood: -118.8432  ## ML residual variance (sigma squared): 1266.5, (sigma: 35.588) ## Number of observations: 99  ## Number of parameters estimated: 3  ## AIC: NA (not available for weighted model) ecarIIaw <- spautolm(ft.SID74 ~ both - 1, data=nc2, listw=sids.nhbr.listw.4, weights=BIR74, family=\"CAR\") summary(ecarIIaw) ##  ## Call:  ## spautolm(formula = ft.SID74 ~ both - 1, data = nc2, listw = sids.nhbr.listw.4,  ##     weights = BIR74, family = \"CAR\") ##  ## Residuals: ##      Min       1Q   Median       3Q      Max  ## -2.55896 -0.46338 -0.02035  0.38935  2.05682  ##  ## Coefficients:  ##         Estimate Std. Error z value  Pr(>|z|) ## both1:2  2.06223    0.20016 10.3031 < 2.2e-16 ## both1:3  2.91823    0.14139 20.6400 < 2.2e-16 ## both1:4  4.11486    0.29939 13.7439 < 2.2e-16 ## both2:1  2.57650    0.26905  9.5762 < 2.2e-16 ## both2:2  2.17403    0.18222 11.9305 < 2.2e-16 ## both2:3  2.67397    0.15329 17.4443 < 2.2e-16 ## both2:4  3.11361    0.24699 12.6062 < 2.2e-16 ## both3:1  2.94400    0.29893  9.8486 < 2.2e-16 ## both3:2  2.65391    0.14098 18.8250 < 2.2e-16 ## both3:3  2.91619    0.17099 17.0552 < 2.2e-16 ## both3:4  3.20425    0.20349 15.7468 < 2.2e-16 ## both4:3  3.80286    0.20806 18.2781 < 2.2e-16 ##  ## Lambda: 0.2109 LR test value: 1.3088 p-value: 0.25261  ## Numerical Hessian standard error of lambda: NaN  ##  ## Log likelihood: -99.25505  ## ML residual variance (sigma squared): 891.48, (sigma: 29.858) ## Number of observations: 99  ## Number of parameters estimated: 14  ## AIC: NA (not available for weighted model) ecarIVaw <- spautolm(ft.SID74 ~ ft.NWBIR74, data=nc2, listw=sids.nhbr.listw.4, weights=BIR74, family=\"CAR\") summary(ecarIVaw) ##  ## Call:  ## spautolm(formula = ft.SID74 ~ ft.NWBIR74, data = nc2, listw = sids.nhbr.listw.4,  ##     weights = BIR74, family = \"CAR\") ##  ## Residuals: ##      Min       1Q   Median       3Q      Max  ## -1.99056 -0.44858  0.15468  0.60623  1.95541  ##  ## Coefficients:  ##              Estimate Std. Error z value  Pr(>|z|) ## (Intercept) 1.4371519  0.2252729  6.3796 1.775e-10 ## ft.NWBIR74  0.0408354  0.0062919  6.4902 8.572e-11 ##  ## Lambda: 0.22391 LR test value: 1.1577 p-value: 0.28194  ## Numerical Hessian standard error of lambda: 0.5537  ##  ## Log likelihood: -114.0376  ## ML residual variance (sigma squared): 1201.5, (sigma: 34.663) ## Number of observations: 99  ## Number of parameters estimated: 4  ## AIC: NA (not available for weighted model) nc2$fitIV <- fitted.values(ecarIVaw) if (tmap4) {   tm_shape(nc2) + tm_polygons(fill=\"fitIV\", fill.scale=tm_scale(values=\"brewer.yl_or_br\"), fill.legend=tm_legend(position=tm_pos_in(\"left\", \"bottom\"), frame=FALSE, item.r = 0), lwd=0.01) } else { tm_shape(nc2) + tm_fill(\"fitIV\") } ecarIawll <- spautolm(ft.SID74 ~ 1, data=nc2, listw=sids.nhbr.listw.4, weights=BIR74, family=\"CAR\", llprof=seq(-0.1, 0.9020532358, length.out=100)) plot(ll ~ lambda, ecarIawll$llprof, type=\"l\")"},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Roger Bivand. Maintainer, author. Gianfranco Piras. Author. Luc Anselin. Contributor. Andrew Bernat. Contributor. Eric Blankmeyer. Contributor. Yongwan Chun. Contributor. Virgilio Gómez-Rubio. Contributor. Daniel Griffith. Contributor. Martin Gubri. Contributor. Rein Halbersma. Contributor. James LeSage. Contributor. Angela Li. Contributor. Hongfei Li. Contributor. Jielai Ma. Contributor. Abhirup Mallik. Contributor, translator. Giovanni Millo. Contributor. Kelley Pace. Contributor. Josiah Parry. Contributor. Pedro Peres-Neto. Contributor. Tobias Rüttenauer. Contributor. Mauricio Sarrias. Contributor. JuanTomas Sayago. Contributor. Michael Tiefelsdorf. Contributor.","code":""},{"path":"https://r-spatial.github.io/spatialreg/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Bivand R, Millo G, Piras G (2021). “Review Software Spatial Econometrics R.” Mathematics, 9(11). doi:10.3390/math9111276, https://www.mdpi.com/2227-7390/9/11/1276. Bivand R, Piras G (2015). “Comparing Implementations Estimation Methods Spatial Econometrics.” Journal Statistical Software, 63(18), 1–36. doi:10.18637/jss.v063.i18. Bivand R, Hauke J, Kossowski T (2013). “Computing Jacobian Gaussian spatial autoregressive models: illustrated comparison available methods.” Geographical Analysis, 45(2), 150–179. doi:10.1111/gean.12008. Bivand R, Pebesma E, Gómez-Rubio V (2013). Applied spatial data analysis R, Second edition. Springer, NY. https://asdar-book.org/. Pebesma E, Bivand R (2023). Spatial Data Science Applications R. Chapman & Hall. https://r-spatial.org/book/.","code":"@Article{,   title = {A Review of Software for Spatial Econometrics in {R}},   author = {Roger Bivand and Giovanni Millo and Gianfranco Piras},   journal = {Mathematics},   year = {2021},   volume = {9},   number = {11},   url = {https://www.mdpi.com/2227-7390/9/11/1276},   doi = {10.3390/math9111276}, } @Article{,   title = {Comparing Implementations of Estimation Methods for Spatial Econometrics},   author = {Roger Bivand and Gianfranco Piras},   journal = {Journal of Statistical Software},   year = {2015},   volume = {63},   number = {18},   pages = {1--36},   doi = {10.18637/jss.v063.i18}, } @Article{,   title = {Computing the Jacobian in Gaussian spatial autoregressive models: An illustrated comparison of available methods},   author = {Roger Bivand and Jan Hauke and Tomasz Kossowski},   journal = {Geographical Analysis},   year = {2013},   volume = {45},   number = {2},   pages = {150--179},   doi = {10.1111/gean.12008}, } @Book{,   author = {Roger S. Bivand and Edzer Pebesma and Virgilio Gómez-Rubio},   title = {Applied spatial data analysis with {R}, Second edition},   year = {2013},   publisher = {Springer, NY},   url = {https://asdar-book.org/}, } @Book{,   author = {Edzer Pebesma and Roger S. Bivand},   title = {Spatial Data Science With Applications in {R}},   year = {2023},   publisher = {Chapman & Hall},   url = {https://r-spatial.org/book/}, }"},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/index.html","id":"spatialreg-spatial-models-estimation-and-testing","dir":"","previous_headings":"","what":"spatialreg: spatial models estimation and testing","title":"Spatial Regression Analysis","text":"collection estimation functions spatial cross-sectional models (lattice/areal data using spatial weights matrices) contained now spdep. model fitting functions include maximum likelihood methods cross-sectional models proposed Cliff Ord (1973, ISBN: 0850860369) (1981, ISBN: 0850860814), fitting methods initially described Ord (1975) https://doi.org/10.1080/01621459.1975.10480272. models described Anselin (1988) https://doi.org/10.1007/978-94-015-7799-1. Spatial two stage least squares spatial general method moment models initially proposed Kelejian Prucha (1998) https://doi.org/10.1023/:1007707430416 (1999) https://doi.org/10.1111/1468-2354.00027 provided. Impact methods MCMC fitting methods proposed LeSage Pace (2009) https://doi.org/10.1201/9781420064254 implemented family cross-sectional spatial regression models. Methods fitting log determinant term maximum likelihood MCMC fitting compared Bivand et al. (2013) https://doi.org/10.1111/gean.12008, model fitting methods Bivand Piras (2015) https://doi.org/10.18637/jss.v063.i18; articles include extensive lists references. recent review provided Bivand, Millo Piras (2021) https://doi.org/10.3390/math9111276. spatialreg >= 1.1-1 corresponds spdep = 1.1-1, model fitting functions deprecated pass spatialreg, mask spatialreg. versions 1.2-1, functions made defunct spdep. version 1.3-6, add Anselin-Kelejian (1997) test stsls residual spatial autocorrelation https://doi.org/10.1177/016001769702000109. Default branch now main.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/GMerrorsar.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial simultaneous autoregressive error model estimation by GMM — GMerrorsar","title":"Spatial simultaneous autoregressive error model estimation by GMM — GMerrorsar","text":"implementation Kelejian Prucha's generalised moments estimator autoregressive parameter spatial model.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/GMerrorsar.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial simultaneous autoregressive error model estimation by GMM — GMerrorsar","text":"","code":"GMerrorsar(formula, data = list(), listw, na.action = na.fail,  zero.policy = attr(listw, \"zero.policy\"), method=\"nlminb\", arnoldWied=FALSE,   control = list(), pars, scaleU=FALSE, verbose=NULL, legacy=FALSE,  se.lambda=TRUE, returnHcov=FALSE, pWOrder=250, tol.Hcov=1.0e-10) # S3 method for class 'Gmsar' summary(object, correlation = FALSE, Hausman=FALSE, ...) GMargminImage(obj, lambdaseq, s2seq)"},{"path":"https://r-spatial.github.io/spatialreg/reference/GMerrorsar.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial simultaneous autoregressive error model estimation by GMM — GMerrorsar","text":"formula symbolic description model fit. details model specification given lm() data optional data frame containing variables model. default variables taken environment function called. listw listw object created example nb2listw na.action function (default na.fail), can also na.omit na.exclude consequences residuals fitted values - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE (default) assign NA - causing GMerrorsar() terminate error method default \"nlminb\", optionally method passed optim use alternative optimizer arnoldWied default FALSE control list control parameters. See details optim nlminb. pars starting values \\(\\lambda\\) \\(\\sigma^2\\) GMM optimisation, missing (default), approximated initial OLS model autocorrelation coefficient corrected weights style model sigma squared scaleU Default FALSE: scale OLS residuals computing moment matrices; used pars argument missing verbose default NULL, use global option value; TRUE, reports function values optimization. legacy default FALSE - compute using unfiltered values response right hand side variables; TRUE - compute fitted value residuals spatially filtered model using spatial error parameter se.lambda default TRUE, use analytical method described http://econweb.umd.edu/~prucha/STATPROG/OLS/desols.pdf returnHcov default FALSE, return Vo matrix spatial Hausman test tol.Hcov tolerance computing Vo matrix (default=1.0e-10) pWOrder default 250, returnHcov=TRUE, pass order powerWeights power series maximum limit object, obj Gmsar object GMerrorsar correlation logical; (default=FALSE), TRUE available Hausman TRUE, results Hausman test error models reported ... summary arguments passed lambdaseq given, increasing sequence lambda values gridding s2seq given, increasing sequence sigma squared values gridding","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/GMerrorsar.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial simultaneous autoregressive error model estimation by GMM — GMerrorsar","text":"control list set care, function converge values close ML estimator without requiring computation Jacobian, resource-intensive part ML estimation. Note fitted() function output object assumes response variable may reconstructed sum trend, signal, noise (residuals). Since values response variable known, spatial lags used calculate signal components (Cressie 1993, p. 564). differs software, including GeoDa, use knowledge response variable making predictions fitting data. GMargminImage may used visualize shape surface argmin function used find lambda.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/GMerrorsar.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial simultaneous autoregressive error model estimation by GMM — GMerrorsar","text":"list object class Gmsar type \"ERROR\" lambda simultaneous autoregressive error coefficient coefficients GMM coefficient estimates rest.se GMM coefficient standard errors s2 GMM residual variance SSE sum squared GMM errors parameters number parameters estimated lm.model lm object returned estimating \\(\\lambda=0\\) call call used create object residuals GMM residuals lm.target lm object returned GMM fit fitted.values Difference residuals response variable formula model formula aliased NULL, details aliased variables zero.policy zero.policy model vv list internal bigG litg components testing optimisation surface optres object returned optimizer pars start parameter values optimisation Hcov Spatial DGP covariance matrix Hausman test available legacy input choice unfiltered filtered values lambda.se value computed input argument TRUE arnoldWied Arnold-Wied moments used GMs2 GM argmin sigma squared scaleU input choice scaled OLS residuals vcov variance-covariance matrix regression coefficients na.action (possibly) named vector excluded omitted observations non-default na.action argument used","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/GMerrorsar.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial simultaneous autoregressive error model estimation by GMM — GMerrorsar","text":"Kelejian, H. H., Prucha, . R., 1999. Generalized Moments Estimator Autoregressive Parameter Spatial Model. International Economic Review, 40, pp. 509–533; Cressie, N. . C. 1993 Statistics spatial data, Wiley, New York. Roger Bivand, Gianfranco Piras (2015). Comparing Implementations Estimation Methods Spatial Econometrics. Journal Statistical Software, 63(18), 1-36. doi:10.18637/jss.v063.i18 .","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/GMerrorsar.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial simultaneous autoregressive error model estimation by GMM — GMerrorsar","text":"Luc Anselin Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/GMerrorsar.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial simultaneous autoregressive error model estimation by GMM — GMerrorsar","text":"","code":"#require(\"spdep\", quietly=TRUE) data(oldcol, package=\"spdep\") COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  spdep::nb2listw(COL.nb, style=\"W\"), method=\"eigen\") (x <- summary(COL.errW.eig, Hausman=TRUE)) #>  #> Call: #> errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,  #>     style = \"W\"), method = \"eigen\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -34.81174  -6.44031  -0.72142   7.61476  23.33626  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 59.893219   5.366163 11.1613 < 2.2e-16 #> INC         -0.941312   0.330569 -2.8476 0.0044057 #> HOVAL       -0.302250   0.090476 -3.3407 0.0008358 #>  #> Lambda: 0.56179, LR test value: 7.9935, p-value: 0.0046945 #> Asymptotic standard error: 0.13387 #>     z-value: 4.1966, p-value: 2.7098e-05 #> Wald statistic: 17.611, p-value: 2.7098e-05 #>  #> Log likelihood: -183.3805 for error model #> ML residual variance (sigma squared): 95.575, (sigma: 9.7762) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 376.76, (AIC for lm: 382.75) #> Hausman test: 4.902, df: 3, p-value: 0.17911 #>  coef(x) #>               Estimate Std. Error   z value     Pr(>|z|) #> (Intercept) 59.8932190 5.36616256 11.161276 0.0000000000 #> INC         -0.9413120 0.33056857 -2.847554 0.0044056574 #> HOVAL       -0.3022502 0.09047605 -3.340665 0.0008357787 COL.errW.GM <- GMerrorsar(CRIME ~ INC + HOVAL, data=COL.OLD,  spdep::nb2listw(COL.nb, style=\"W\"), returnHcov=TRUE) (x <- summary(COL.errW.GM, Hausman=TRUE)) #>  #> Call: #> GMerrorsar(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,  #>     style = \"W\"), returnHcov = TRUE) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -30.5432  -6.5553  -2.1921  10.0553  28.7497  #>  #> Type: GM SAR estimator #> Coefficients: (GM standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 62.513752   5.121339  12.207 < 2.2e-16 #> INC         -1.128283   0.339745  -3.321  0.000897 #> HOVAL       -0.296957   0.095699  -3.103  0.001915 #>  #> Lambda: 0.40196 (standard error): 0.42334 (z-value): 0.94948 #> Residual variance (sigma squared): 106.64, (sigma: 10.327) #> GM argmin sigma squared: 106.36 #> Number of observations: 49  #> Number of parameters estimated: 5  #> Hausman test: 6.6406, df: 3, p-value: 0.08428 #>  coef(x) #>               Estimate Std. Error   z value     Pr(>|z|) #> (Intercept) 62.5137525 5.12133863 12.206526 0.0000000000 #> INC         -1.1282834 0.33974492 -3.320972 0.0008970455 #> HOVAL       -0.2969573 0.09569889 -3.103038 0.0019154486 aa <- GMargminImage(COL.errW.GM) levs <- quantile(aa$z, seq(0, 1, 1/12)) image(aa, breaks=levs, xlab=\"lambda\", ylab=\"s2\") points(COL.errW.GM$lambda, COL.errW.GM$s2, pch=3, lwd=2) contour(aa, levels=signif(levs, 4), add=TRUE)  COL.errW.GM1 <- GMerrorsar(CRIME ~ INC + HOVAL, data=COL.OLD,  spdep::nb2listw(COL.nb, style=\"W\")) summary(COL.errW.GM1) #>  #> Call: #> GMerrorsar(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,  #>     style = \"W\")) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -30.5432  -6.5553  -2.1921  10.0553  28.7497  #>  #> Type: GM SAR estimator #> Coefficients: (GM standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 62.513752   5.121339  12.207 < 2.2e-16 #> INC         -1.128283   0.339745  -3.321  0.000897 #> HOVAL       -0.296957   0.095699  -3.103  0.001915 #>  #> Lambda: 0.40196 (standard error): 0.42334 (z-value): 0.94948 #> Residual variance (sigma squared): 106.64, (sigma: 10.327) #> GM argmin sigma squared: 106.36 #> Number of observations: 49  #> Number of parameters estimated: 5  #>  require(\"sf\", quietly=TRUE) nydata <- st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\")[1], quiet=TRUE) suppressMessages(nyadjmat <- as.matrix(foreign::read.dbf(system.file(  \"misc/nyadjwts.dbf\", package=\"spData\")[1])[-1])) suppressMessages(ID <- as.character(names(foreign::read.dbf(system.file(  \"misc/nyadjwts.dbf\", package=\"spData\")[1]))[-1])) identical(substring(ID, 2, 10), substring(as.character(nydata$AREAKEY), 2, 10)) #> [1] TRUE listw_NY <- spdep::mat2listw(nyadjmat, as.character(nydata$AREAKEY), style=\"B\") esar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, family=\"SAR\", method=\"eigen\") summary(esar1f) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, family = \"SAR\", method = \"eigen\") #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.56754 -0.38239 -0.02643  0.33109  4.01219  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.618193   0.176784 -3.4969 0.0004707 #> PEXPOSURE    0.071014   0.042051  1.6888 0.0912635 #> PCTAGE65P    3.754200   0.624722  6.0094 1.862e-09 #> PCTOWNHOME  -0.419890   0.191329 -2.1946 0.0281930 #>  #> Lambda: 0.040487 LR test value: 5.2438 p-value: 0.022026  #> Numerical Hessian standard error of lambda: 0.017201  #>  #> Log likelihood: -276.1069  #> ML residual variance (sigma squared): 0.41388, (sigma: 0.64333) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 564.21 #>  esar1gm <- GMerrorsar(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  data=nydata, listw=listw_NY) summary(esar1gm) #>  #> Call:GMerrorsar(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  #>     data = nydata, listw = listw_NY) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -1.641411 -0.396370 -0.026618  0.341740  4.204264  #>  #> Type: GM SAR estimator #> Coefficients: (GM standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.604364   0.174576 -3.4619 0.0005364 #> PEXPOSURE    0.067902   0.041164  1.6496 0.0990337 #> PCTAGE65P    3.775308   0.622965  6.0602 1.359e-09 #> PCTOWNHOME  -0.437545   0.188906 -2.3162 0.0205468 #>  #> Lambda: 0.03605 (standard error): 0.2022 (z-value): 0.17829 #> Residual variance (sigma squared): 0.41585, (sigma: 0.64487) #> GM argmin sigma squared: 0.45141 #> Number of observations: 281  #> Number of parameters estimated: 6  #>  esar1gm1 <- GMerrorsar(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  data=nydata, listw=listw_NY, method=\"Nelder-Mead\") summary(esar1gm1) #>  #> Call:GMerrorsar(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  #>     data = nydata, listw = listw_NY, method = \"Nelder-Mead\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -1.641390 -0.396374 -0.026616  0.341745  4.204277  #>  #> Type: GM SAR estimator #> Coefficients: (GM standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.604384   0.174580 -3.4619 0.0005363 #> PEXPOSURE    0.067907   0.041165  1.6496 0.0990225 #> PCTAGE65P    3.775275   0.622969  6.0601  1.36e-09 #> PCTOWNHOME  -0.437518   0.188910 -2.3160 0.0205572 #>  #> Lambda: 0.036057 (standard error): 0.20221 (z-value): 0.17832 #> Residual variance (sigma squared): 0.41585, (sigma: 0.64487) #> GM argmin sigma squared: 0.45139 #> Number of observations: 281  #> Number of parameters estimated: 6  #>"},{"path":"https://r-spatial.github.io/spatialreg/reference/MCMCsamp.html","id":null,"dir":"Reference","previous_headings":"","what":"MCMC sample from fitted spatial regression — MCMCsamp","title":"MCMC sample from fitted spatial regression — MCMCsamp","text":"MCMCsamp method uses rwmetrop, random walk Metropolis algorithm, LearnBayes make MCMC samples fitted maximum likelihood spatial regression models.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/MCMCsamp.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"MCMC sample from fitted spatial regression — MCMCsamp","text":"","code":"MCMCsamp(object, mcmc = 1L, verbose = NULL, ...) # S3 method for class 'Spautolm' MCMCsamp(object, mcmc = 1L, verbose = NULL, ...,  burnin = 0L, scale=1, listw, control = list()) # S3 method for class 'Sarlm' MCMCsamp(object, mcmc = 1L, verbose = NULL, ...,     burnin=0L, scale=1, listw, listw2=NULL, control=list())"},{"path":"https://r-spatial.github.io/spatialreg/reference/MCMCsamp.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"MCMC sample from fitted spatial regression — MCMCsamp","text":"object spatial regression model object fitted maximum likelihood spautolm mcmc number MCMC iterations burnin verbose default NULL, use global option value; TRUE, reports progress ... Arguments passed burnin number burn-iterations sampler scale positive scale parameter listw, listw2 listw objects created example nb2listw; object(s) used fitting model control list extra control arguments - see spautolm","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/MCMCsamp.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"MCMC sample from fitted spatial regression — MCMCsamp","text":"object class “mcmc” suited coda, attributes: “accept” acceptance rate; “type” input ML fitted model type “SAR”, “CAR”, “SMA”, “lag”, “mixed”, “error”, “sac”, “sacmixed”; “timings” run times","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/MCMCsamp.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"MCMC sample from fitted spatial regression — MCMCsamp","text":"acceptance rate 0.05, warning issued; consider increasing mcmc.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/MCMCsamp.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"MCMC sample from fitted spatial regression — MCMCsamp","text":"Jim Albert (2007) Bayesian Computation R, Springer, New York, pp. 104-105.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/MCMCsamp.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"MCMC sample from fitted spatial regression — MCMCsamp","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/MCMCsamp.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"MCMC sample from fitted spatial regression — MCMCsamp","text":"","code":"require(\"sf\", quietly=TRUE) nydata <- st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\")[1], quiet=TRUE) suppressMessages(nyadjmat <- as.matrix(foreign::read.dbf(system.file(  \"misc/nyadjwts.dbf\", package=\"spData\")[1])[-1])) suppressMessages(ID <- as.character(names(foreign::read.dbf(system.file(  \"misc/nyadjwts.dbf\", package=\"spData\")[1]))[-1])) identical(substring(ID, 2, 10), substring(as.character(nydata$AREAKEY), 2, 10)) #> [1] TRUE #require(\"spdep\", quietly=TRUE) listw_NY <- spdep::mat2listw(nyadjmat, as.character(nydata$AREAKEY), style=\"B\") esar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, family=\"SAR\", method=\"eigen\") summary(esar1f) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, family = \"SAR\", method = \"eigen\") #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.56754 -0.38239 -0.02643  0.33109  4.01219  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.618193   0.176784 -3.4969 0.0004707 #> PEXPOSURE    0.071014   0.042051  1.6888 0.0912635 #> PCTAGE65P    3.754200   0.624722  6.0094 1.862e-09 #> PCTOWNHOME  -0.419890   0.191329 -2.1946 0.0281930 #>  #> Lambda: 0.040487 LR test value: 5.2438 p-value: 0.022026  #> Numerical Hessian standard error of lambda: 0.017201  #>  #> Log likelihood: -276.1069  #> ML residual variance (sigma squared): 0.41388, (sigma: 0.64333) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 564.21 #>  res <- MCMCsamp(esar1f, mcmc=1000, burnin=200, listw=listw_NY) summary(res) #>  #> Iterations = 1:1000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 1000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean      SD  Naive SE Time-series SE #> lambda       0.04611 0.01498 0.0004736       0.001756 #> (Intercept) -0.65331 0.19263 0.0060916       0.026540 #> PEXPOSURE    0.08968 0.04897 0.0015486       0.006607 #> PCTAGE65P    3.69656 0.52425 0.0165784       0.057839 #> PCTOWNHOME  -0.39485 0.23949 0.0075732       0.037397 #>  #> 2. Quantiles for each variable: #>  #>                  2.5%      25%      50%      75%    97.5% #> lambda       0.015004  0.03557  0.04640  0.05531  0.07351 #> (Intercept) -1.089847 -0.77125 -0.63878 -0.51969 -0.34027 #> PEXPOSURE   -0.001914  0.05288  0.09113  0.12367  0.18519 #> PCTAGE65P    2.672002  3.33982  3.67753  4.04290  4.74392 #> PCTOWNHOME  -0.845780 -0.56384 -0.41154 -0.21860  0.07637 #>  # \\dontrun{ esar1fw <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, weights=POP8, family=\"SAR\", method=\"eigen\") summary(esar1fw) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, weights = POP8, family = \"SAR\", method = \"eigen\") #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.48488 -0.26823  0.09489  0.46552  4.28343  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.797063   0.144054 -5.5331 3.146e-08 #> PEXPOSURE    0.080545   0.028334  2.8428  0.004473 #> PCTAGE65P    3.816731   0.576037  6.6258 3.453e-11 #> PCTOWNHOME  -0.380778   0.156507 -2.4330  0.014975 #>  #> Lambda: 0.0095636 LR test value: 0.32665 p-value: 0.56764  #> Numerical Hessian standard error of lambda: 0.016522  #>  #> Log likelihood: -251.6017  #> ML residual variance (sigma squared): 1104.1, (sigma: 33.229) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: NA (not available for weighted model) #>  res <- MCMCsamp(esar1fw, mcmc=5000, burnin=500, listw=listw_NY) summary(res) #>  #> Iterations = 1:5000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 5000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean      SD  Naive SE Time-series SE #> lambda       0.01296 0.01568 0.0002218      0.0008193 #> (Intercept) -0.79417 0.15064 0.0021303      0.0085373 #> PEXPOSURE    0.07886 0.02974 0.0004206      0.0016661 #> PCTAGE65P    3.79201 0.58160 0.0082250      0.0316924 #> PCTOWNHOME  -0.38114 0.16875 0.0023864      0.0100745 #>  #> 2. Quantiles for each variable: #>  #>                 2.5%      25%      50%      75%    97.5% #> lambda      -0.01785  0.00281  0.01326  0.02352  0.04254 #> (Intercept) -1.09757 -0.89163 -0.79274 -0.69957 -0.47937 #> PEXPOSURE    0.02125  0.05871  0.07958  0.09926  0.13413 #> PCTAGE65P    2.68865  3.36618  3.80173  4.17535  4.89445 #> PCTOWNHOME  -0.70327 -0.49343 -0.37753 -0.27046 -0.03549 #>  ecar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, family=\"CAR\", method=\"eigen\") summary(ecar1f) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, family = \"CAR\", method = \"eigen\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -1.539732 -0.384311 -0.030646  0.335126  3.808848  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.648362   0.181129 -3.5796 0.0003442 #> PEXPOSURE    0.077899   0.043692  1.7829 0.0745986 #> PCTAGE65P    3.703830   0.627185  5.9055 3.516e-09 #> PCTOWNHOME  -0.382789   0.195564 -1.9574 0.0503053 #>  #> Lambda: 0.084123 LR test value: 5.8009 p-value: 0.016018  #> Numerical Hessian standard error of lambda: 0.030872  #>  #> Log likelihood: -275.8283  #> ML residual variance (sigma squared): 0.40758, (sigma: 0.63842) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 563.66 #>  res <- MCMCsamp(ecar1f, mcmc=5000, burnin=500, listw=listw_NY) summary(res) #>  #> Iterations = 1:5000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 5000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean      SD  Naive SE Time-series SE #> lambda       0.08485 0.03007 0.0004252       0.001841 #> (Intercept) -0.66321 0.21541 0.0030463       0.014591 #> PEXPOSURE    0.08242 0.04990 0.0007057       0.003038 #> PCTAGE65P    3.65269 0.64308 0.0090945       0.039341 #> PCTOWNHOME  -0.35759 0.22515 0.0031840       0.014851 #>  #> 2. Quantiles for each variable: #>  #>                  2.5%      25%      50%     75%   97.5% #> lambda       0.021075  0.06565  0.08492  0.1070  0.1398 #> (Intercept) -1.173329 -0.78618 -0.63961 -0.5233 -0.2863 #> PEXPOSURE   -0.008489  0.04927  0.07836  0.1125  0.1967 #> PCTAGE65P    2.400330  3.17755  3.65477  4.0908  4.9428 #> PCTOWNHOME  -0.761115 -0.51656 -0.37324 -0.2168  0.1507 #>  esar1fw <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, weights=POP8, family=\"SAR\", method=\"eigen\") summary(esar1fw) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, weights = POP8, family = \"SAR\", method = \"eigen\") #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.48488 -0.26823  0.09489  0.46552  4.28343  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.797063   0.144054 -5.5331 3.146e-08 #> PEXPOSURE    0.080545   0.028334  2.8428  0.004473 #> PCTAGE65P    3.816731   0.576037  6.6258 3.453e-11 #> PCTOWNHOME  -0.380778   0.156507 -2.4330  0.014975 #>  #> Lambda: 0.0095636 LR test value: 0.32665 p-value: 0.56764  #> Numerical Hessian standard error of lambda: 0.016522  #>  #> Log likelihood: -251.6017  #> ML residual variance (sigma squared): 1104.1, (sigma: 33.229) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: NA (not available for weighted model) #>  res <- MCMCsamp(esar1fw, mcmc=5000, burnin=500, listw=listw_NY) summary(res) #>  #> Iterations = 1:5000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 5000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean      SD Naive SE Time-series SE #> lambda       0.01421 0.01648 0.000233      0.0009767 #> (Intercept) -0.79603 0.15920 0.002251      0.0097286 #> PEXPOSURE    0.08092 0.03097 0.000438      0.0018774 #> PCTAGE65P    3.77070 0.60576 0.008567      0.0381835 #> PCTOWNHOME  -0.37884 0.17038 0.002410      0.0102914 #>  #> 2. Quantiles for each variable: #>  #>                 2.5%       25%      50%      75%    97.5% #> lambda      -0.01732  0.002764  0.01370  0.02629  0.04646 #> (Intercept) -1.12961 -0.899430 -0.80307 -0.69685 -0.48183 #> PEXPOSURE    0.02262  0.059634  0.08016  0.10062  0.14212 #> PCTAGE65P    2.58384  3.361796  3.81098  4.18747  4.90361 #> PCTOWNHOME  -0.69813 -0.495245 -0.38500 -0.26182 -0.03602 #>  ecar1fw <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, weights=POP8, family=\"CAR\", method=\"eigen\") summary(ecar1fw) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, weights = POP8, family = \"CAR\", method = \"eigen\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -1.491042 -0.270906  0.081435  0.451556  4.198134  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.790154   0.144862 -5.4545 4.910e-08 #> PEXPOSURE    0.081922   0.028593  2.8651  0.004169 #> PCTAGE65P    3.825858   0.577720  6.6223 3.536e-11 #> PCTOWNHOME  -0.386820   0.157436 -2.4570  0.014010 #>  #> Lambda: 0.022419 LR test value: 0.38785 p-value: 0.53343  #> Numerical Hessian standard error of lambda: 0.038977  #>  #> Log likelihood: -251.5711  #> ML residual variance (sigma squared): 1102.9, (sigma: 33.21) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: NA (not available for weighted model) #>  res <- MCMCsamp(ecar1fw, mcmc=5000, burnin=500, listw=listw_NY) summary(res) #>  #> Iterations = 1:5000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 5000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean      SD  Naive SE Time-series SE #> lambda       0.03646 0.04020 0.0005686       0.002593 #> (Intercept) -0.83219 0.15755 0.0022281       0.009562 #> PEXPOSURE    0.09116 0.03438 0.0004863       0.002139 #> PCTAGE65P    3.74091 0.59000 0.0083439       0.035836 #> PCTOWNHOME  -0.34906 0.17055 0.0024119       0.010630 #>  #> 2. Quantiles for each variable: #>  #>                 2.5%       25%      50%      75%     97.5% #> lambda      -0.04545  0.009909  0.04055  0.06473  0.108790 #> (Intercept) -1.15043 -0.936965 -0.82876 -0.72797 -0.532623 #> PEXPOSURE    0.02618  0.068120  0.08997  0.11245  0.165457 #> PCTAGE65P    2.56456  3.350294  3.72433  4.13057  4.958447 #> PCTOWNHOME  -0.69327 -0.461490 -0.34685 -0.24507 -0.001185 #>  # } esar0 <- errorsarlm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY) summary(esar0) #>  #> Call:errorsarlm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  #>     data = nydata, listw = listw_NY) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.56754 -0.38239 -0.02643  0.33109  4.01219  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.618193   0.176784 -3.4969 0.0004707 #> PEXPOSURE    0.071014   0.042051  1.6888 0.0912635 #> PCTAGE65P    3.754200   0.624722  6.0094 1.862e-09 #> PCTOWNHOME  -0.419890   0.191329 -2.1946 0.0281930 #>  #> Lambda: 0.040487, LR test value: 5.2438, p-value: 0.022026 #> Asymptotic standard error: 0.016214 #>     z-value: 2.4971, p-value: 0.01252 #> Wald statistic: 6.2356, p-value: 0.01252 #>  #> Log likelihood: -276.1069 for error model #> ML residual variance (sigma squared): 0.41388, (sigma: 0.64333) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 564.21, (AIC for lm: 567.46) #>  res <- MCMCsamp(esar0, mcmc=1000, burnin=200, listw=listw_NY) summary(res) #>  #> Iterations = 1:1000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 1000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean      SD  Naive SE Time-series SE #> lambda       0.04682 0.01895 0.0005993       0.002739 #> (Intercept) -0.65775 0.21896 0.0069243       0.031633 #> PEXPOSURE    0.08543 0.05260 0.0016634       0.007626 #> PCTAGE65P    3.65044 0.57371 0.0181422       0.060983 #> PCTOWNHOME  -0.36116 0.23745 0.0075089       0.036472 #>  #> 2. Quantiles for each variable: #>  #>                   2.5%      25%      50%      75%    97.5% #> lambda       0.0109828  0.03340  0.04839  0.05958  0.08139 #> (Intercept) -1.0771095 -0.81427 -0.62781 -0.51408 -0.23029 #> PEXPOSURE   -0.0004135  0.04738  0.07927  0.11564  0.20607 #> PCTAGE65P    2.5911599  3.20769  3.63005  4.09097  4.74100 #> PCTOWNHOME  -0.8037868 -0.54136 -0.35322 -0.20277  0.17058 #>  # \\dontrun{ esar0w <- errorsarlm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, weights=POP8) summary(esar0) #>  #> Call:errorsarlm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  #>     data = nydata, listw = listw_NY) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.56754 -0.38239 -0.02643  0.33109  4.01219  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.618193   0.176784 -3.4969 0.0004707 #> PEXPOSURE    0.071014   0.042051  1.6888 0.0912635 #> PCTAGE65P    3.754200   0.624722  6.0094 1.862e-09 #> PCTOWNHOME  -0.419890   0.191329 -2.1946 0.0281930 #>  #> Lambda: 0.040487, LR test value: 5.2438, p-value: 0.022026 #> Asymptotic standard error: 0.016214 #>     z-value: 2.4971, p-value: 0.01252 #> Wald statistic: 6.2356, p-value: 0.01252 #>  #> Log likelihood: -276.1069 for error model #> ML residual variance (sigma squared): 0.41388, (sigma: 0.64333) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 564.21, (AIC for lm: 567.46) #>  res <- MCMCsamp(esar0w, mcmc=5000, burnin=500, listw=listw_NY) summary(res) #>  #> Iterations = 1:5000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 5000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean      SD  Naive SE Time-series SE #> lambda       0.01177 0.01571 0.0002221      0.0008781 #> (Intercept) -0.79575 0.14274 0.0020186      0.0078442 #> PEXPOSURE    0.08036 0.02929 0.0004143      0.0017545 #> PCTAGE65P    3.81500 0.57129 0.0080793      0.0330363 #> PCTOWNHOME  -0.38426 0.15508 0.0021932      0.0087813 #>  #> 2. Quantiles for each variable: #>  #>                 2.5%      25%      50%      75%    97.5% #> lambda      -0.01899  0.00175  0.01220  0.02213  0.04328 #> (Intercept) -1.07330 -0.89063 -0.79366 -0.70020 -0.51399 #> PEXPOSURE    0.02200  0.06082  0.08123  0.10067  0.13675 #> PCTAGE65P    2.70738  3.41885  3.80976  4.20150  4.94589 #> PCTOWNHOME  -0.70906 -0.47931 -0.38839 -0.28703 -0.06345 #>  esar1 <- errorsarlm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, etype=\"emixed\") summary(esar1) #>  #> Call:errorsarlm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  #>     data = nydata, listw = listw_NY, etype = \"emixed\") #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.81562 -0.37641 -0.02224  0.33638  4.00054  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>                  Estimate Std. Error z value  Pr(>|z|) #> (Intercept)     -1.118019   0.247425 -4.5186 6.225e-06 #> PEXPOSURE        0.218279   0.079245  2.7545  0.005879 #> PCTAGE65P        3.416477   0.645587  5.2920 1.210e-07 #> PCTOWNHOME       0.036593   0.249835  0.1465  0.883551 #> lag.(Intercept)  0.121515   0.057636  2.1083  0.035003 #> lag.PEXPOSURE   -0.035075   0.015943 -2.2000  0.027808 #> lag.PCTAGE65P    0.263096   0.220118  1.1953  0.231989 #> lag.PCTOWNHOME  -0.155680   0.059213 -2.6291  0.008560 #>  #> Lambda: 0.022723, LR test value: 1.6846, p-value: 0.19432 #> Asymptotic standard error: 0.017169 #>     z-value: 1.3235, p-value: 0.18567 #> Wald statistic: 1.7516, p-value: 0.18567 #>  #> Log likelihood: -269.5398 for error model #> ML residual variance (sigma squared): 0.39759, (sigma: 0.63055) #> Number of observations: 281  #> Number of parameters estimated: 10  #> AIC: 559.08, (AIC for lm: 558.76) #>  res <- MCMCsamp(esar1, mcmc=5000, burnin=500, listw=listw_NY) summary(res) #>  #> Iterations = 1:5000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 5000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                     Mean      SD  Naive SE Time-series SE #> lambda           0.02791 0.01696 0.0002398       0.001257 #> (Intercept)     -1.11089 0.24295 0.0034359       0.019066 #> PEXPOSURE        0.20998 0.08066 0.0011407       0.006616 #> PCTAGE65P        3.44550 0.61861 0.0087484       0.045120 #> PCTOWNHOME       0.03249 0.25058 0.0035437       0.022380 #> lag.(Intercept)  0.11788 0.05850 0.0008273       0.004548 #> lag.PEXPOSURE   -0.03381 0.01626 0.0002299       0.001358 #> lag.PCTAGE65P    0.25893 0.23503 0.0033238       0.019521 #> lag.PCTOWNHOME  -0.15337 0.05824 0.0008236       0.004496 #>  #> 2. Quantiles for each variable: #>  #>                      2.5%      25%      50%      75%      97.5% #> lambda          -0.004792  0.01604  0.02829  0.03980  0.0616941 #> (Intercept)     -1.549205 -1.28823 -1.12499 -0.91520 -0.6509996 #> PEXPOSURE        0.063165  0.15363  0.20577  0.26455  0.3711420 #> PCTAGE65P        2.335975  3.01533  3.44864  3.91005  4.6644758 #> PCTOWNHOME      -0.505045 -0.11695  0.05420  0.19038  0.5171339 #> lag.(Intercept)  0.006027  0.07616  0.11689  0.16220  0.2310606 #> lag.PEXPOSURE   -0.064845 -0.04488 -0.03385 -0.02339 -0.0009086 #> lag.PCTAGE65P   -0.195440  0.09430  0.24778  0.43584  0.6912104 #> lag.PCTOWNHOME  -0.263176 -0.19213 -0.15386 -0.11592 -0.0317401 #>  lsar0 <- lagsarlm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY) summary(lsar0) #>  #> Call:lagsarlm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -1.586752 -0.391580 -0.022469  0.338017  4.029430  #>  #> Type: lag  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.514495   0.156154 -3.2948  0.000985 #> PEXPOSURE    0.047627   0.034509  1.3801  0.167542 #> PCTAGE65P    3.648198   0.599046  6.0900 1.129e-09 #> PCTOWNHOME  -0.414601   0.169554 -2.4453  0.014475 #>  #> Rho: 0.038893, LR test value: 6.9683, p-value: 0.0082967 #> Asymptotic standard error: 0.015053 #>     z-value: 2.5837, p-value: 0.0097755 #> Wald statistic: 6.6754, p-value: 0.0097755 #>  #> Log likelihood: -275.2447 for lag model #> ML residual variance (sigma squared): 0.41166, (sigma: 0.6416) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 562.49, (AIC for lm: 567.46) #> LM test for residual autocorrelation #> test value: 1.4633, p-value: 0.22641 #>  res <- MCMCsamp(lsar0, mcmc=5000, burnin=500, listw=listw_NY) summary(res) #>  #> Iterations = 1:5000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 5000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean      SD  Naive SE Time-series SE #> rho          0.03924 0.01531 0.0002166      0.0009369 #> (Intercept) -0.51482 0.16721 0.0023647      0.0103798 #> PEXPOSURE    0.05057 0.03374 0.0004771      0.0019411 #> PCTAGE65P    3.58543 0.66827 0.0094508      0.0442173 #> PCTOWNHOME  -0.41083 0.18638 0.0026358      0.0118147 #>  #> 2. Quantiles for each variable: #>  #>                 2.5%      25%      50%      75%    97.5% #> rho          0.01129  0.02805  0.03879  0.05012  0.07010 #> (Intercept) -0.84632 -0.62884 -0.50852 -0.39309 -0.20739 #> PEXPOSURE   -0.01768  0.02886  0.04981  0.07205  0.11808 #> PCTAGE65P    2.28982  3.12634  3.60888  4.03227  4.88549 #> PCTOWNHOME  -0.74664 -0.54787 -0.40497 -0.28735 -0.03815 #>  lsar1 <- lagsarlm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, type=\"mixed\") summary(lsar1) #>  #> Call:lagsarlm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, type = \"mixed\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -1.799308 -0.390125 -0.021371  0.346128  3.965251  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>                  Estimate Std. Error z value  Pr(>|z|) #> (Intercept)     -1.131233   0.249631 -4.5316 5.853e-06 #> PEXPOSURE        0.218364   0.079301  2.7536  0.005894 #> PCTAGE65P        3.361158   0.654123  5.1384 2.771e-07 #> PCTOWNHOME       0.071903   0.253967  0.2831  0.777085 #> lag.(Intercept)  0.132544   0.056175  2.3595  0.018300 #> lag.PEXPOSURE   -0.035239   0.015536 -2.2681  0.023322 #> lag.PCTAGE65P    0.161685   0.223690  0.7228  0.469798 #> lag.PCTOWNHOME  -0.140681   0.058529 -2.4036  0.016234 #>  #> Rho: 0.026981, LR test value: 2.558, p-value: 0.10974 #> Asymptotic standard error: 0.016766 #>     z-value: 1.6093, p-value: 0.10755 #> Wald statistic: 2.5899, p-value: 0.10755 #>  #> Log likelihood: -269.1031 for mixed model #> ML residual variance (sigma squared): 0.39587, (sigma: 0.62918) #> Number of observations: 281  #> Number of parameters estimated: 10  #> AIC: 558.21, (AIC for lm: 558.76) #> LM test for residual autocorrelation #> test value: 4.908, p-value: 0.026732 #>  res <- MCMCsamp(lsar1, mcmc=5000, burnin=500, listw=listw_NY) summary(res) #>  #> Iterations = 1:5000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 5000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                     Mean      SD  Naive SE Time-series SE #> rho              0.02471 0.01629 0.0002304       0.001219 #> (Intercept)     -1.12989 0.24291 0.0034353       0.017687 #> PEXPOSURE        0.21704 0.08665 0.0012254       0.007356 #> PCTAGE65P        3.40551 0.61299 0.0086689       0.043441 #> PCTOWNHOME       0.04146 0.25683 0.0036321       0.019859 #> lag.(Intercept)  0.12868 0.05650 0.0007991       0.004535 #> lag.PEXPOSURE   -0.03472 0.01732 0.0002449       0.001526 #> lag.PCTAGE65P    0.17214 0.20763 0.0029364       0.015671 #> lag.PCTOWNHOME  -0.13618 0.06186 0.0008749       0.005326 #>  #> 2. Quantiles for each variable: #>  #>                      2.5%      25%      50%      75%     97.5% #> rho             -0.008938  0.01339  0.02554  0.03617  0.054650 #> (Intercept)     -1.604105 -1.28894 -1.12504 -0.97119 -0.660270 #> PEXPOSURE        0.053725  0.15881  0.21725  0.27236  0.389018 #> PCTAGE65P        2.213387  2.99625  3.42281  3.85452  4.551724 #> PCTOWNHOME      -0.451879 -0.14346  0.04721  0.22476  0.545593 #> lag.(Intercept)  0.019705  0.09016  0.13030  0.16767  0.243720 #> lag.PEXPOSURE   -0.067460 -0.04719 -0.03527 -0.02388  0.003145 #> lag.PCTAGE65P   -0.238603  0.04557  0.17728  0.29777  0.562834 #> lag.PCTOWNHOME  -0.246111 -0.18197 -0.13460 -0.09357 -0.018730 #>  ssar0 <- sacsarlm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY) summary(ssar0) #>  #> Call:sacsarlm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -1.468382 -0.375687 -0.034996  0.314714  3.833950  #>  #> Type: sac  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.386572   0.123188 -3.1381  0.001701 #> PEXPOSURE    0.026684   0.024013  1.1112  0.266479 #> PCTAGE65P    3.089824   0.562851  5.4896 4.029e-08 #> PCTOWNHOME  -0.323052   0.137449 -2.3503  0.018756 #>  #> Rho: 0.089451 #> Asymptotic standard error: 0.019427 #>     z-value: 4.6046, p-value: 4.1325e-06 #> Lambda: -0.08192 #> Asymptotic standard error: 0.033201 #>     z-value: -2.4674, p-value: 0.01361 #>  #> LR test value: 10.114, p-value: 0.0063661 #>  #> Log likelihood: -273.672 for sac model #> ML residual variance (sigma squared): 0.3766, (sigma: 0.61368) #> Number of observations: 281  #> Number of parameters estimated: 7  #> AIC: 561.34, (AIC for lm: 567.46) #>  res <- MCMCsamp(ssar0, mcmc=5000, burnin=500, listw=listw_NY) summary(res) #>  #> Iterations = 1:5000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 5000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean      SD Naive SE Time-series SE #> rho         -0.04897 0.07268 0.001028        0.02171 #> lambda       0.07158 0.07109 0.001005        0.01911 #> (Intercept) -0.79253 0.30171 0.004267        0.05929 #> PEXPOSURE    0.12518 0.08005 0.001132        0.01428 #> PCTAGE65P    3.33373 0.62239 0.008802        0.04114 #> PCTOWNHOME  -0.24558 0.24700 0.003493        0.03231 #>  #> 2. Quantiles for each variable: #>  #>                  2.5%      25%      50%        75%    97.5% #> rho         -0.148205 -0.10220 -0.07484 -0.0003653  0.09879 #> lambda      -0.097739  0.03709  0.10543  0.1218063  0.13809 #> (Intercept) -1.371833 -1.01584 -0.80342 -0.5327538 -0.26199 #> PEXPOSURE   -0.001867  0.05674  0.12102  0.1859304  0.27450 #> PCTAGE65P    2.139989  2.91933  3.33752  3.7143648  4.58803 #> PCTOWNHOME  -0.743597 -0.40260 -0.25567 -0.0792356  0.24964 #>  ssar1 <- sacsarlm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, type=\"sacmixed\") summary(ssar1) #>  #> Call:sacsarlm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, type = \"sacmixed\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -1.633958 -0.363826 -0.019927  0.348238  3.655509  #>  #> Type: sacmixed  #> Coefficients: (asymptotic standard errors)  #>                  Estimate Std. Error z value  Pr(>|z|) #> (Intercept)     -1.133298   0.247495 -4.5791 4.670e-06 #> PEXPOSURE        0.206963   0.074480  2.7788  0.005456 #> PCTAGE65P        3.083983   0.671081  4.5955 4.316e-06 #> PCTOWNHOME       0.174800   0.256280  0.6821  0.495196 #> lag.(Intercept)  0.153427   0.050817  3.0192  0.002534 #> lag.PEXPOSURE   -0.033400   0.013817 -2.4173  0.015634 #> lag.PCTAGE65P   -0.079738   0.222144 -0.3589  0.719634 #> lag.PCTOWNHOME  -0.102502   0.056760 -1.8059  0.070940 #>  #> Rho: 0.092495 #> Asymptotic standard error: 0.023829 #>     z-value: 3.8817, p-value: 0.00010375 #> Lambda: -0.091069 #> Asymptotic standard error: 0.038431 #>     z-value: -2.3697, p-value: 0.017804 #>  #> LR test value: 22.379, p-value: 0.0010335 #>  #> Log likelihood: -267.5392 for sacmixed model #> ML residual variance (sigma squared): 0.35617, (sigma: 0.5968) #> Number of observations: 281  #> Number of parameters estimated: 11  #> AIC: 557.08, (AIC for lm: 567.46) #>  res <- MCMCsamp(ssar1, mcmc=5000, burnin=500, listw=listw_NY) summary(res) #>  #> Iterations = 1:5000 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 5000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                      Mean      SD  Naive SE Time-series SE #> rho             -0.005935 0.06247 0.0008835       0.012391 #> lambda           0.025149 0.06578 0.0009302       0.012564 #> (Intercept)     -1.104966 0.25946 0.0036694       0.020691 #> PEXPOSURE        0.220056 0.08072 0.0011415       0.006564 #> PCTAGE65P        3.448064 0.68477 0.0096841       0.053253 #> PCTOWNHOME       0.002352 0.25423 0.0035954       0.018914 #> lag.(Intercept)  0.107623 0.06651 0.0009406       0.007925 #> lag.PEXPOSURE   -0.034004 0.01609 0.0002276       0.001352 #> lag.PCTAGE65P    0.279208 0.31780 0.0044943       0.037387 #> lag.PCTOWNHOME  -0.134012 0.06451 0.0009123       0.005533 #>  #> 2. Quantiles for each variable: #>  #>                     2.5%      25%       50%      75%     97.5% #> rho             -0.10755 -0.05711 -0.014110  0.05341  0.099104 #> lambda          -0.09950 -0.03206  0.037324  0.08249  0.118177 #> (Intercept)     -1.60962 -1.28203 -1.096564 -0.93087 -0.597130 #> PEXPOSURE        0.05429  0.16818  0.217623  0.27874  0.368060 #> PCTAGE65P        2.11661  3.00219  3.455553  3.93036  4.829667 #> PCTOWNHOME      -0.46367 -0.19124 -0.002169  0.17287  0.544393 #> lag.(Intercept) -0.02153  0.05985  0.109887  0.15841  0.231289 #> lag.PEXPOSURE   -0.06423 -0.04610 -0.033598 -0.02331 -0.001144 #> lag.PCTAGE65P   -0.29223  0.02822  0.266936  0.50401  0.926973 #> lag.PCTOWNHOME  -0.26326 -0.17692 -0.130161 -0.08812 -0.009731 #>  # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/ME.html","id":null,"dir":"Reference","previous_headings":"","what":"Moran eigenvector GLM filtering — ME","title":"Moran eigenvector GLM filtering — ME","text":"Moran eigenvector filtering function intended remove spatial autocorrelation residuals generalised linear models. uses brute force eigenvector selection reach subset vectors added RHS GLM model reduce residual autocorrelation specified alpha value. Since eigenvector selection works symmetric weights, weights made symmetric eigenvectors found (spdep 0.5-50).","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/ME.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Moran eigenvector GLM filtering — ME","text":"","code":"ME(formula, data=list(), family = gaussian, weights, offset,  na.action=na.fail,listw=NULL, alpha=0.05, nsim=99, verbose=NULL,  stdev=FALSE, zero.policy=NULL)"},{"path":"https://r-spatial.github.io/spatialreg/reference/ME.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Moran eigenvector GLM filtering — ME","text":"formula symbolic description model fit data optional data frame containing variables model family description error distribution link function           used model weights optional vector weights used fitting process offset can used specify priori known component included linear predictor fitting na.action function (default options(\"na.action\")), can also na.omit na.exclude consequences residuals fitted values - cases spatial weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. listw listw object created example nb2listw alpha used stopping rule choose eigenvectors including one p-value exceeding alpha nsim number permutations permutation bootstrap finding p-values verbose default NULL, use global option value; TRUE report eigenvectors selected stdev TRUE, p-value calculated bootstrap permutation standard deviate using pnorm alternative=\"greater\", FALSE Hope-type p-value zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/ME.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Moran eigenvector GLM filtering — ME","text":"eigenvectors inclusion chosen calculating empirical Moran's values initial model plus doubly centred symmetric spatial weights matrix eigenvectors turn. first eigenvector chosen lowest Moran's value. procedure repeated lowest remaining Moran's value permutation-based probability value alpha. probability value either Hope-type based using mean standard deviation permutations calculate ZI based stdev argument.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/ME.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Moran eigenvector GLM filtering — ME","text":"object class Me_res: selection matrix summarising selection eigenvectors inclusion, columns: Eigenvector number selected eigenvector ZI permutation-based standardized deviate Moran's stdev=TRUE pr(ZI) probability value: stdev=TRUE permutation-based standardized deviate, FALSE Hope-type probability value, cases -sided first row value start search vectors matrix selected eigenvectors order selection","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/ME.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Moran eigenvector GLM filtering — ME","text":"Dray S, Legendre P Peres-Neto PR (2005) Spatial modeling: comprehensive framework principle coordinate analysis neigbbor matrices (PCNM), Ecological Modelling; Griffith DA Peres-Neto PR (2006) Spatial modeling ecology: flexibility eigenfunction spatial analyses.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/ME.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Moran eigenvector GLM filtering — ME","text":"Roger Bivand Pedro Peres-Neto","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/ME.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Moran eigenvector GLM filtering — ME","text":"","code":"#require(\"spdep\", quietly=TRUE) data(hopkins, package=\"spData\") hopkins_part <- hopkins[21:36,36:21] hopkins_part[which(hopkins_part > 0, arr.ind=TRUE)] <- 1 hopkins.rook.nb <- spdep::cell2nb(16, 16, type=\"rook\") glmbase <- glm(c(hopkins_part) ~ 1, family=\"binomial\") lw <- spdep::nb2listw(hopkins.rook.nb, style=\"B\") set.seed(123) system.time(MEbinom1 <- ME(c(hopkins_part) ~ 1, family=\"binomial\",  listw=lw, alpha=0.05, verbose=TRUE, nsim=49)) #> eV[,1], I: 0.08290518 ZI: NA, pr(ZI): 0.04 #> eV[,9], I: 0.06426565 ZI: NA, pr(ZI): 0.14 #>    user  system elapsed  #>   1.258   0.007   1.272  glmME <- glm(c(hopkins_part) ~ 1 + fitted(MEbinom1), family=\"binomial\") #anova(glmME, test=\"Chisq\") coef(summary(glmME)) #>                       Estimate Std. Error   z value     Pr(>|z|) #> (Intercept)          -1.146132  0.1542253 -7.431543 1.073378e-13 #> fitted(MEbinom1)vec1  8.293309  2.4532307  3.380566 7.233663e-04 #> fitted(MEbinom1)vec9  5.215112  2.3949596  2.177537 2.944054e-02 anova(glmbase, glmME, test=\"Chisq\") #> Analysis of Deviance Table #>  #> Model 1: c(hopkins_part) ~ 1 #> Model 2: c(hopkins_part) ~ 1 + fitted(MEbinom1) #>   Resid. Df Resid. Dev Df Deviance  Pr(>Chi)     #> 1       255     292.23                           #> 2       253     275.39  2   16.841 0.0002203 *** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 # \\dontrun{ require(\"sf\", quietly=TRUE) columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) #require(\"spdep\", quietly=TRUE) col.gal.nb <- spdep::read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) lw <- spdep::nb2listw(col.gal.nb) lmbase <- lm(CRIME ~ INC + HOVAL, data=columbus) lagcol <- SpatialFiltering(CRIME ~ 1, ~ INC + HOVAL, data=columbus,  nb=col.gal.nb, style=\"W\", alpha=0.1, verbose=TRUE) #> Step 0 SelEvec 0 MinMi 0.2123742 ZMinMi 2.681 Pr(ZI) 0.007340246  #> Step 1 SelEvec 6 MinMi 0.1178225 ZMinMi 1.84512 Pr(ZI) 0.06502014  #> Step 2 SelEvec 4 MinMi 0.06242664 ZMinMi 1.494821 Pr(ZI) 0.1349611  lagcol #>   Step SelEvec      Eval      MinMi   ZMinMi      Pr(ZI)        R2    gamma #> 0    0       0 0.0000000 0.21237415 2.681000 0.007340246 0.5524040  0.00000 #> 1    1       6 0.7161123 0.11782248 1.845120 0.065020139 0.6038801 25.46181 #> 2    2       4 0.8682938 0.06242664 1.494821 0.134961136 0.6531288 26.68319 lmlag <- lm(CRIME ~ INC + HOVAL + fitted(lagcol), data=columbus) anova(lmbase, lmlag) #> Analysis of Variance Table #>  #> Model 1: CRIME ~ INC + HOVAL #> Model 2: CRIME ~ INC + HOVAL + fitted(lagcol) #>   Res.Df    RSS Df Sum of Sq      F   Pr(>F)    #> 1     46 6014.9                                 #> 2     44 4661.3  2    1353.6 6.3884 0.003666 ** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 set.seed(123) system.time(lagcol1 <- ME(CRIME ~ INC + HOVAL, data=columbus, family=\"gaussian\",  listw=lw, alpha=0.1, verbose=TRUE)) #> eV[,6], I: 0.1178225 ZI: NA, pr(ZI): 0.08 #> eV[,4], I: 0.06242664 ZI: NA, pr(ZI): 0.27 #>    user  system elapsed  #>   0.528   0.000   0.532  lagcol1 #>   Eigenvector ZI pr(ZI) #> 0          NA NA   0.01 #> 1           6 NA   0.08 #> 2           4 NA   0.27 lmlag1 <- lm(CRIME ~ INC + HOVAL + fitted(lagcol1), data=columbus) anova(lmbase, lmlag1) #> Analysis of Variance Table #>  #> Model 1: CRIME ~ INC + HOVAL #> Model 2: CRIME ~ INC + HOVAL + fitted(lagcol1) #>   Res.Df    RSS Df Sum of Sq      F   Pr(>F)    #> 1     46 6014.9                                 #> 2     44 4661.3  2    1353.6 6.3884 0.003666 ** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  set.seed(123) lagcol2 <- ME(CRIME ~ INC + HOVAL, data=columbus, family=\"gaussian\",  listw=lw, alpha=0.1, stdev=TRUE, verbose=TRUE) #> eV[,6], I: 0.1178225 ZI: 1.5509, pr(ZI): 0.06046283 #> eV[,4], I: 0.06242664 ZI: 0.681174, pr(ZI): 0.2478807 lagcol2 #>   Eigenvector       ZI      pr(ZI) #> 0          NA 2.351591 0.009346653 #> 1           6 1.550900 0.060462832 #> 2           4 0.681174 0.247880696 lmlag2 <- lm(CRIME ~ INC + HOVAL + fitted(lagcol2), data=columbus) anova(lmbase, lmlag2) #> Analysis of Variance Table #>  #> Model 1: CRIME ~ INC + HOVAL #> Model 2: CRIME ~ INC + HOVAL + fitted(lagcol2) #>   Res.Df    RSS Df Sum of Sq      F   Pr(>F)    #> 1     46 6014.9                                 #> 2     44 4661.3  2    1353.6 6.3884 0.003666 ** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 NA.columbus <- columbus NA.columbus$CRIME[20:25] <- NA COL.ME.NA <- ME(CRIME ~ INC + HOVAL, data=NA.columbus, family=\"gaussian\",  listw=lw, alpha=0.1, stdev=TRUE, verbose=TRUE,  na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count #> eV[,8], I: 0.1426723 ZI: 1.483169, pr(ZI): 0.06901474 #> eV[,1], I: 0.09838877 ZI: 0.9862904, pr(ZI): 0.1619953 COL.ME.NA$na.action #> 20 21 22 23 24 25  #> 20 21 22 23 24 25  #> attr(,\"class\") #> [1] \"exclude\" summary(lm(CRIME ~ INC + HOVAL + fitted(COL.ME.NA), data=NA.columbus,  na.action=na.exclude)) #>  #> Call: #> lm(formula = CRIME ~ INC + HOVAL + fitted(COL.ME.NA), data = NA.columbus,  #>     na.action = na.exclude) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -30.1382  -6.0105   0.4095   7.1504  19.9399  #>  #> Coefficients: #>                    Estimate Std. Error t value Pr(>|t|)     #> (Intercept)        66.92248    5.28663  12.659 3.33e-15 *** #> INC                -1.40484    0.35678  -3.938  0.00034 *** #> HOVAL              -0.30446    0.09831  -3.097  0.00366 **  #> fitted(COL.ME.NA)1 29.69422   10.58481   2.805  0.00788 **  #> fitted(COL.ME.NA)2 26.61612   11.29187   2.357  0.02367 *   #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>  #> Residual standard error: 10.48 on 38 degrees of freedom #>   (6 observations deleted due to missingness) #> Multiple R-squared:  0.6294,\tAdjusted R-squared:  0.5904  #> F-statistic: 16.13 on 4 and 38 DF,  p-value: 8.353e-08 #>  nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) rn <- as.character(nc.sids$FIPS) ncCC89_nb <- spdep::read.gal(system.file(\"weights/ncCC89.gal\", package=\"spData\")[1],  region.id=rn) #> Warning: neighbour object has 3 sub-graphs ncCR85_nb <- spdep::read.gal(system.file(\"weights/ncCR85.gal\", package=\"spData\")[1],  region.id=rn) glmbase <- glm(SID74 ~ 1, data=nc.sids, offset=log(BIR74),  family=\"poisson\") set.seed(123) MEpois1 <- ME(SID74 ~ 1, data=nc.sids, offset=log(BIR74),  family=\"poisson\", listw=spdep::nb2listw(ncCR85_nb, style=\"B\"), alpha=0.2, verbose=TRUE) #> eV[,1], I: 0.1327384 ZI: NA, pr(ZI): 0.03 #> eV[,8], I: 0.06936385 ZI: NA, pr(ZI): 0.12 #> eV[,4], I: 0.03584503 ZI: NA, pr(ZI): 0.3 MEpois1 #>   Eigenvector ZI pr(ZI) #> 0          NA NA   0.01 #> 1           1 NA   0.03 #> 2           8 NA   0.12 #> 3           4 NA   0.30 glmME <- glm(SID74 ~ 1 + fitted(MEpois1), data=nc.sids, offset=log(BIR74),  family=\"poisson\") anova(glmME, test=\"Chisq\") #> Analysis of Deviance Table #>  #> Model: poisson, link: log #>  #> Response: SID74 #>  #> Terms added sequentially (first to last) #>  #>  #>                 Df Deviance Resid. Df Resid. Dev  Pr(>Chi)     #> NULL                               99     203.34               #> fitted(MEpois1)  3   32.499        96     170.84 4.108e-07 *** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 anova(glmbase, glmME, test=\"Chisq\") #> Analysis of Deviance Table #>  #> Model 1: SID74 ~ 1 #> Model 2: SID74 ~ 1 + fitted(MEpois1) #>   Resid. Df Resid. Dev Df Deviance  Pr(>Chi)     #> 1        99     203.34                           #> 2        96     170.84  3   32.499 4.108e-07 *** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/ML_models.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial simultaneous autoregressive model estimation by maximum likelihood — ML_models","title":"Spatial simultaneous autoregressive model estimation by maximum likelihood — ML_models","text":"lagsarlm function provides Maximum likelihood estimation spatial simultaneous autoregressive lag spatial Durbin (mixed) models form: $$y = \\rho W y + X \\beta + \\varepsilon$$ \\(\\rho\\) found optimize() first, \\(\\beta\\) parameters generalized least squares subsequently (one-dimensional search using optim performs badly platforms). spatial Durbin (mixed) model, spatially lagged independent variables added X. Note interpretation fitted coefficients use impact measures, feedback loops induced data generation process model. one sparse matrix methods, larger numbers observations can handled, interval= argument may need set weights row-standardised. Maximum likelihood estimation spatial simultaneous autoregressive error models form: $$y = X \\beta + u, u = \\lambda W u + \\varepsilon$$ \\(\\lambda\\) found optimize() first, \\(\\beta\\) parameters generalized least squares subsequently. one sparse matrix methods, larger numbers observations can handled, interval= argument may need set weights row-standardised. etype “emixed”, -called spatial Durbin error model fitted. Maximum likelihood estimation spatial simultaneous autoregressive “SAC/SARAR” models form: $$y = \\rho W1 y + X \\beta + u, u = \\lambda W2 u + \\varepsilon$$ \\(\\rho\\) \\(\\lambda\\) found nlminb optim() first, \\(\\beta\\) parameters generalized least squares subsequently.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/ML_models.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial simultaneous autoregressive model estimation by maximum likelihood — ML_models","text":"","code":"lagsarlm(formula, data = list(), listw, na.action, Durbin, type,  method=\"eigen\", quiet=NULL, zero.policy=NULL, interval=NULL,  tol.solve=.Machine$double.eps, trs=NULL, control=list()) errorsarlm(formula, data=list(), listw, na.action, weights=NULL,  Durbin, etype, method=\"eigen\", quiet=NULL, zero.policy=NULL,  interval = NULL, tol.solve=.Machine$double.eps, trs=NULL, control=list()) sacsarlm(formula, data = list(), listw, listw2 = NULL, na.action, Durbin, type,  method=\"eigen\", quiet=NULL, zero.policy=NULL, tol.solve=.Machine$double.eps,  llprof=NULL, interval1=NULL, interval2=NULL, trs1=NULL, trs2=NULL,  control = list()) # S3 method for class 'Sarlm' summary(object, correlation = FALSE, Nagelkerke = FALSE,  Hausman=FALSE, adj.se=FALSE, ...) # S3 method for class 'Sarlm' print(x, ...) # S3 method for class 'summary.Sarlm' print(x, digits = max(5, .Options$digits - 3),  signif.stars = FALSE, ...) # S3 method for class 'Sarlm' residuals(object, ...) # S3 method for class 'Sarlm' deviance(object, ...) # S3 method for class 'Sarlm' coef(object, ...) # S3 method for class 'Sarlm' vcov(object, ...) # S3 method for class 'Sarlm' fitted(object, ...)"},{"path":"https://r-spatial.github.io/spatialreg/reference/ML_models.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial simultaneous autoregressive model estimation by maximum likelihood — ML_models","text":"formula symbolic description model fit. details model specification given lm() data optional data frame containing variables model. default variables taken environment function called. listw, listw2 listw object created example nb2listw; nb2listw given, set spatial weights listw argument na.action function (default options(\"na.action\")), can also na.omit na.exclude consequences residuals fitted values - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. weights optional vector weights used fitting process. Non-NULL weights can used indicate different observations different variances (values weights inversely proportional variances); equivalently, elements weights positive integers w_i, response y_i mean w_i unit-weight observations (including case w_i observations equal y_i data summarized) - lm Durbin default FALSE (spatial lag model); TRUE, full spatial Durbin model; formula object, subset explanatory variables lag type (use ‘Durbin=’ argument - retained backwards compatibility ) default \"lag\", may set \"mixed\"; \"mixed\", lagged intercept dropped spatial weights style \"W\", row-standardised weights, otherwise included; “Durbin” may used instead “mixed” etype (use ‘Durbin=’ argument - retained backwards compatibility ) default \"error\", may set \"emixed\" include spatially lagged independent variables added X; \"emixed\", lagged intercept dropped spatial weights style \"W\", row-standardised weights, otherwise included method \"eigen\" (default) - Jacobian computed product (1 - rho*eigenvalue) using eigenw, \"spam\" \"Matrix_J\" strictly symmetric weights lists styles \"B\" \"C\", made symmetric similarity (Ord, 1975, Appendix C) possible styles \"W\" \"S\", using code spam Matrix packages calculate determinant; “Matrix” “spam_update” provide updating Cholesky decomposition methods; \"LU\" provides alternative sparse matrix decomposition approach. addition, \"Chebyshev\" Monte Carlo \"MC\" approximate log-determinant methods; Smirnov/Anselin (2009) trace approximation available \"moments\". Three methods: \"SE_classic\", \"SE_whichMin\", \"SE_interp\" provided experimentally, first attempt emulate behaviour Spatial Econometrics toolbox ML fitting functions. use grids log determinant values, latter two attempt ameliorate features \"SE_classic\". quiet default NULL, use !verbose global option value; FALSE, reports function values optimization. zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE (default) assign NA - causing lagsarlm() terminate error interval default NULL, search interval autoregressive parameter tol.solve tolerance detecting linear dependencies columns matrices inverted - passed solve() (default=1.0e-10). may used necessary extract coefficient standard errors (instance lowering 1e-12), errors solve() may constitute indications poorly scaled variables: variables scales differing much autoregressive coefficient, values matrix may different scale, inverting matrix analytically possible definition, numerically unstable; rescaling RHS variables alleviates better setting tol.solve small value llprof default NULL, can either integer, divide feasible ranges grid points, two-column matrix spatial coefficient values, evaluate likelihood function trs1, trs2 default NULL, given, vectors weights object powered spatial weights matrix traces output trW; given, used Jacobian methods interval1, interval2 default NULL, search intervals weights object autoregressive parameters trs default NULL, given, vector powered spatial weights matrix traces output trW; given, insert asymptotic analytical values numerical Hessian instead approximated values; may used get around problems raised numerical Hessian poorly conditioned, generating NaNs subsequent operations; use trs recommended control list extra control arguments - see section object Sarlm object lagsarlm, errorsarlm sacsarlm correlation logical; 'TRUE', correlation matrix estimated parameters including sigma returned printed (default=FALSE) Nagelkerke TRUE, Nagelkerke pseudo R-squared reported Hausman TRUE, results Hausman test error models reported adj.se TRUE, adjust coefficient standard errors number fitted coefficients x Sarlm object lagsarlm, errorsarlm sacsarlm print.Sarlm, summary object summary.Sarlm print.summary.Sarlm digits number significant digits use printing signif.stars logical. TRUE, \"significance stars\" printed           coefficient. ... arguments passed methods","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/ML_models.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial simultaneous autoregressive model estimation by maximum likelihood — ML_models","text":"asymptotic standard error \\(\\rho\\) computed method=“eigen”, full matrix operations involved costly large n typically associated choice method=\"spam\" \"Matrix\". applies coefficient covariance matrix. Taken asymptotic matrix literature, typically badly scaled, elements involving \\(\\rho\\) (lag model) \\(\\lambda\\) (error model) small, parts matrix can large (often many orders magnitude difference). often happens tol.solve argument needs set smaller value default, RHS variables can centred reduced range. Versions package 0.4-38 include numerical Hessian values asymptotic standard errors available. change introduced permit simulation distributions impact measures. warnings made regard variable scaling also apply case. Note fitted() function output object assumes response variable may reconstructed sum trend, signal, noise (residuals). Since values response variable known, spatial lags used calculate signal components (Cressie 1993, p. 564). differs software, including GeoDa, use knowledge response variable making predictions fitting data. Refer help page predict.Sarlm discussions references. numerical optimisation used find values lambda rho sacsarlm, care needs shown. found surface 2D likelihood function often forms “banana trench” (low rho, high lambda) (high rho, high lambda) (high rho, low lambda) values. addition, sometimes banana optima towards ends, one local, global, conseqently choice starting point final optimization becomes crucial. default approach use just (0, 0) starting point, (rho, lambda) values gstsls, lie central part “trench”, either four values (low rho, high lambda), (0, 0), (high rho, high lambda), (high rho, low lambda), use best start points final optimization. Optionally, nine points can used spanning whole (lower, upper) space.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/ML_models.html","id":"control-arguments","dir":"Reference","previous_headings":"","what":"Control arguments","title":"Spatial simultaneous autoregressive model estimation by maximum likelihood — ML_models","text":"tol.opt: desired accuracy optimization - passed optimize() (default=square root double precision machine tolerance, larger root may used needed, see help(boston) example) returnHcov: (error model) default TRUE, return Vo matrix spatial Hausman test pWOrder: (error model) default 250, returnHcov=TRUE method “eigen”, pass order powerWeights power series maximum limit fdHess: default NULL, set (method != \"eigen\") internally; use fdHess compute approximate Hessian using finite differences using sparse matrix methods; used make coefficient covariance matrix number observations large; may turned save resources need optimHess: default FALSE, use fdHess nlme, TRUE, use optim calculate Hessian optimum optimHessMethod: default “optimHess”, may “nlm” one optim methods compiled_sse: default FALSE; logical value used log likelihood function choose compiled code computing SSE Imult: default 2; used preparing Cholesky decompositions updating Jacobian function super: NULL (default), set FALSE use simplicial decomposition sparse Cholesky decomposition method “Matrix_J”, set  .logical(NA) method “Matrix”, TRUE, use supernodal decomposition cheb_q: default 5; highest power approximating polynomial Chebyshev approximation MC_p: default 16; number random variates MC_m: default 30; number products random variates matrix spatial weights matrix spamPivot: default “MMD”, alternative “RCM” in_coef default 0.1, coefficient value initial Cholesky decomposition “spam_update” type default “MC”, used method “moments”; alternatives “mult” “moments”, use trs missing, trW correct default TRUE, used method “moments” compute Smirnov/Anselin correction term trunc default TRUE, used method “moments” truncate Smirnov/Anselin correction term SE_method default “LU”, may “MC” nrho default 200, SE toolbox; size first stage lndet grid; may reduced example 40 interpn default 2000, SE toolbox; size second stage lndet grid small_asy default TRUE; method “eigen”, use asymmetric covariances rather numerical Hessian ones n <= small small default 1500; threshold number observations asymmetric covariances method “eigen” SElndet default NULL, may used pass pre-computed SE toolbox style matrix coefficients lndet values \"SE_classic\" \"SE_whichMin\" methods LU_order default FALSE; used “LU_prepermutate”, note warnings given lu method pre_eig default NULL; may used pass pre-computed vector eigenvalues return_impacts default TRUE; may set FALSE avoid problems calculating impacts aliased variables OrdVsign default 1; used set sign final component negative -1 (alpha times ((sigma squared) squared) Ord (1975) equation B.1). opt_method: default “nlminb”, may set “L-BFGS-B” use box-constrained optimisation optim opt_control: default list(), control list pass nlminb optim pars: default NULL, five trial starting values spanning lower/upper range tried best selected, starting values \\(\\rho\\) \\(\\lambda\\) npars default integer 4L, four trial points; default value, nine trial points pre_eig1, pre_eig2 default NULL; may used pass pre-computed vectors eigenvalues","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/ML_models.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial simultaneous autoregressive model estimation by maximum likelihood — ML_models","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion; Ord, J. K. 1975 Estimation methods models spatial interaction, Journal American Statistical Association, 70, 120-126; Anselin, L. 1988 Spatial econometrics: methods models. (Dordrecht: Kluwer); Anselin, L. 1995 SpaceStat, software program analysis spatial data, version 1.80. Regional Research Institute, West Virginia University, Morgantown, WV; Anselin L, Bera AK (1998) Spatial dependence linear regression models introduction spatial econometrics. : Ullah , Giles DEA (eds) Handbook applied economic statistics. Marcel Dekker, New York, pp. 237-289; Nagelkerke NJD (1991) note general definition coefficient determination. Biometrika 78: 691-692; Cressie, N. . C. 1993 Statistics spatial data, Wiley, New York; LeSage J RK Pace (2009) Introduction Spatial Econometrics. CRC Press, Boca Raton. Roger Bivand, Gianfranco Piras (2015). Comparing Implementations Estimation Methods Spatial Econometrics. Journal Statistical Software, 63(18), 1-36. doi:10.18637/jss.v063.i18 . Bivand, R. S., Hauke, J., Kossowski, T. (2013). Computing Jacobian Gaussian spatial autoregressive models: illustrated comparison available methods. Geographical Analysis, 45(2), 150-179.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/ML_models.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial simultaneous autoregressive model estimation by maximum likelihood — ML_models","text":"Roger Bivand Roger.Bivand@nhh., thanks Andrew Bernat contributions asymptotic standard error code.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/ML_models.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial simultaneous autoregressive model estimation by maximum likelihood — ML_models","text":"","code":"data(oldcol, package=\"spdep\") listw <- spdep::nb2listw(COL.nb, style=\"W\") ev <- eigenw(listw) W <- as(listw, \"CsparseMatrix\") trMatc <- trW(W, type=\"mult\") COL.lag.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, listw=listw,  method=\"eigen\", quiet=FALSE, control=list(pre_eig=ev, OrdVsign=1)) #>  #> Spatial lag model #> Jacobian calculated using neighbourhood matrix eigenvalues #>  #> rho:\t -0.5674437 \tfunction value:\t -202.2909  #> rho:\t 0.03126655 \tfunction value:\t -186.749  #> rho:\t 0.4012898 \tfunction value:\t -182.419  #> rho:\t 0.6138418 \tfunction value:\t -183.5636  #> rho:\t 0.4157662 \tfunction value:\t -182.398  #> rho:\t 0.4295565 \tfunction value:\t -182.3905  #> rho:\t 0.4311288 \tfunction value:\t -182.3904  #> rho:\t 0.4310273 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  (x <- summary(COL.lag.eig, correlation=TRUE)) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     method = \"eigen\", quiet = FALSE, control = list(pre_eig = ev,  #>         OrdVsign = 1)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.68585  -5.35636   0.05421   6.02013  23.20555  #>  #> Type: lag  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 45.079249   7.177346  6.2808 3.369e-10 #> INC         -1.031616   0.305143 -3.3808 0.0007229 #> HOVAL       -0.265926   0.088499 -3.0049 0.0026570 #>  #> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588 #> Asymptotic standard error: 0.11768 #>     z-value: 3.6626, p-value: 0.00024962 #> Wald statistic: 13.415, p-value: 0.00024962 #>  #> Log likelihood: -182.3904 for lag model #> ML residual variance (sigma squared): 95.494, (sigma: 9.7721) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 374.78, (AIC for lm: 382.75) #> LM test for residual autocorrelation #> test value: 0.31954, p-value: 0.57188 #>  #>  Correlation of coefficients  #>             sigma rho   (Intercept) INC   #> rho         -0.14                         #> (Intercept)  0.12 -0.83                   #> INC         -0.05  0.35 -0.61             #> HOVAL       -0.01  0.08 -0.25       -0.44 #>  coef(x) #>               Estimate Std. Error   z value     Pr(>|z|) #> (Intercept) 45.0792493 7.17734647  6.280768 3.369043e-10 #> INC         -1.0316157 0.30514297 -3.380762 7.228519e-04 #> HOVAL       -0.2659263 0.08849862 -3.004863 2.657002e-03 # \\dontrun{ COL.lag.eig$fdHess #> [1] FALSE COL.lag.eig$resvar #>                    sigma           rho (Intercept)         INC         HOVAL #> sigma       379.77510023 -0.3236306420  16.3015085 -0.29590802 -0.0202478469 #> rho          -0.32363064  0.0138487528  -0.6975717  0.01266245  0.0008664428 #> (Intercept)  16.30150847 -0.6975716519  51.5143024 -1.32602702 -0.1616379845 #> INC          -0.29590802  0.0126624508  -1.3260270  0.09311223 -0.0117959714 #> HOVAL        -0.02024785  0.0008664428  -0.1616380 -0.01179597  0.0078320057 # using the apparent sign in Ord (1975, equation B.1)  COL.lag.eigb <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, listw=listw,  method=\"eigen\", control=list(pre_eig=ev, OrdVsign=-1)) summary(COL.lag.eigb) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     method = \"eigen\", control = list(pre_eig = ev, OrdVsign = -1)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.68585  -5.35636   0.05421   6.02013  23.20555  #>  #> Type: lag  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 45.079249   9.617835  4.6870 2.772e-06 #> INC         -1.031616   0.326524 -3.1594  0.001581 #> HOVAL       -0.265926   0.088855 -2.9928  0.002764 #>  #> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588 #> Asymptotic standard error: 0.17322 #>     z-value: 2.4884, p-value: 0.012833 #> Wald statistic: 6.1919, p-value: 0.012833 #>  #> Log likelihood: -182.3904 for lag model #> ML residual variance (sigma squared): 95.494, (sigma: 9.7721) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 374.78, (AIC for lm: 382.75) #> LM test for residual autocorrelation #> test value: -0.93825, p-value: 1 #>  COL.lag.eigb$fdHess #> [1] FALSE COL.lag.eigb$resvar #>                    sigma          rho (Intercept)         INC        HOVAL #> sigma       388.59742708 -0.701154300  35.3176470 -0.64109252 -0.043867493 #> rho          -0.70115430  0.030003687  -1.5113073  0.02743353  0.001877171 #> (Intercept)  35.31764699 -1.511307337  92.5027548 -2.07005706 -0.212549096 #> INC          -0.64109252  0.027433533  -2.0700571  0.10661800 -0.010871823 #> HOVAL        -0.04386749  0.001877171  -0.2125491 -0.01087182  0.007895242 # force numerical Hessian COL.lag.eig1 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw=listw, method=\"Matrix\", control=list(small=25)) summary(COL.lag.eig1) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     method = \"Matrix\", control = list(small = 25)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.68585  -5.35636   0.05421   6.02013  23.20555  #>  #> Type: lag  #> Coefficients: (numerical Hessian approximate standard errors)  #>             Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 45.07925    7.87142   5.727 1.022e-08 #> INC         -1.03162    0.32843  -3.141  0.001683 #> HOVAL       -0.26593    0.08823  -3.014  0.002578 #>  #> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588 #> Approximate (numerical Hessian) standard error: 0.12363 #>     z-value: 3.4865, p-value: 0.00048934 #> Wald statistic: 12.156, p-value: 0.00048934 #>  #> Log likelihood: -182.3904 for lag model #> ML residual variance (sigma squared): 95.494, (sigma: 9.7721) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 374.78, (AIC for lm: 382.75) #>  COL.lag.eig1$fdHess #>                       rho (Intercept)         INC         HOVAL #> rho          0.0152832589  -0.8346578  0.02005909  0.0002832041 #> (Intercept) -0.8346577895  61.9591934 -1.78361966 -0.1334688151 #> INC          0.0200590872  -1.7836197  0.10786711 -0.0122201879 #> HOVAL        0.0002832041  -0.1334688 -0.01222019  0.0077846116 # force LeSage & Pace (2008, p. 57) approximation  COL.lag.eig1a <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw=listw, method=\"Matrix\", control=list(small=25), trs=trMatc) summary(COL.lag.eig1a) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     method = \"Matrix\", trs = trMatc, control = list(small = 25)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.68585  -5.35636   0.05421   6.02013  23.20555  #>  #> Type: lag  #> Coefficients: (numerical Hessian approximate standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 45.079249   7.937572  5.6792 1.353e-08 #> INC         -1.031616   0.329337 -3.1324  0.001734 #> HOVAL       -0.265926   0.088222 -3.0143  0.002576 #>  #> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588 #> Approximate (numerical Hessian) standard error: 0.12503 #>     z-value: 3.4473, p-value: 0.00056624 #> Wald statistic: 11.884, p-value: 0.00056624 #>  #> Log likelihood: -182.3904 for lag model #> ML residual variance (sigma squared): 95.494, (sigma: 9.7721) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 374.78, (AIC for lm: 382.75) #>  COL.lag.eig1a$fdHess #>                    sigma2           rho (Intercept)         INC         HOVAL #> sigma2      380.749548407 -0.3653290756  19.9519208 -0.47947507 -0.0067851124 #> rho          -0.365329076  0.0156331058  -0.8537795  0.02051762  0.0002903475 #> (Intercept)  19.951920812 -0.8537795385  63.0050547 -1.80875071 -0.1338515483 #> INC          -0.479475072  0.0205176238  -1.8087507  0.10846276 -0.0122071279 #> HOVAL        -0.006785112  0.0002903475  -0.1338515 -0.01220713  0.0077831895 COL.lag.eig$resvar[2,2] #> [1] 0.01384875 # using the apparent sign in Ord (1975, equation B.1)  COL.lag.eigb$resvar[2,2] #> [1] 0.03000369 # force numerical Hessian COL.lag.eig1$fdHess[1,1] #> [1] 0.01528326 # force LeSage & Pace (2008, p. 57) approximation  COL.lag.eig1a$fdHess[2,2] #> [1] 0.01563311 # } system.time(COL.lag.M <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"Matrix\", quiet=FALSE)) #>  #> Spatial lag model #> Jacobian calculated using sparse matrix Cholesky decomposition #> rho:\t -0.2364499 \tfunction value:\t -192.9523  #> rho:\t 0.2354499 \tfunction value:\t -183.542  #> rho:\t 0.5271001 \tfunction value:\t -182.7039  #> rho:\t 0.4455543 \tfunction value:\t -182.3974  #> rho:\t 0.4267907 \tfunction value:\t -182.391  #> rho:\t 0.4311986 \tfunction value:\t -182.3904  #> rho:\t 0.4310114 \tfunction value:\t -182.3904  #> rho:\t 0.4310231 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> Computing eigenvalues ... #>  #>    user  system elapsed  #>   0.187   0.000   0.188  summary(COL.lag.M) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     method = \"Matrix\", quiet = FALSE) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.68585  -5.35636   0.05421   6.02013  23.20555  #>  #> Type: lag  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 45.079249   7.177346  6.2808 3.369e-10 #> INC         -1.031616   0.305143 -3.3808 0.0007229 #> HOVAL       -0.265926   0.088499 -3.0049 0.0026570 #>  #> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588 #> Asymptotic standard error: 0.11768 #>     z-value: 3.6626, p-value: 0.00024962 #> Wald statistic: 13.415, p-value: 0.00024962 #>  #> Log likelihood: -182.3904 for lag model #> ML residual variance (sigma squared): 95.494, (sigma: 9.7721) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 374.78, (AIC for lm: 382.75) #> LM test for residual autocorrelation #> test value: 0.31954, p-value: 0.57188 #>  impacts(COL.lag.M, listw=listw) #> Impact measures (lag, exact): #>           Direct   Indirect      Total #> INC   -1.0860220 -0.7270848 -1.8131068 #> HOVAL -0.2799509 -0.1874254 -0.4673763 # \\dontrun{ system.time(COL.lag.sp <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw=listw, method=\"spam\", quiet=FALSE)) #>  #> Spatial lag model #> Jacobian calculated using sparse matrix Cholesky decomposition #> rho:\t -0.2364499 \tfunction value:\t -192.9523  #> rho:\t 0.2354499 \tfunction value:\t -183.542  #> rho:\t 0.5271001 \tfunction value:\t -182.7039  #> rho:\t 0.4455543 \tfunction value:\t -182.3974  #> rho:\t 0.4267907 \tfunction value:\t -182.391  #> rho:\t 0.4311986 \tfunction value:\t -182.3904  #> rho:\t 0.4310114 \tfunction value:\t -182.3904  #> rho:\t 0.4310231 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> rho:\t 0.4310232 \tfunction value:\t -182.3904  #> Computing eigenvalues ... #>  #>    user  system elapsed  #>   0.449   0.003   0.454  summary(COL.lag.sp) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     method = \"spam\", quiet = FALSE) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.68585  -5.35636   0.05421   6.02013  23.20555  #>  #> Type: lag  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 45.079250   7.177347  6.2808 3.369e-10 #> INC         -1.031616   0.305143 -3.3808 0.0007229 #> HOVAL       -0.265926   0.088499 -3.0049 0.0026570 #>  #> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588 #> Asymptotic standard error: 0.11768 #>     z-value: 3.6626, p-value: 0.00024962 #> Wald statistic: 13.415, p-value: 0.00024962 #>  #> Log likelihood: -182.3904 for lag model #> ML residual variance (sigma squared): 95.494, (sigma: 9.7721) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 374.78, (AIC for lm: 382.75) #> LM test for residual autocorrelation #> test value: 0.31954, p-value: 0.57188 #>  COL.lag.B <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  spdep::nb2listw(COL.nb, style=\"B\"), control=list(pre_eig=ev)) summary(COL.lag.B) #>  #> Call: #> lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,  #>     style = \"B\"), control = list(pre_eig = ev)) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -33.6620  -4.8615  -1.3576   5.1567  25.7563  #>  #> Type: lag  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 51.604815   6.075285  8.4942 < 2.2e-16 #> INC         -1.154463   0.301808 -3.8252 0.0001307 #> HOVAL       -0.251633   0.087612 -2.8721 0.0040773 #>  #> Rho: 0.054543, LR test value: 13.453, p-value: 0.00024461 #> Asymptotic standard error: 0.014836 #>     z-value: 3.6763, p-value: 0.00023662 #> Wald statistic: 13.515, p-value: 0.00023662 #>  #> Log likelihood: -180.6507 for lag model #> ML residual variance (sigma squared): 93.22, (sigma: 9.655) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 371.3, (AIC for lm: 382.75) #> LM test for residual autocorrelation #> test value: 0.006827, p-value: 0.93415 #>  COL.mixed.B <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  spdep::nb2listw(COL.nb, style=\"B\"), type=\"mixed\", tol.solve=1e-9,  control=list(pre_eig=ev)) summary(COL.mixed.B) #>  #> Call: #> lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,  #>     style = \"B\"), type = \"mixed\", tol.solve = 1e-09, control = list(pre_eig = ev)) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -34.8460  -4.2057  -0.1195   4.6525  21.6112  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>                    Estimate  Std. Error z value  Pr(>|z|) #> (Intercept)      5.4215e+01  5.6639e+00  9.5719 < 2.2e-16 #> INC             -8.2386e-01  3.1643e-01 -2.6036 0.0092262 #> HOVAL           -3.0085e-01  8.5629e-02 -3.5134 0.0004424 #> lag.(Intercept) -7.5493e+00  1.7307e+00 -4.3620 1.289e-05 #> lag.INC          2.1531e-05  1.2216e-01  0.0002 0.9998594 #> lag.HOVAL        7.2458e-02  3.9007e-02  1.8576 0.0632281 #>  #> Rho: 0.15212, LR test value: 7.435, p-value: 0.0063967 #> Asymptotic standard error: 0.015565 #>     z-value: 9.7735, p-value: < 2.22e-16 #> Wald statistic: 95.522, p-value: < 2.22e-16 #>  #> Log likelihood: -177.7722 for mixed model #> ML residual variance (sigma squared): 82.502, (sigma: 9.0831) #> Number of observations: 49  #> Number of parameters estimated: 8  #> AIC: 371.54, (AIC for lm: 376.98) #> LM test for residual autocorrelation #> test value: -26.79, p-value: 1 #>  COL.mixed.W <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, type=\"mixed\", control=list(pre_eig=ev)) summary(COL.mixed.W) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     type = \"mixed\", control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.47829  -6.46731  -0.33835   6.05200  22.62969  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 42.822414  12.667204  3.3806 0.0007233 #> INC         -0.914223   0.331094 -2.7612 0.0057586 #> HOVAL       -0.293738   0.089212 -3.2926 0.0009927 #> lag.INC     -0.520284   0.565129 -0.9206 0.3572355 #> lag.HOVAL    0.245640   0.178917  1.3729 0.1697756 #>  #> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494 #> Asymptotic standard error: 0.15623 #>     z-value: 2.7288, p-value: 0.0063561 #> Wald statistic: 7.4465, p-value: 0.0063561 #>  #> Log likelihood: -181.3935 for mixed model #> ML residual variance (sigma squared): 91.791, (sigma: 9.5808) #> Number of observations: 49  #> Number of parameters estimated: 7  #> AIC: 376.79, (AIC for lm: 380.16) #> LM test for residual autocorrelation #> test value: 0.28919, p-value: 0.59074 #>  COL.mixed.D00 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, Durbin=TRUE, control=list(pre_eig=ev)) summary(COL.mixed.D00) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     Durbin = TRUE, control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.47829  -6.46731  -0.33835   6.05200  22.62969  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 42.822414  12.667204  3.3806 0.0007233 #> INC         -0.914223   0.331094 -2.7612 0.0057586 #> HOVAL       -0.293738   0.089212 -3.2926 0.0009927 #> lag.INC     -0.520284   0.565129 -0.9206 0.3572355 #> lag.HOVAL    0.245640   0.178917  1.3729 0.1697756 #>  #> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494 #> Asymptotic standard error: 0.15623 #>     z-value: 2.7288, p-value: 0.0063561 #> Wald statistic: 7.4465, p-value: 0.0063561 #>  #> Log likelihood: -181.3935 for mixed model #> ML residual variance (sigma squared): 91.791, (sigma: 9.5808) #> Number of observations: 49  #> Number of parameters estimated: 7  #> AIC: 376.79, (AIC for lm: 380.16) #> LM test for residual autocorrelation #> test value: 0.28919, p-value: 0.59074 #>  COL.mixed.D01 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, Durbin=FALSE, control=list(pre_eig=ev)) summary(COL.mixed.D01) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     Durbin = FALSE, control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.68585  -5.35636   0.05421   6.02013  23.20555  #>  #> Type: lag  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 45.079249   7.177346  6.2808 3.369e-10 #> INC         -1.031616   0.305143 -3.3808 0.0007229 #> HOVAL       -0.265926   0.088499 -3.0049 0.0026570 #>  #> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588 #> Asymptotic standard error: 0.11768 #>     z-value: 3.6626, p-value: 0.00024962 #> Wald statistic: 13.415, p-value: 0.00024962 #>  #> Log likelihood: -182.3904 for lag model #> ML residual variance (sigma squared): 95.494, (sigma: 9.7721) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 374.78, (AIC for lm: 382.75) #> LM test for residual autocorrelation #> test value: 0.31954, p-value: 0.57188 #>  COL.mixed.D1 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, Durbin= ~ INC + HOVAL, control=list(pre_eig=ev)) summary(COL.mixed.D1) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     Durbin = ~INC + HOVAL, control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.47829  -6.46731  -0.33835   6.05200  22.62969  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 42.822414  12.667204  3.3806 0.0007233 #> INC         -0.914223   0.331094 -2.7612 0.0057586 #> HOVAL       -0.293738   0.089212 -3.2926 0.0009927 #> lag.INC     -0.520284   0.565129 -0.9206 0.3572355 #> lag.HOVAL    0.245640   0.178917  1.3729 0.1697756 #>  #> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494 #> Asymptotic standard error: 0.15623 #>     z-value: 2.7288, p-value: 0.0063561 #> Wald statistic: 7.4465, p-value: 0.0063561 #>  #> Log likelihood: -181.3935 for mixed model #> ML residual variance (sigma squared): 91.791, (sigma: 9.5808) #> Number of observations: 49  #> Number of parameters estimated: 7  #> AIC: 376.79, (AIC for lm: 380.16) #> LM test for residual autocorrelation #> test value: 0.28919, p-value: 0.59074 #>  f <- CRIME ~ INC + HOVAL COL.mixed.D2 <- lagsarlm(f, data=COL.OLD, listw,  Durbin=as.formula(delete.response(terms(f))),  control=list(pre_eig=ev)) summary(COL.mixed.D2) #>  #> Call: #> lagsarlm(formula = f, data = COL.OLD, listw = listw, Durbin = as.formula(delete.response(terms(f))),  #>     control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.47829  -6.46731  -0.33835   6.05200  22.62969  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 42.822414  12.667204  3.3806 0.0007233 #> INC         -0.914223   0.331094 -2.7612 0.0057586 #> HOVAL       -0.293738   0.089212 -3.2926 0.0009927 #> lag.INC     -0.520284   0.565129 -0.9206 0.3572355 #> lag.HOVAL    0.245640   0.178917  1.3729 0.1697756 #>  #> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494 #> Asymptotic standard error: 0.15623 #>     z-value: 2.7288, p-value: 0.0063561 #> Wald statistic: 7.4465, p-value: 0.0063561 #>  #> Log likelihood: -181.3935 for mixed model #> ML residual variance (sigma squared): 91.791, (sigma: 9.5808) #> Number of observations: 49  #> Number of parameters estimated: 7  #> AIC: 376.79, (AIC for lm: 380.16) #> LM test for residual autocorrelation #> test value: 0.28919, p-value: 0.59074 #>  COL.mixed.D1a <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, Durbin= ~ INC, control=list(pre_eig=ev)) summary(COL.mixed.D1a) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     Durbin = ~INC, control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.82800  -5.85207   0.12047   6.00137  23.19963  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 48.814687  12.198232  4.0018 6.287e-05 #> INC         -1.006620   0.330641 -3.0445  0.002331 #> HOVAL       -0.265514   0.088768 -2.9911  0.002780 #> lag.INC     -0.186684   0.530550 -0.3519  0.724936 #>  #> Rho: 0.39229, LR test value: 4.5007, p-value: 0.033881 #> Asymptotic standard error: 0.1561 #>     z-value: 2.513, p-value: 0.011971 #> Wald statistic: 6.3151, p-value: 0.011971 #>  #> Log likelihood: -182.3328 for mixed model #> ML residual variance (sigma squared): 96.122, (sigma: 9.8042) #> Number of observations: 49  #> Number of parameters estimated: 6  #> AIC: 376.67, (AIC for lm: 379.17) #> LM test for residual autocorrelation #> test value: 2.6134, p-value: 0.10596 #>  try(COL.mixed.D1 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, Durbin= ~ inc + HOVAL, control=list(pre_eig=ev))) #> Error in eval(predvars, data, env) : object 'inc' not found try(COL.mixed.D1 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, Durbin= ~ DISCBD + HOVAL, control=list(pre_eig=ev))) #> Error in lagsarlm(CRIME ~ INC + HOVAL, data = COL.OLD, listw, Durbin = ~DISCBD +  :  #>   WX variables not in X: DISCBD NA.COL.OLD <- COL.OLD NA.COL.OLD$CRIME[20:25] <- NA COL.lag.NA <- lagsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,  listw, na.action=na.exclude) COL.lag.NA$na.action #> 1020 1021 1022 1023 1024 1025  #>   20   21   22   23   24   25  #> attr(,\"class\") #> [1] \"exclude\" COL.lag.NA #>  #> Call: #> lagsarlm(formula = CRIME ~ INC + HOVAL, data = NA.COL.OLD, listw = listw,  #>     na.action = na.exclude) #> Type: lag  #>  #> Coefficients: #>         rho (Intercept)         INC       HOVAL  #>   0.4537820  43.1054975  -0.9267352  -0.2715541  #>  #> Log likelihood: -160.8867  resid(COL.lag.NA) #>        1001        1002        1003        1004        1005        1006  #>  -4.4352945 -13.2750948  -2.9233555 -37.3067542   1.3568011  -3.8828027  #>        1007        1008        1009        1010        1011        1012  #>   5.9980436 -12.8113318  -4.0482558  18.1813323   5.9714203   1.0035599  #>        1013        1014        1015        1016        1017        1018  #>  -1.7490666  -1.7490651   5.8456328  10.1074158  -4.3706895   3.3713771  #>        1019        1020        1021        1022        1023        1024  #>  -4.0823022          NA          NA          NA          NA          NA  #>        1025        1026        1027        1028        1029        1030  #>          NA  -6.0553296 -11.5813311  -8.0011389  -1.9047478   3.9744243  #>        1031        1032        1033        1034        1035        1036  #>   4.8148614   6.0673483  10.2059847  22.7419913  -2.0830998   0.1422777  #>        1037        1038        1039        1040        1041        1042  #>   8.6436388   8.8150864   6.4974685  15.4121789   9.4182148   5.6427603  #>        1043        1044        1045        1046        1047        1048  #>  -7.5727123  -7.5983733  -9.7792620 -10.0870764  -3.1242393   3.4921796  #>        1049  #>   0.7173251  COL.lag.NA1 <- lagsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,  listw, Durbin=~INC) # https://github.com/r-spatial/spatialreg/issues/10 COL.lag.NA1$na.action #> 1020 1021 1022 1023 1024 1025  #>   20   21   22   23   24   25  #> attr(,\"class\") #> [1] \"omit\" COL.lag.NA2 <- lagsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,  listw, Durbin=~INC, na.action=na.exclude) COL.lag.NA2$na.action #> 1020 1021 1022 1023 1024 1025  #>   20   21   22   23   24   25  #> attr(,\"class\") #> [1] \"exclude\" # https://github.com/r-spatial/spatialreg/issues/11 COL.lag.NA3 <- lagsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,  listw, control=list(pre_eig=ev)) #> Warning: NAs found, precomputed eigenvalues ignored COL.lag.NA3$na.action #> 1020 1021 1022 1023 1024 1025  #>   20   21   22   23   24   25  #> attr(,\"class\") #> [1] \"omit\" # }  # \\dontrun{ data(boston, package=\"spData\") gp2mM <- lagsarlm(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +  I(RM^2) +  AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),  data=boston.c, spdep::nb2listw(boston.soi), type=\"mixed\", method=\"Matrix\") summary(gp2mM) #>  #> Call:lagsarlm(formula = log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +  #>     I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B +  #>     log(LSTAT), data = boston.c, listw = spdep::nb2listw(boston.soi),  #>     type = \"mixed\", method = \"Matrix\") #>  #> Residuals: #>        Min         1Q     Median         3Q        Max  #> -0.6316833 -0.0629790 -0.0090776  0.0682421  0.6991072  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>                   Estimate  Std. Error  z value  Pr(>|z|) #> (Intercept)     1.89816225  0.22759605   8.3400 < 2.2e-16 #> CRIM           -0.00571021  0.00093504  -6.1069 1.016e-09 #> ZN              0.00069091  0.00051869   1.3320  0.182851 #> INDUS          -0.00111343  0.00307354  -0.3623  0.717155 #> CHAS1          -0.04163225  0.02739364  -1.5198  0.128567 #> I(NOX^2)       -0.01034950  0.19360214  -0.0535  0.957367 #> I(RM^2)         0.00794979  0.00102063   7.7891 6.661e-15 #> AGE            -0.00128789  0.00048920  -2.6326  0.008473 #> log(DIS)       -0.12404108  0.09510940  -1.3042  0.192168 #> log(RAD)        0.05863502  0.02257078   2.5978  0.009382 #> TAX            -0.00049084  0.00012145  -4.0416 5.308e-05 #> PTRATIO        -0.01319853  0.00595352  -2.2169  0.026628 #> B               0.00056383  0.00011089   5.0847 3.682e-07 #> log(LSTAT)     -0.24724454  0.02262033 -10.9302 < 2.2e-16 #> lag.CRIM       -0.00464215  0.00172935  -2.6843  0.007267 #> lag.ZN         -0.00037937  0.00070584  -0.5375  0.590940 #> lag.INDUS       0.00025064  0.00385901   0.0649  0.948215 #> lag.CHAS1       0.12518252  0.04071559   3.0746  0.002108 #> lag.I(NOX^2)   -0.38640403  0.22157523  -1.7439  0.081177 #> lag.I(RM^2)    -0.00451252  0.00153180  -2.9459  0.003220 #> lag.AGE         0.00149678  0.00068418   2.1877  0.028693 #> lag.log(DIS)   -0.00453785  0.10046478  -0.0452  0.963973 #> lag.log(RAD)   -0.00940702  0.03104930  -0.3030  0.761912 #> lag.TAX         0.00041083  0.00017867   2.2994  0.021481 #> lag.PTRATIO     0.00060355  0.00788837   0.0765  0.939012 #> lag.B          -0.00050781  0.00014155  -3.5874  0.000334 #> lag.log(LSTAT)  0.09846781  0.03399423   2.8966  0.003772 #>  #> Rho: 0.59578, LR test value: 181.68, p-value: < 2.22e-16 #> Asymptotic standard error: 0.038445 #>     z-value: 15.497, p-value: < 2.22e-16 #> Wald statistic: 240.16, p-value: < 2.22e-16 #>  #> Log likelihood: 300.6131 for mixed model #> ML residual variance (sigma squared): 0.016011, (sigma: 0.12654) #> Number of observations: 506  #> Number of parameters estimated: 29  #> AIC: -543.23, (AIC for lm: -363.55) #> LM test for residual autocorrelation #> test value: 29.772, p-value: 4.8604e-08 #>  W <- as(spdep::nb2listw(boston.soi), \"CsparseMatrix\") trMatb <- trW(W, type=\"mult\") gp2mMi <- lagsarlm(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +  I(RM^2) +  AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),  data=boston.c, spdep::nb2listw(boston.soi), type=\"mixed\", method=\"Matrix\",  trs=trMatb) summary(gp2mMi) #>  #> Call:lagsarlm(formula = log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +  #>     I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B +  #>     log(LSTAT), data = boston.c, listw = spdep::nb2listw(boston.soi),  #>     type = \"mixed\", method = \"Matrix\", trs = trMatb) #>  #> Residuals: #>        Min         1Q     Median         3Q        Max  #> -0.6316833 -0.0629790 -0.0090776  0.0682421  0.6991072  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>                   Estimate  Std. Error  z value  Pr(>|z|) #> (Intercept)     1.89816225  0.22759605   8.3400 < 2.2e-16 #> CRIM           -0.00571021  0.00093504  -6.1069 1.016e-09 #> ZN              0.00069091  0.00051869   1.3320  0.182851 #> INDUS          -0.00111343  0.00307354  -0.3623  0.717155 #> CHAS1          -0.04163225  0.02739364  -1.5198  0.128567 #> I(NOX^2)       -0.01034950  0.19360214  -0.0535  0.957367 #> I(RM^2)         0.00794979  0.00102063   7.7891 6.661e-15 #> AGE            -0.00128789  0.00048920  -2.6326  0.008473 #> log(DIS)       -0.12404108  0.09510940  -1.3042  0.192168 #> log(RAD)        0.05863502  0.02257078   2.5978  0.009382 #> TAX            -0.00049084  0.00012145  -4.0416 5.308e-05 #> PTRATIO        -0.01319853  0.00595352  -2.2169  0.026628 #> B               0.00056383  0.00011089   5.0847 3.682e-07 #> log(LSTAT)     -0.24724454  0.02262033 -10.9302 < 2.2e-16 #> lag.CRIM       -0.00464215  0.00172935  -2.6843  0.007267 #> lag.ZN         -0.00037937  0.00070584  -0.5375  0.590940 #> lag.INDUS       0.00025064  0.00385901   0.0649  0.948215 #> lag.CHAS1       0.12518252  0.04071559   3.0746  0.002108 #> lag.I(NOX^2)   -0.38640403  0.22157523  -1.7439  0.081177 #> lag.I(RM^2)    -0.00451252  0.00153180  -2.9459  0.003220 #> lag.AGE         0.00149678  0.00068418   2.1877  0.028693 #> lag.log(DIS)   -0.00453785  0.10046478  -0.0452  0.963973 #> lag.log(RAD)   -0.00940702  0.03104930  -0.3030  0.761912 #> lag.TAX         0.00041083  0.00017867   2.2994  0.021481 #> lag.PTRATIO     0.00060355  0.00788837   0.0765  0.939012 #> lag.B          -0.00050781  0.00014155  -3.5874  0.000334 #> lag.log(LSTAT)  0.09846781  0.03399423   2.8966  0.003772 #>  #> Rho: 0.59578, LR test value: 181.68, p-value: < 2.22e-16 #> Asymptotic standard error: 0.038445 #>     z-value: 15.497, p-value: < 2.22e-16 #> Wald statistic: 240.16, p-value: < 2.22e-16 #>  #> Log likelihood: 300.6131 for mixed model #> ML residual variance (sigma squared): 0.016011, (sigma: 0.12654) #> Number of observations: 506  #> Number of parameters estimated: 29  #> AIC: -543.23, (AIC for lm: -363.55) #> LM test for residual autocorrelation #> test value: 29.772, p-value: 4.8604e-08 #>  # } COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, quiet=FALSE, control=list(pre_eig=ev)) #>  #> Spatial autoregressive error model #>  #> Jacobian calculated using neighbourhood matrix eigenvalues #>  #> lambda: -0.5674437  function: -195.8051  Jacobian: -1.636549  SSE: 7936.201  #> lambda: 0.03126655  function: -187.0219  Jacobian: -0.005318373  SSE: 5927.009  #> lambda: 0.4012898  function: -183.8422  Jacobian: -0.9953987  SSE: 4999.419  #> lambda: 0.6299767  function: -183.4895  Jacobian: -2.818134  SSE: 4574.641  #> lambda: 0.5811116  function: -183.3887  Jacobian: -2.314073  SSE: 4650.566  #> lambda: 0.554104  function: -183.3817  Jacobian: -2.066354  SSE: 4696.49  #> lambda: 0.5621834  function: -183.3805  Jacobian: -2.138326  SSE: 4682.474  #> lambda: 0.5617028  function: -183.3805  Jacobian: -2.133995  SSE: 4683.301  #> lambda: 0.5617888  function: -183.3805  Jacobian: -2.134769  SSE: 4683.153  #> lambda: 0.5617902  function: -183.3805  Jacobian: -2.134782  SSE: 4683.151  #> lambda: 0.5617903  function: -183.3805  Jacobian: -2.134782  SSE: 4683.151  #> lambda: 0.5617902  function: -183.3805  Jacobian: -2.134782  SSE: 4683.151  #> lambda: 0.5617902  function: -183.3805  Jacobian: -2.134782  SSE: 4683.151  summary(COL.errW.eig) #>  #> Call:errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     quiet = FALSE, control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -34.81174  -6.44031  -0.72142   7.61476  23.33626  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 59.893220   5.366162 11.1613 < 2.2e-16 #> INC         -0.941312   0.330569 -2.8476 0.0044057 #> HOVAL       -0.302250   0.090476 -3.3407 0.0008358 #>  #> Lambda: 0.56179, LR test value: 7.9935, p-value: 0.0046945 #> Asymptotic standard error: 0.13387 #>     z-value: 4.1966, p-value: 2.7098e-05 #> Wald statistic: 17.611, p-value: 2.7098e-05 #>  #> Log likelihood: -183.3805 for error model #> ML residual variance (sigma squared): 95.575, (sigma: 9.7762) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 376.76, (AIC for lm: 382.75) #>  COL.errW.eig_ev <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, control=list(pre_eig=ev)) all.equal(coefficients(COL.errW.eig), coefficients(COL.errW.eig_ev)) #> [1] TRUE COL.errB.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  spdep::nb2listw(COL.nb, style=\"B\")) summary(COL.errB.eig) #>  #> Call: #> errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,  #>     style = \"B\")) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -32.19010  -5.22646  -0.69952   7.92588  24.23511  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 55.383119   5.449775 10.1625 < 2.2e-16 #> INC         -0.936595   0.319355 -2.9328 0.0033596 #> HOVAL       -0.299857   0.088678 -3.3814 0.0007212 #>  #> Lambda: 0.12686, LR test value: 10.654, p-value: 0.0010983 #> Asymptotic standard error: 0.021745 #>     z-value: 5.8342, p-value: 5.4044e-09 #> Wald statistic: 34.038, p-value: 5.4044e-09 #>  #> Log likelihood: -182.0502 for error model #> ML residual variance (sigma squared): 88.744, (sigma: 9.4204) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 374.1, (AIC for lm: 382.75) #>  COL.errW.M <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"Matrix\", quiet=FALSE, trs=trMatc) #>  #> Spatial autoregressive error model #>  #> Jacobian calculated using sparse matrix Cholesky decomposition #> lambda: -0.2364499  function: -190.4287  Jacobian: -0.2899343  SSE: 6732.556  #> lambda: 0.2354499  function: -185.0024  Jacobian: -0.3201148  SSE: 5388.346  #> lambda: 0.5271001  function: -183.4053  Jacobian: -1.838306  SSE: 4744.975  #> lambda: 0.728364  function: -184.1244  Jacobian: -4.106761  SSE: 4454.203  #> lambda: 0.5304163  function: -183.4009  Jacobian: -1.865308  SSE: 4738.889  #> lambda: 0.5557478  function: -183.3812  Jacobian: -2.080853  SSE: 4693.62  #> lambda: 0.6216813  function: -183.4637  Jacobian: -2.727084  SSE: 4586.84  #> lambda: 0.5627129  function: -183.3805  Jacobian: -2.143105  SSE: 4681.563  #> lambda: 0.5618852  function: -183.3805  Jacobian: -2.135638  SSE: 4682.987  #> lambda: 0.5617866  function: -183.3805  Jacobian: -2.134749  SSE: 4683.157  #> lambda: 0.5617903  function: -183.3805  Jacobian: -2.134783  SSE: 4683.15  #> lambda: 0.5617903  function: -183.3805  Jacobian: -2.134782  SSE: 4683.151  #> lambda: 0.5617903  function: -183.3805  Jacobian: -2.134782  SSE: 4683.151  #> lambda: 0.5617903  function: -183.3805  Jacobian: -2.134783  SSE: 4683.151  #> lambda: 0.5617903  function: -183.3805  Jacobian: -2.134783  SSE: 4683.151  #> lambda: 0.5617903  function: -183.3805  Jacobian: -2.134783  SSE: 4683.151  summary(COL.errW.M) #>  #> Call:errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     method = \"Matrix\", quiet = FALSE, trs = trMatc) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -34.81174  -6.44031  -0.72142   7.61476  23.33626  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 59.893219   5.366163 11.1613 < 2.2e-16 #> INC         -0.941312   0.330569 -2.8476 0.0044057 #> HOVAL       -0.302250   0.090476 -3.3407 0.0008358 #>  #> Lambda: 0.56179, LR test value: 7.9935, p-value: 0.0046945 #> Asymptotic standard error: 0.13387 #>     z-value: 4.1966, p-value: 2.7098e-05 #> Wald statistic: 17.611, p-value: 2.7098e-05 #>  #> Log likelihood: -183.3805 for error model #> ML residual variance (sigma squared): 95.575, (sigma: 9.7762) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 376.76, (AIC for lm: 382.75) #>  COL.SDEM.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, etype=\"emixed\", control=list(pre_eig=ev)) summary(COL.SDEM.eig) #>  #> Call:errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     etype = \"emixed\", control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.31635  -6.54376  -0.22212   6.44591  23.15801  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 73.545133   8.783543  8.3731 < 2.2e-16 #> INC         -1.051673   0.319514 -3.2915 0.0009966 #> HOVAL       -0.275608   0.091151 -3.0236 0.0024976 #> lag.INC     -1.156711   0.578629 -1.9991 0.0456024 #> lag.HOVAL    0.111691   0.198993  0.5613 0.5746048 #>  #> Lambda: 0.4254, LR test value: 4.9871, p-value: 0.025537 #> Asymptotic standard error: 0.15842 #>     z-value: 2.6852, p-value: 0.0072485 #> Wald statistic: 7.2103, p-value: 0.0072485 #>  #> Log likelihood: -181.5846 for error model #> ML residual variance (sigma squared): 92.531, (sigma: 9.6193) #> Number of observations: 49  #> Number of parameters estimated: 7  #> AIC: 377.17, (AIC for lm: 380.16) #>  # \\dontrun{ COL.SDEM.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, Durbin=TRUE, control=list(pre_eig=ev)) summary(COL.SDEM.eig) #>  #> Call:errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     Durbin = TRUE, control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.31635  -6.54376  -0.22212   6.44591  23.15801  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 73.545133   8.783543  8.3731 < 2.2e-16 #> INC         -1.051673   0.319514 -3.2915 0.0009966 #> HOVAL       -0.275608   0.091151 -3.0236 0.0024976 #> lag.INC     -1.156711   0.578629 -1.9991 0.0456024 #> lag.HOVAL    0.111691   0.198993  0.5613 0.5746048 #>  #> Lambda: 0.4254, LR test value: 4.9871, p-value: 0.025537 #> Asymptotic standard error: 0.15842 #>     z-value: 2.6852, p-value: 0.0072485 #> Wald statistic: 7.2103, p-value: 0.0072485 #>  #> Log likelihood: -181.5846 for error model #> ML residual variance (sigma squared): 92.531, (sigma: 9.6193) #> Number of observations: 49  #> Number of parameters estimated: 7  #> AIC: 377.17, (AIC for lm: 380.16) #>  COL.SDEM.eig <- errorsarlm(CRIME ~ DISCBD + INC + HOVAL, data=COL.OLD,  listw, Durbin=~INC, control=list(pre_eig=ev)) summary(COL.SDEM.eig) #>  #> Call:errorsarlm(formula = CRIME ~ DISCBD + INC + HOVAL, data = COL.OLD,  #>     listw = listw, Durbin = ~INC, control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -34.61867  -7.31993   0.82879   5.92877  17.82211  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 68.961912   6.985784  9.8717 < 2.2e-16 #> DISCBD      -5.412936   2.009281 -2.6940  0.007061 #> INC         -0.899425   0.315174 -2.8537  0.004321 #> HOVAL       -0.202846   0.090125 -2.2507  0.024403 #> lag.INC      0.161858   0.603859  0.2680  0.788669 #>  #> Lambda: 0.24524, LR test value: 1.2719, p-value: 0.25942 #> Asymptotic standard error: 0.18393 #>     z-value: 1.3334, p-value: 0.18241 #> Wald statistic: 1.7778, p-value: 0.18241 #>  #> Log likelihood: -178.9895 for error model #> ML residual variance (sigma squared): 85.935, (sigma: 9.2701) #> Number of observations: 49  #> Number of parameters estimated: 7  #> AIC: 371.98, (AIC for lm: 371.25) #>  summary(impacts(COL.SDEM.eig)) #> Impact measures (SDEM, glht, n): #>            Direct  Indirect      Total #> DISCBD -5.4129365        NA -5.4129365 #> INC    -0.8994251 0.1618581 -0.7375670 #> HOVAL  -0.2028457        NA -0.2028457 #> ======================================================== #> Standard errors: #>            Direct  Indirect      Total #> DISCBD 2.00928140        NA 2.00928140 #> INC    0.31517363 0.6038588 0.67559401 #> HOVAL  0.09012493        NA 0.09012493 #> ======================================================== #> Z-values: #>           Direct  Indirect     Total #> DISCBD -2.693966        NA -2.693966 #> INC    -2.853745 0.2680396 -1.091731 #> HOVAL  -2.250717        NA -2.250717 #>  #> p-values: #>        Direct    Indirect Total     #> DISCBD 0.0070607 NA       0.0070607 #> INC    0.0043207 0.78867  0.2749513 #> HOVAL  0.0244035 NA       0.0244035 #>  NA.COL.OLD <- COL.OLD NA.COL.OLD$CRIME[20:25] <- NA COL.err.NA <- errorsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,  listw, na.action=na.exclude) COL.err.NA$na.action #> 1020 1021 1022 1023 1024 1025  #>   20   21   22   23   24   25  #> attr(,\"class\") #> [1] \"exclude\" COL.err.NA #>  #> Call: #> errorsarlm(formula = CRIME ~ INC + HOVAL, data = NA.COL.OLD,  #>     listw = listw, na.action = na.exclude) #> Type: error  #>  #> Coefficients: #>      lambda (Intercept)         INC       HOVAL  #>   0.5748430  58.2460528  -0.8473028  -0.3024909  #>  #> Log likelihood: -161.8763  resid(COL.err.NA) #>         1001         1002         1003         1004         1005         1006  #>  -4.18270830 -11.44133843   0.31874928 -34.47163074   2.42244758  -4.32095072  #>         1007         1008         1009         1010         1011         1012  #>   8.66744165 -13.38669934  -1.92276585  17.85753950  -1.11484596  -2.30434792  #>         1013         1014         1015         1016         1017         1018  #>  -8.16935116  -5.80500231   0.14973721   5.93191445  -7.03028271   2.39112829  #>         1019         1020         1021         1022         1023         1024  #>  -8.95099917           NA           NA           NA           NA           NA  #>         1025         1026         1027         1028         1029         1030  #>           NA  -2.52940712  -9.60025384  -6.95635586  -0.43630579   5.98493664  #>         1031         1032         1033         1034         1035         1036  #>   6.25882669   7.75527032  10.83413236  23.23927250  -0.05594957   1.43808573  #>         1037         1038         1039         1040         1041         1042  #>   9.51995266  12.18295373   8.31031724  17.06834503   7.04418393   7.50088924  #>         1043         1044         1045         1046         1047         1048  #>  -7.78485976  -6.79207447  -7.94977534 -11.25362117  -5.68994630   5.04837399  #>         1049  #>   2.22497381  print(system.time(ev <- eigenw(similar.listw(listw)))) #>    user  system elapsed  #>   0.001   0.000   0.001  print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"eigen\", control=list(pre_eig=ev)))) #>    user  system elapsed  #>   0.165   0.000   0.166  ocoef <- coefficients(COL.errW.eig) print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"eigen\", control=list(pre_eig=ev, LAPACK=FALSE)))) #>    user  system elapsed  #>   0.161   0.000   0.161  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"eigen\", control=list(pre_eig=ev, compiled_sse=TRUE)))) #>    user  system elapsed  #>   0.160   0.000   0.161  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"Matrix_J\", control=list(super=TRUE)))) #> Warning: the default value of argument 'sqrt' of method 'determinant(, )' may change from TRUE to FALSE as soon as the next release of Matrix; set 'sqrt' when programming #>    user  system elapsed  #>   0.185   0.000   0.186  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"Matrix_J\", control=list(super=FALSE)))) #>    user  system elapsed  #>   0.177   0.000   0.178  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"Matrix_J\", control=list(super=as.logical(NA))))) #>    user  system elapsed  #>   0.178   0.000   0.178  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"Matrix\", control=list(super=TRUE)))) #>    user  system elapsed  #>   0.169   0.000   0.169  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"Matrix\", control=list(super=FALSE)))) #>    user  system elapsed  #>   0.164   0.000   0.165  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"Matrix\", control=list(super=as.logical(NA))))) #>    user  system elapsed  #>   0.165   0.000   0.166  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"spam\", control=list(spamPivot=\"MMD\")))) #>    user  system elapsed  #>   0.175   0.001   0.176  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"spam\", control=list(spamPivot=\"RCM\")))) #>    user  system elapsed  #>   0.184   0.000   0.184  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"spam_update\", control=list(spamPivot=\"MMD\")))) #>    user  system elapsed  #>   0.216   0.000   0.216  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, method=\"spam_update\", control=list(spamPivot=\"RCM\")))) #>    user  system elapsed  #>   0.182   0.000   0.183  print(all.equal(ocoef, coefficients(COL.errW.eig))) #> [1] TRUE # } COL.sacW.eig <- sacsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, listw,  control=list(pre_eig1=ev, pre_eig2=ev)) summary(COL.sacW.eig) #>  #> Call:sacsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     control = list(pre_eig1 = ev, pre_eig2 = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.32081  -5.33662  -0.20219   6.59672  23.25604  #>  #> Type: sac  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 47.783766   9.902659  4.8253 1.398e-06 #> INC         -1.025894   0.326326 -3.1438  0.001668 #> HOVAL       -0.281651   0.090033 -3.1283  0.001758 #>  #> Rho: 0.36807 #> Asymptotic standard error: 0.19668 #>     z-value: 1.8714, p-value: 0.061285 #> Lambda: 0.16668 #> Asymptotic standard error: 0.29661 #>     z-value: 0.56196, p-value: 0.57415 #>  #> LR test value: 10.285, p-value: 0.0058432 #>  #> Log likelihood: -182.2348 for sac model #> ML residual variance (sigma squared): 95.604, (sigma: 9.7777) #> Number of observations: 49  #> Number of parameters estimated: 6  #> AIC: 376.47, (AIC for lm: 382.75) #>  set.seed(1) summary(impacts(COL.sacW.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE) #> Impact measures (sac, trace): #>           Direct   Indirect      Total #> INC   -1.0632723 -0.5601501 -1.6234223 #> HOVAL -0.2919129 -0.1537847 -0.4456977 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3200735 0.8453130 0.9606199 #> HOVAL 0.0947660 0.2823186 0.3278763 #>  #> Simulated z-values: #>          Direct   Indirect     Total #> INC   -3.376570 -0.8371024 -1.861677 #> HOVAL -3.159909 -0.7431009 -1.553156 #>  #> Simulated p-values: #>       Direct     Indirect Total    #> INC   0.00073396 0.40254  0.062649 #> HOVAL 0.00157818 0.45742  0.120386 COL.msacW.eig <- sacsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, listw,  type=\"sacmixed\", control=list(pre_eig1=ev, pre_eig2=ev)) summary(COL.msacW.eig) #>  #> Call:sacsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     type = \"sacmixed\", control = list(pre_eig1 = ev, pre_eig2 = ev)) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -37.8045  -6.5244  -0.2207   5.9944  22.8691  #>  #> Type: sacmixed  #> Coefficients: (asymptotic standard errors)  #>             Estimate Std. Error z value Pr(>|z|) #> (Intercept) 50.92026   68.25722  0.7460 0.455664 #> INC         -0.95072    0.44033 -2.1591 0.030841 #> HOVAL       -0.28650    0.09994 -2.8667 0.004148 #> lag.INC     -0.69261    1.69113 -0.4096 0.682132 #> lag.HOVAL    0.20852    0.28702  0.7265 0.467546 #>  #> Rho: 0.31557 #> Asymptotic standard error: 0.94581 #>     z-value: 0.33365, p-value: 0.73864 #> Lambda: 0.15415 #> Asymptotic standard error: 1.0643 #>     z-value: 0.14484, p-value: 0.88484 #>  #> LR test value: 12.07, p-value: 0.016837 #>  #> Log likelihood: -181.3422 for sacmixed model #> ML residual variance (sigma squared): 93.149, (sigma: 9.6514) #> Number of observations: 49  #> Number of parameters estimated: 8  #> AIC: 378.68, (AIC for lm: 382.75) #>  set.seed(1) summary(impacts(COL.msacW.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE) #> Impact measures (sacmixed, trace): #>           Direct   Indirect      Total #> INC   -1.0317003 -1.3693141 -2.4010144 #> HOVAL -0.2768608  0.1629265 -0.1139344 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct Indirect     Total #> INC   0.3799971 2.356727 2.5113549 #> HOVAL 0.1091241 0.761200 0.8220231 #>  #> Simulated z-values: #>          Direct   Indirect       Total #> INC   -2.706969 -0.6434228 -1.01340192 #> HOVAL -2.478740  0.2512075 -0.09643407 #>  #> Simulated p-values: #>       Direct    Indirect Total   #> INC   0.0067901 0.51995  0.31087 #> HOVAL 0.0131847 0.80165  0.92318 COL.msacW1.eig <- sacsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, listw,  Durbin=TRUE, control=list(pre_eig1=ev, pre_eig2=ev)) summary(COL.msacW1.eig) #>  #> Call:sacsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     Durbin = TRUE, control = list(pre_eig1 = ev, pre_eig2 = ev)) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -37.8045  -6.5244  -0.2207   5.9944  22.8691  #>  #> Type: sacmixed  #> Coefficients: (asymptotic standard errors)  #>             Estimate Std. Error z value Pr(>|z|) #> (Intercept) 50.92026   68.25722  0.7460 0.455664 #> INC         -0.95072    0.44033 -2.1591 0.030841 #> HOVAL       -0.28650    0.09994 -2.8667 0.004148 #> lag.INC     -0.69261    1.69113 -0.4096 0.682132 #> lag.HOVAL    0.20852    0.28702  0.7265 0.467546 #>  #> Rho: 0.31557 #> Asymptotic standard error: 0.94581 #>     z-value: 0.33365, p-value: 0.73864 #> Lambda: 0.15415 #> Asymptotic standard error: 1.0643 #>     z-value: 0.14484, p-value: 0.88484 #>  #> LR test value: 12.07, p-value: 0.016837 #>  #> Log likelihood: -181.3422 for sacmixed model #> ML residual variance (sigma squared): 93.149, (sigma: 9.6514) #> Number of observations: 49  #> Number of parameters estimated: 8  #> AIC: 378.68, (AIC for lm: 382.75) #>  set.seed(1) summary(impacts(COL.msacW1.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE) #> Impact measures (sacmixed, trace): #>           Direct   Indirect      Total #> INC   -1.0317003 -1.3693141 -2.4010144 #> HOVAL -0.2768608  0.1629265 -0.1139344 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct Indirect     Total #> INC   0.3799971 2.356727 2.5113549 #> HOVAL 0.1091241 0.761200 0.8220231 #>  #> Simulated z-values: #>          Direct   Indirect       Total #> INC   -2.706969 -0.6434228 -1.01340192 #> HOVAL -2.478740  0.2512075 -0.09643407 #>  #> Simulated p-values: #>       Direct    Indirect Total   #> INC   0.0067901 0.51995  0.31087 #> HOVAL 0.0131847 0.80165  0.92318 COL.msacW2.eig <- sacsarlm(CRIME ~ DISCBD + INC + HOVAL, data=COL.OLD,   listw, Durbin= ~ INC, control=list(pre_eig1=ev, pre_eig2=ev)) summary(COL.msacW2.eig) #>  #> Call:sacsarlm(formula = CRIME ~ DISCBD + INC + HOVAL, data = COL.OLD,  #>     listw = listw, Durbin = ~INC, control = list(pre_eig1 = ev,  #>         pre_eig2 = ev)) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -34.2794  -7.0786   1.0543   6.0019  17.8891  #>  #> Type: sacmixed  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value Pr(>|z|) #> (Intercept) 74.064502  37.738940  1.9625 0.049699 #> DISCBD      -5.707678   3.248629 -1.7569 0.078926 #> INC         -0.900975   0.314996 -2.8603 0.004233 #> HOVAL       -0.203399   0.092982 -2.1875 0.028705 #> lag.INC      0.061568   0.926947  0.0664 0.947043 #>  #> Rho: -0.077599 #> Asymptotic standard error: 0.57955 #>     z-value: -0.1339, p-value: 0.89348 #> Lambda: 0.29646 #> Asymptotic standard error: 0.51021 #>     z-value: 0.58104, p-value: 0.56121 #>  #> LR test value: 1.4982, p-value: 0.68269 #>  #> Log likelihood: -178.963 for sacmixed model #> ML residual variance (sigma squared): 85.135, (sigma: 9.2269) #> Number of observations: 49  #> Number of parameters estimated: 8  #> AIC: 373.93, (AIC for lm: 369.42) #>  summary(impacts(COL.msacW2.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE) #> Impact measures (sacmixed, trace): #>            Direct   Indirect      Total #> DISCBD -5.7150799 0.41841671 -5.2966632 #> INC    -0.9031729 0.12421198 -0.7789609 #> HOVAL  -0.2036631 0.01491074 -0.1887524 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>           Direct  Indirect    Total #> DISCBD 3.1446963 5.7201657 5.757459 #> INC    0.3621137 1.7150155 1.876353 #> HOVAL  0.1090172 0.6360488 0.698836 #>  #> Simulated z-values: #>           Direct   Indirect      Total #> DISCBD -1.852002  0.0280018 -0.9837341 #> INC    -2.461864  0.1861184 -0.3049951 #> HOVAL  -2.021743 -0.1841543 -0.4829973 #>  #> Simulated p-values: #>        Direct   Indirect Total   #> DISCBD 0.064026 0.97766  0.32525 #> INC    0.013822 0.85235  0.76037 #> HOVAL  0.043203 0.85389  0.62910 # \\dontrun{ COL.mix.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, type=\"mixed\", method=\"eigen\") summary(COL.mix.eig, correlation=TRUE, Nagelkerke=TRUE) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     type = \"mixed\", method = \"eigen\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.47829  -6.46731  -0.33835   6.05200  22.62969  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 42.822413  12.667204  3.3806 0.0007233 #> INC         -0.914223   0.331094 -2.7612 0.0057586 #> HOVAL       -0.293738   0.089212 -3.2926 0.0009927 #> lag.INC     -0.520283   0.565129 -0.9206 0.3572355 #> lag.HOVAL    0.245640   0.178917  1.3729 0.1697756 #>  #> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494 #> Asymptotic standard error: 0.15623 #>     z-value: 2.7288, p-value: 0.0063561 #> Wald statistic: 7.4465, p-value: 0.0063561 #>  #> Log likelihood: -181.3935 for mixed model #> ML residual variance (sigma squared): 91.791, (sigma: 9.5808) #> Nagelkerke pseudo-R-squared: 0.6494  #> Number of observations: 49  #> Number of parameters estimated: 7  #> AIC: 376.79, (AIC for lm: 380.16) #> LM test for residual autocorrelation #> test value: 0.28919, p-value: 0.59074 #>  #>  Correlation of coefficients  #>             sigma rho   (Intercept) INC   HOVAL lag.INC #> rho         -0.18                                       #> (Intercept)  0.16 -0.89                                 #> INC         -0.03  0.14 -0.19                           #> HOVAL        0.02 -0.09  0.03       -0.45               #> lag.INC     -0.09  0.49 -0.53       -0.36  0.05         #> lag.HOVAL   -0.04  0.19 -0.36        0.19 -0.24 -0.41   #>  COL.mix.M <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  listw, type=\"mixed\", method=\"Matrix\") summary(COL.mix.M, correlation=TRUE, Nagelkerke=TRUE) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,  #>     type = \"mixed\", method = \"Matrix\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.47829  -6.46731  -0.33835   6.05200  22.62969  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 42.822416  12.667205  3.3806 0.0007233 #> INC         -0.914223   0.331094 -2.7612 0.0057586 #> HOVAL       -0.293738   0.089212 -3.2926 0.0009927 #> lag.INC     -0.520284   0.565129 -0.9206 0.3572354 #> lag.HOVAL    0.245640   0.178917  1.3729 0.1697756 #>  #> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494 #> Asymptotic standard error: 0.15623 #>     z-value: 2.7288, p-value: 0.0063561 #> Wald statistic: 7.4465, p-value: 0.0063561 #>  #> Log likelihood: -181.3935 for mixed model #> ML residual variance (sigma squared): 91.791, (sigma: 9.5808) #> Nagelkerke pseudo-R-squared: 0.6494  #> Number of observations: 49  #> Number of parameters estimated: 7  #> AIC: 376.79, (AIC for lm: 380.16) #> LM test for residual autocorrelation #> test value: 0.28919, p-value: 0.59074 #>  #>  Correlation of coefficients  #>             sigma rho   (Intercept) INC   HOVAL lag.INC #> rho         -0.18                                       #> (Intercept)  0.16 -0.89                                 #> INC         -0.03  0.14 -0.19                           #> HOVAL        0.02 -0.09  0.03       -0.45               #> lag.INC     -0.09  0.49 -0.53       -0.36  0.05         #> lag.HOVAL   -0.04  0.19 -0.36        0.19 -0.24 -0.41   #>  COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,   spdep::nb2listw(COL.nb, style=\"W\"), method=\"eigen\") summary(COL.errW.eig, correlation=TRUE, Nagelkerke=TRUE, Hausman=TRUE) #>  #> Call: #> errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,  #>     style = \"W\"), method = \"eigen\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -34.81174  -6.44031  -0.72142   7.61476  23.33626  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 59.893219   5.366163 11.1613 < 2.2e-16 #> INC         -0.941312   0.330569 -2.8476 0.0044057 #> HOVAL       -0.302250   0.090476 -3.3407 0.0008358 #>  #> Lambda: 0.56179, LR test value: 7.9935, p-value: 0.0046945 #> Asymptotic standard error: 0.13387 #>     z-value: 4.1966, p-value: 2.7098e-05 #> Wald statistic: 17.611, p-value: 2.7098e-05 #>  #> Log likelihood: -183.3805 for error model #> ML residual variance (sigma squared): 95.575, (sigma: 9.7762) #> Nagelkerke pseudo-R-squared: 0.61978  #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 376.76, (AIC for lm: 382.75) #> Hausman test: 4.902, df: 3, p-value: 0.17911 #>  #>  Correlation of coefficients  #>             sigma lambda (Intercept) INC   #> lambda      -0.24                          #> (Intercept)  0.00  0.00                    #> INC          0.00  0.00  -0.56             #> HOVAL        0.00  0.00  -0.26       -0.45 #>  # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/SET_MCMC.html","id":null,"dir":"Reference","previous_headings":"","what":"Bayesian MCMC spatial simultaneous autoregressive model estimation — spBreg_lag","title":"Bayesian MCMC spatial simultaneous autoregressive model estimation — spBreg_lag","text":"spBreg_lag function early-release version Matlab Spatial Econometrics Toolbox function sar_g.m, using drawing inversion, accommodating heteroskedastic disturbances.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SET_MCMC.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Bayesian MCMC spatial simultaneous autoregressive model estimation — spBreg_lag","text":"","code":"spBreg_lag(formula, data = list(), listw, na.action, Durbin, type,     zero.policy=NULL, control=list()) spBreg_sac(formula, data = list(), listw, listw2=NULL, na.action,      Durbin, type, zero.policy=NULL, control=list()) spBreg_err(formula, data = list(), listw, na.action, Durbin, etype,     zero.policy=NULL, control=list()) # S3 method for class 'MCMC_sar_G' impacts(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL) # S3 method for class 'MCMC_sem_G' impacts(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL) # S3 method for class 'MCMC_sac_G' impacts(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL)"},{"path":"https://r-spatial.github.io/spatialreg/reference/SET_MCMC.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Bayesian MCMC spatial simultaneous autoregressive model estimation — spBreg_lag","text":"formula symbolic description model fit. details model specification given lm() data optional data frame containing variables model. default variables taken environment function called. listw, listw2 listw object created example nb2listw na.action function (default options(\"na.action\")), can also na.omit na.exclude consequences residuals fitted values - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. Durbin default FALSE (spatial lag model); TRUE, full spatial Durbin model; formula object, subset explanatory variables lag type, etype (use ‘Durbin=’ argument - retained backwards compatibility ) default \"lag\", may set \"mixed\"; \"mixed\", lagged intercept dropped spatial weights style \"W\", row-standardised weights, otherwise included; “Durbin” may used instead “mixed” zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE (default) assign NA control list extra control arguments - see section obj spatial regression object ... Arguments passed methods coda package tr vector traces powers spatial weights matrix created using trW, approximate impact measures; given, listw must given exact measures (small moderate spatial weights matrices); traces must spatial weights used fitting spatial regression, must row-standardised evalues vector eigenvalues spatial weights matrix impacts calculations Q default NULL, else integer number cumulative power series impacts calculate tr given","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SET_MCMC.html","id":"control-arguments","dir":"Reference","previous_headings":"","what":"Control arguments","title":"Bayesian MCMC spatial simultaneous autoregressive model estimation — spBreg_lag","text":"tol.opt: desired accuracy optimization - passed optimize() (default=square root double precision machine tolerance, larger root may used needed, see help(boston) example) fdHess: default NULL, set (method != \"eigen\") internally; use fdHess compute approximate Hessian using finite differences using sparse matrix methods; used make coefficient covariance matrix number observations large; may turned save resources need optimHess: default FALSE, use fdHess nlme, TRUE, use optim calculate Hessian optimum optimHessMethod: default “optimHess”, may “nlm” one optim methods compiled_sse: default FALSE; logical value used log likelihood function choose compiled code computing SSE Imult: default 2; used preparing Cholesky decompositions updating Jacobian function super: NULL (default), set FALSE use simplicial decomposition sparse Cholesky decomposition method “Matrix_J”, set  .logical(NA) method “Matrix”, TRUE, use supernodal decomposition cheb_q: default 5; highest power approximating polynomial Chebyshev approximation MC_p: default 16; number random variates MC_m: default 30; number products random variates matrix spatial weights matrix spamPivot: default “MMD”, alternative “RCM” in_coef default 0.1, coefficient value initial Cholesky decomposition “spam_update” type default “MC”, used method “moments”; alternatives “mult” “moments”, use trs missing, trW correct default TRUE, used method “moments” compute Smirnov/Anselin correction term trunc default TRUE, used method “moments” truncate Smirnov/Anselin correction term SE_method default “LU”, may “MC” nrho default 200, SE toolbox; size first stage lndet grid; may reduced example 40 interpn default 2000, SE toolbox; size second stage lndet grid small_asy default TRUE; method “eigen”, use asymmetric covariances rather numerical Hessian ones n <= small small default 1500; threshold number observations asymmetric covariances method “eigen” SElndet default NULL, may used pass pre-computed SE toolbox style matrix coefficients lndet values \"SE_classic\" \"SE_whichMin\" methods LU_order default FALSE; used “LU_prepermutate”, note warnings given lu method pre_eig default NULL; may used pass pre-computed vector eigenvalues OrdVsign default 1; used set sign final component negative -1 (alpha times ((sigma squared) squared) Ord (1975) equation B.1).","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SET_MCMC.html","id":"extra-bayesian-control-arguments","dir":"Reference","previous_headings":"","what":"Extra Bayesian control arguments","title":"Bayesian MCMC spatial simultaneous autoregressive model estimation — spBreg_lag","text":"ldet_method default “SE_classic”; equivalent method argument lagsarlm interval default c(-1, 1); used unmodified set internally jacobianSetup ndraw default 2500L; integer total number draws nomit default 500L; integer total number omitted burn-draws thin default 1L; integer thinning proportion verbose default FALSE; inverse quiet argument lagsarlm detval default NULL; yet use, precomputed matrix log determinants prior list following components: rhoMH, lambdaMH default FALSE; use Metropolis griddy Gibbs Tbeta default NULL; values betas variance-covariance matrix, set diag(k)*1e+12 NULL c_beta default NULL; values betas set 0 NULL rho default 0.5; value autoregressive coefficient sige default 1; value residual variance nu default 0; informative Gamma(nu,d0) prior sige d0 default 0; informative Gamma(nu,d0) prior sige a1 default 1.01; parameter beta(a1,a2) prior rho a2 default 1.01; parameter beta(a1,a2) prior rho cc default 0.2; initial tuning parameter M-H sampling gG_sige default TRUE; include sige lambda griddy Gibbs update cc1 default 0.2; initial tuning parameter M-H sampling cc2 default 0.2; initial tuning parameter M-H sampling","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SET_MCMC.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Bayesian MCMC spatial simultaneous autoregressive model estimation — spBreg_lag","text":"LeSage J RK Pace (2009) Introduction Spatial Econometrics. CRC Press, Boca Raton.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SET_MCMC.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Bayesian MCMC spatial simultaneous autoregressive model estimation — spBreg_lag","text":"Roger Bivand Roger.Bivand@nhh., thanks Abhirup Mallik Virgilio Gómez-Rubio initial coding GSoC 2011","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SET_MCMC.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Bayesian MCMC spatial simultaneous autoregressive model estimation — spBreg_lag","text":"","code":"#require(\"spdep\", quietly=TRUE) data(oldcol, package=\"spdep\") lw <- spdep::nb2listw(COL.nb, style=\"W\") require(\"coda\", quietly=TRUE) set.seed(1) COL.err.Bayes <- spBreg_err(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw) print(summary(COL.err.Bayes)) #>  #> Iterations = 501:2500 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 2000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean       SD Naive SE Time-series SE #> (Intercept)  59.6663  6.99423 0.156396       0.156396 #> INC          -0.9421  0.39894 0.008921       0.008921 #> HOVAL        -0.3011  0.09984 0.002233       0.002233 #> lambda        0.5664  0.15362 0.003435       0.003435 #> sige        115.0482 25.96435 0.580581       0.622638 #>  #> 2. Quantiles for each variable: #>  #>                2.5%     25%      50%      75%    97.5% #> (Intercept) 45.6439 55.3852  60.1164  64.5665  72.1349 #> INC         -1.7360 -1.2047  -0.9445  -0.6803  -0.1379 #> HOVAL       -0.4977 -0.3683  -0.3010  -0.2346  -0.1070 #> lambda       0.2335  0.4717   0.5773   0.6758   0.8309 #> sige        74.4245 96.7013 111.9152 129.2463 176.8133 #>  print(raftery.diag(COL.err.Bayes, r=0.01)) #>  #> Quantile (q) = 0.025 #> Accuracy (r) = +/- 0.01 #> Probability (s) = 0.95  #>                                                     #>              Burn-in  Total Lower bound  Dependence #>              (M)      (N)   (Nmin)       factor (I) #>  (Intercept) 3        1052  937          1.120      #>  INC         2        969   937          1.030      #>  HOVAL       3        1052  937          1.120      #>  lambda      3        1010  937          1.080      #>  sige        2        930   937          0.993      #>  # \\dontrun{ ev <- eigenw(lw) W <- as(lw, \"CsparseMatrix\") trMatc <- trW(W, type=\"mult\") set.seed(1) COL.err.Bayes <- spBreg_err(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw,  control=list(prior=list(lambdaMH=TRUE))) print(summary(COL.err.Bayes)) #>  #> Iterations = 501:2500 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 2000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean      SD Naive SE Time-series SE #> (Intercept)  59.5304  8.9916 0.201059       0.275885 #> INC          -0.9142  0.3969 0.008874       0.011266 #> HOVAL        -0.3027  0.1021 0.002282       0.002282 #> lambda        0.6011  0.1502 0.003358       0.007723 #> sige        116.6773 27.9707 0.625443       0.660902 #>  #> 2. Quantiles for each variable: #>  #>                2.5%    25%      50%      75%    97.5% #> (Intercept) 44.0607 54.802  59.6796  64.2473  72.9189 #> INC         -1.6866 -1.184  -0.9177  -0.6422  -0.1429 #> HOVAL       -0.5102 -0.370  -0.3005  -0.2359  -0.1019 #> lambda       0.2826  0.511   0.6135   0.7023   0.8676 #> sige        74.1788 97.167 113.2955 130.2498 182.6024 #>  print(raftery.diag(COL.err.Bayes, r=0.01)) #>  #> Quantile (q) = 0.025 #> Accuracy (r) = +/- 0.01 #> Probability (s) = 0.95  #>                                                     #>              Burn-in  Total Lower bound  Dependence #>              (M)      (N)   (Nmin)       factor (I) #>  (Intercept) 3        1143  937          1.220      #>  INC         2        969   937          1.030      #>  HOVAL       2        892   937          0.952      #>  lambda      17       4454  937          4.750      #>  sige        2        930   937          0.993      #>  set.seed(1) COL.err.Bayes <- spBreg_err(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw,  Durbin=TRUE) print(summary(COL.err.Bayes)) #>  #> Iterations = 501:2500 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 2000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                  Mean      SD Naive SE Time-series SE #> (Intercept)  72.66146 11.7776 0.263354       0.263354 #> INC          -1.01262  0.3770 0.008430       0.008430 #> HOVAL        -0.28032  0.1057 0.002363       0.002363 #> lag.INC      -1.07754  0.7304 0.016333       0.016333 #> lag.HOVAL     0.09151  0.2395 0.005356       0.005702 #> lambda        0.48878  0.1732 0.003873       0.003873 #> sige        114.61924 26.8321 0.599984       0.653970 #>  #> 2. Quantiles for each variable: #>  #>                2.5%      25%       50%      75%     97.5% #> (Intercept) 48.2063 65.55434  73.00434  80.0130  95.69254 #> INC         -1.7385 -1.27266  -1.01806  -0.7591  -0.25126 #> HOVAL       -0.4883 -0.35221  -0.27730  -0.2111  -0.07194 #> lag.INC     -2.4291 -1.54241  -1.09764  -0.6156   0.38091 #> lag.HOVAL   -0.3892 -0.06269   0.09028   0.2468   0.55625 #> lambda       0.1165  0.37669   0.49775   0.6118   0.79690 #> sige        73.4822 95.76803 110.90096 128.2633 177.00970 #>  print(summary(impacts(COL.err.Bayes))) #> Impact measures (SDEM, MCMC, n): #>           Direct    Indirect     Total #> INC   -1.0126232 -1.07753574 -2.090159 #> HOVAL -0.2803178  0.09150584 -0.188812 #> ======================================================== #> Standard errors: #>          Direct  Indirect     Total #> INC   0.3572678 0.6921465 0.8161704 #> HOVAL 0.1001564 0.2269602 0.2729228 #> ======================================================== #> Z-values: #>          Direct   Indirect      Total #> INC   -2.834354 -1.5568031 -2.5609345 #> HOVAL -2.798799  0.4031801 -0.6918146 #>  #> p-values: #>       Direct    Indirect Total    #> INC   0.0045918 0.11952  0.010439 #> HOVAL 0.0051293 0.68682  0.489054 #>  print(raftery.diag(COL.err.Bayes, r=0.01)) #>  #> Quantile (q) = 0.025 #> Accuracy (r) = +/- 0.01 #> Probability (s) = 0.95  #>                                                     #>              Burn-in  Total Lower bound  Dependence #>              (M)      (N)   (Nmin)       factor (I) #>  (Intercept) 2        930   937          0.993      #>  INC         3        1096  937          1.170      #>  HOVAL       3        1052  937          1.120      #>  lag.INC     2        892   937          0.952      #>  lag.HOVAL   2        930   937          0.993      #>  lambda      2        930   937          0.993      #>  sige        2        930   937          0.993      #>  set.seed(1) COL.err.Bayes <- spBreg_err(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw,  Durbin=TRUE, control=list(prior=list(lambdaMH=TRUE))) print(summary(COL.err.Bayes)) #>  #> Iterations = 501:2500 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 2000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                  Mean      SD Naive SE Time-series SE #> (Intercept)  71.32778 18.0269 0.403094       0.382389 #> INC          -0.99169  0.3978 0.008896       0.008896 #> HOVAL        -0.27840  0.1115 0.002494       0.002494 #> lag.INC      -0.95360  0.8293 0.018543       0.021986 #> lag.HOVAL     0.06812  0.2557 0.005717       0.005904 #> lambda        0.58149  0.1895 0.004238       0.010821 #> sige        119.53101 28.0026 0.626158       0.839390 #>  #> 2. Quantiles for each variable: #>  #>                2.5%      25%       50%      75%     97.5% #> (Intercept) 37.9514 62.67210  72.07446  80.4143  99.84194 #> INC         -1.7844 -1.24565  -0.99600  -0.7380  -0.21146 #> HOVAL       -0.4977 -0.35256  -0.27741  -0.2077  -0.05449 #> lag.INC     -2.4414 -1.50144  -0.99500  -0.4736   0.79318 #> lag.HOVAL   -0.4571 -0.09065   0.07663   0.2398   0.55644 #> lambda       0.1781  0.45916   0.59241   0.7231   0.90210 #> sige        75.6501 99.39723 116.16515 135.1114 184.61449 #>  print(summary(impacts(COL.err.Bayes))) #> Impact measures (SDEM, MCMC, n): #>           Direct    Indirect     Total #> INC   -0.9916937 -0.95359651 -1.945290 #> HOVAL -0.2784029  0.06812087 -0.210282 #> ======================================================== #> Standard errors: #>          Direct  Indirect     Total #> INC   0.3770053 0.7858279 0.9655825 #> HOVAL 0.1056706 0.2422841 0.2998021 #> ======================================================== #> Z-values: #>         Direct   Indirect      Total #> INC   -2.63045 -1.2134929 -2.0146288 #> HOVAL -2.63463  0.2811611 -0.7014028 #>  #> p-values: #>       Direct    Indirect Total    #> INC   0.0085272 0.22494  0.043944 #> HOVAL 0.0084229 0.77859  0.483052 #>  print(raftery.diag(COL.err.Bayes, r=0.01)) #>  #> Quantile (q) = 0.025 #> Accuracy (r) = +/- 0.01 #> Probability (s) = 0.95  #>                                                     #>              Burn-in  Total Lower bound  Dependence #>              (M)      (N)   (Nmin)       factor (I) #>  (Intercept) 4        1192  937          1.270      #>  INC         2        930   937          0.993      #>  HOVAL       2        930   937          0.993      #>  lag.INC     3        1013  937          1.080      #>  lag.HOVAL   2        969   937          1.030      #>  lambda      17       4647  937          4.960      #>  sige        3        1052  937          1.120      #>  set.seed(1) COL.err.Bayes <- spBreg_err(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw,  Durbin=~INC) print(summary(COL.err.Bayes)) #>  #> Iterations = 501:2500 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 2000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean       SD Naive SE Time-series SE #> (Intercept)  74.5397 10.99197 0.245788       0.245788 #> INC          -1.0322  0.38342 0.008574       0.008574 #> HOVAL        -0.2861  0.09986 0.002233       0.002233 #> lag.INC      -0.9210  0.59074 0.013209       0.012745 #> lambda        0.4879  0.17196 0.003845       0.003672 #> sige        112.0817 25.47154 0.569561       0.568218 #>  #> 2. Quantiles for each variable: #>  #>                2.5%     25%      50%      75%     97.5% #> (Intercept) 52.0865 67.8131  74.9358  81.6887  95.01447 #> INC         -1.7848 -1.2893  -1.0382  -0.7802  -0.24806 #> HOVAL       -0.4794 -0.3497  -0.2860  -0.2203  -0.08916 #> lag.INC     -2.0803 -1.3131  -0.9206  -0.5438   0.27869 #> lambda       0.1355  0.3737   0.4987   0.6088   0.80100 #> sige        73.0279 94.1912 108.3141 125.5058 173.13320 #>  print(summary(impacts(COL.err.Bayes))) #> Impact measures (SDEM, MCMC, n): #>           Direct   Indirect      Total #> INC   -1.0321950 -0.9210334 -1.9532284 #> HOVAL -0.2860547         NA -0.2860547 #> ======================================================== #> Standard errors: #>           Direct  Indirect      Total #> INC   0.36744116 0.5661167 0.69838314 #> HOVAL 0.09570117        NA 0.09570117 #> ======================================================== #> Z-values: #>          Direct  Indirect     Total #> INC   -2.809144 -1.626932 -2.796786 #> HOVAL -2.989041        NA -2.989041 #>  #> p-values: #>       Direct    Indirect Total     #> INC   0.0049673 0.10375  0.0051614 #> HOVAL 0.0027985 NA       0.0027985 #>  print(raftery.diag(COL.err.Bayes, r=0.01)) #>  #> Quantile (q) = 0.025 #> Accuracy (r) = +/- 0.01 #> Probability (s) = 0.95  #>                                                     #>              Burn-in  Total Lower bound  Dependence #>              (M)      (N)   (Nmin)       factor (I) #>  (Intercept) 3        1010  937          1.080      #>  INC         2        930   937          0.993      #>  HOVAL       2        930   937          0.993      #>  lag.INC     2        930   937          0.993      #>  lambda      2        892   937          0.952      #>  sige        3        1010  937          1.080      #>  set.seed(1) COL.err.Bayes <- spBreg_err(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw,  Durbin=~INC, control=list(prior=list(lambdaMH=TRUE))) print(summary(COL.err.Bayes)) #>  #> Iterations = 501:2500 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 2000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean       SD Naive SE Time-series SE #> (Intercept)  72.7704 14.13707 0.316114       0.351470 #> INC          -0.9865  0.39508 0.008834       0.008834 #> HOVAL        -0.2904  0.09878 0.002209       0.002209 #> lag.INC      -0.8506  0.67466 0.015086       0.016187 #> lambda        0.5688  0.17577 0.003930       0.009250 #> sige        116.1069 27.61223 0.617428       0.789579 #>  #> 2. Quantiles for each variable: #>  #>                2.5%     25%      50%      75%     97.5% #> (Intercept) 40.6365 65.4333  73.7510  81.2815  97.03388 #> INC         -1.7216 -1.2471  -1.0006  -0.7335  -0.15124 #> HOVAL       -0.4820 -0.3577  -0.2903  -0.2257  -0.09267 #> lag.INC     -2.0923 -1.2942  -0.8863  -0.4615   0.58595 #> lambda       0.2251  0.4389   0.5731   0.6982   0.89484 #> sige        74.0162 96.6611 112.0106 130.7735 181.83168 #>  print(summary(impacts(COL.err.Bayes))) #> Impact measures (SDEM, MCMC, n): #>           Direct   Indirect      Total #> INC   -0.9865093 -0.8506053 -1.8371146 #> HOVAL -0.2904128         NA -0.2904128 #> ======================================================== #> Standard errors: #>           Direct  Indirect      Total #> INC   0.37860903 0.6465345 0.82479429 #> HOVAL 0.09466321        NA 0.09466321 #> ======================================================== #> Z-values: #>          Direct  Indirect     Total #> INC   -2.605615 -1.315638 -2.227361 #> HOVAL -3.067853        NA -3.067853 #>  #> p-values: #>       Direct   Indirect Total    #> INC   0.009171 0.1883   0.025923 #> HOVAL 0.002156 NA       0.002156 #>  print(raftery.diag(COL.err.Bayes, r=0.01)) #>  #> Quantile (q) = 0.025 #> Accuracy (r) = +/- 0.01 #> Probability (s) = 0.95  #>                                                     #>              Burn-in  Total Lower bound  Dependence #>              (M)      (N)   (Nmin)       factor (I) #>  (Intercept) 10       3436  937          3.670      #>  INC         2        930   937          0.993      #>  HOVAL       2        892   937          0.952      #>  lag.INC     3        1143  937          1.220      #>  lambda      13       3579  937          3.820      #>  sige        3        1096  937          1.170      #>  set.seed(1) COL.sacW.B0 <- spBreg_sac(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw,  Durbin=FALSE, control=list(ndraw=1500L, nomit=500L)) print(summary(COL.sacW.B0)) #>  #> Iterations = 501:1500 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 1000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean       SD Naive SE Time-series SE #> (Intercept)  49.3672  9.23725 0.292108       0.847100 #> INC          -0.9925  0.35777 0.011314       0.012624 #> HOVAL        -0.2847  0.09798 0.003099       0.003307 #> rho           0.3117  0.19633 0.006208       0.020392 #> lambda        0.1927  0.27130 0.008579       0.027162 #> sige        105.0462 23.96805 0.757936       0.757936 #>  #> 2. Quantiles for each variable: #>  #>                2.5%      25%      50%      75%    97.5% #> (Intercept) 31.8783 43.12583  48.9398  55.3573  68.1858 #> INC         -1.6817 -1.24459  -0.9872  -0.7516  -0.3168 #> HOVAL       -0.4952 -0.34433  -0.2827  -0.2201  -0.1028 #> rho         -0.1548  0.21285   0.3406   0.4438   0.6176 #> lambda      -0.3788  0.01455   0.2171   0.3794   0.6988 #> sige        68.5025 88.13909 101.6888 118.2545 160.2792 #>  print(summary(impacts(COL.sacW.B0, tr=trMatc), zstats=TRUE, short=TRUE)) #> Impact measures (sac, trace): #>          Direct   Indirect      Total #> INC   -1.017325 -0.4246675 -1.4419930 #> HOVAL -0.291816 -0.1218143 -0.4136303 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3668822 0.4180525 0.6533395 #> HOVAL 0.1016518 0.1341689 0.1983041 #>  #> Simulated z-values: #>          Direct  Indirect     Total #> INC   -2.808257 -1.219897 -2.357550 #> HOVAL -2.910868 -1.106171 -2.240542 #>  #> Simulated p-values: #>       Direct    Indirect Total    #> INC   0.0049810 0.22250  0.018396 #> HOVAL 0.0036043 0.26865  0.025056 set.seed(1) COL.sacW.B1 <- spBreg_sac(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw,  Durbin=TRUE, control=list(ndraw=1500L, nomit=500L)) print(summary(COL.sacW.B1)) #>  #> Iterations = 501:1500 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 1000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean       SD Naive SE Time-series SE #> (Intercept)  60.1834 24.14830 0.763636       3.169805 #> INC          -0.9888  0.36234 0.011458       0.016240 #> HOVAL        -0.2861  0.09785 0.003094       0.003094 #> lag.INC      -0.8734  0.77381 0.024470       0.060097 #> lag.HOVAL     0.1735  0.21943 0.006939       0.013468 #> rho           0.1808  0.32007 0.010121       0.044327 #> lambda        0.2106  0.32071 0.010142       0.041657 #> sige        100.9463 24.32264 0.769149       0.946662 #>  #> 2. Quantiles for each variable: #>  #>                2.5%       25%     50%      75%    97.5% #> (Intercept) 22.2042 42.280965 56.1010  76.4887 113.5316 #> INC         -1.6963 -1.228821 -0.9813  -0.7271  -0.3299 #> HOVAL       -0.4747 -0.350819 -0.2877  -0.2214  -0.1097 #> lag.INC     -2.5274 -1.342333 -0.8558  -0.3281   0.5407 #> lag.HOVAL   -0.2876  0.037091  0.1824   0.3249   0.5910 #> rho         -0.5076 -0.021227  0.2386   0.4320   0.6655 #> lambda      -0.5106 -0.007594  0.2129   0.4482   0.7389 #> sige        64.6867 84.395156 96.9599 114.4101 159.7252 #>  print(summary(impacts(COL.sacW.B1, tr=trMatc), zstats=TRUE, short=TRUE)) #> Impact measures (sacmixed, trace): #>           Direct   Indirect      Total #> INC   -1.0341008 -1.2391410 -2.2732417 #> HOVAL -0.2808381  0.1434285 -0.1374096 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3510018 0.9466895 1.0370366 #> HOVAL 0.1010491 0.2773738 0.3171738 #>  #> Simulated z-values: #>          Direct   Indirect      Total #> INC   -2.966104 -1.4250264 -2.3048033 #> HOVAL -2.775326  0.5576145 -0.3965541 #>  #> Simulated p-values: #>       Direct    Indirect Total    #> INC   0.0030160 0.15415  0.021178 #> HOVAL 0.0055146 0.57711  0.691696 set.seed(1) COL.lag.Bayes <- spBreg_lag(CRIME ~ INC + HOVAL, data=COL.OLD,  listw=lw) print(summary(COL.lag.Bayes)) #>  #> Iterations = 501:2500 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 2000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean       SD Naive SE Time-series SE #> (Intercept)  45.8256  8.04911 0.179984       0.179984 #> INC          -1.0459  0.34746 0.007770       0.007770 #> HOVAL        -0.2662  0.09366 0.002094       0.002094 #> rho           0.4146  0.12434 0.002780       0.002780 #> sige        107.8827 23.75095 0.531087       0.561152 #>  #> 2. Quantiles for each variable: #>  #>                2.5%     25%      50%      75%     97.5% #> (Intercept) 30.3334 40.3140  45.9376  51.0903  61.51008 #> INC         -1.7252 -1.2774  -1.0477  -0.8158  -0.35423 #> HOVAL       -0.4533 -0.3312  -0.2686  -0.2019  -0.08107 #> rho          0.1645  0.3327   0.4157   0.5008   0.64982 #> sige        70.5778 90.6316 104.8556 120.4706 164.75421 #>  print(summary(impacts(COL.lag.Bayes, tr=trMatc), short=TRUE, zstats=TRUE)) #> Impact measures (lag, trace): #>           Direct   Indirect      Total #> INC   -1.0962113 -0.6903627 -1.7865741 #> HOVAL -0.2790451 -0.1757347 -0.4547797 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3680189 0.4927553 0.7674941 #> HOVAL 0.1002735 0.1393959 0.2171077 #>  #> Simulated z-values: #>          Direct  Indirect     Total #> INC   -3.003178 -1.554252 -2.437925 #> HOVAL -2.809370 -1.425055 -2.212507 #>  #> Simulated p-values: #>       Direct    Indirect Total    #> INC   0.0026718 0.12012  0.014772 #> HOVAL 0.0049639 0.15414  0.026932 print(summary(impacts(COL.lag.Bayes, evalues=ev), short=TRUE, zstats=TRUE)) #> Impact measures (lag, evalues): #>           Direct   Indirect      Total #> INC   -1.0962113 -0.6903627 -1.7865741 #> HOVAL -0.2790451 -0.1757347 -0.4547797 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3680193 0.4929524 0.7676307 #> HOVAL 0.1002746 0.1395496 0.2172252 #>  #> Simulated z-values: #>          Direct  Indirect     Total #> INC   -3.003178 -1.553686 -2.437527 #> HOVAL -2.809345 -1.423571 -2.211367 #>  #> Simulated p-values: #>       Direct    Indirect Total    #> INC   0.0026718 0.12026  0.014788 #> HOVAL 0.0049642 0.15457  0.027010 set.seed(1) COL.D0.Bayes <- spBreg_lag(CRIME ~ INC + HOVAL, data=COL.OLD,  listw=lw, Durbin=TRUE) print(summary(COL.D0.Bayes)) #>  #> Iterations = 501:2500 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 2000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean       SD Naive SE Time-series SE #> (Intercept)  45.3105 13.74662 0.307384       0.307384 #> INC          -0.9246  0.36837 0.008237       0.008237 #> HOVAL        -0.2959  0.09778 0.002187       0.002126 #> lag.INC      -0.5917  0.63940 0.014297       0.014297 #> lag.HOVAL     0.2443  0.18959 0.004239       0.004239 #> rho           0.3932  0.16296 0.003644       0.003644 #> sige        109.7428 24.97328 0.558419       0.607251 #>  #> 2. Quantiles for each variable: #>  #>                 2.5%     25%      50%      75%    97.5% #> (Intercept) 19.18483 35.9928  45.0377  54.5246  72.8590 #> INC         -1.62602 -1.1728  -0.9198  -0.6633  -0.2117 #> HOVAL       -0.48546 -0.3597  -0.2944  -0.2310  -0.1012 #> lag.INC     -1.83696 -1.0334  -0.5786  -0.1739   0.6326 #> lag.HOVAL   -0.13032  0.1164   0.2417   0.3715   0.6133 #> rho          0.06053  0.2826   0.3977   0.5078   0.6949 #> sige        71.19421 91.4872 106.1690 123.7826 170.9503 #>  print(summary(impacts(COL.D0.Bayes, tr=trMatc), short=TRUE, zstats=TRUE)) #> Impact measures (mixed, trace): #>           Direct  Indirect       Total #> INC   -1.0277896 -1.471320 -2.49911007 #> HOVAL -0.2820493  0.197023 -0.08502627 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3831777 1.3179822 1.4600855 #> HOVAL 0.1017455 0.3302926 0.3686927 #>  #> Simulated z-values: #>          Direct   Indirect      Total #> INC   -2.735660 -1.2618796 -1.8570000 #> HOVAL -2.785094  0.5880284 -0.2417988 #>  #> Simulated p-values: #>       Direct    Indirect Total    #> INC   0.0062255 0.20699  0.063311 #> HOVAL 0.0053512 0.55651  0.808936 set.seed(1) COL.D1.Bayes <- spBreg_lag(CRIME ~ DISCBD + INC + HOVAL, data=COL.OLD,  listw=lw, Durbin= ~ INC) print(summary(COL.D1.Bayes)) #>  #> Iterations = 501:2500 #> Thinning interval = 1  #> Number of chains = 1  #> Sample size per chain = 2000  #>  #> 1. Empirical mean and standard deviation for each variable, #>    plus standard error of the mean: #>  #>                 Mean       SD Naive SE Time-series SE #> (Intercept)  56.4193 13.40915 0.299838       0.299838 #> DISCBD       -4.7794  2.14113 0.047877       0.047877 #> INC          -0.9422  0.34677 0.007754       0.007754 #> HOVAL        -0.1806  0.09837 0.002200       0.002200 #> lag.INC       0.4213  0.63243 0.014141       0.014141 #> rho           0.1873  0.18174 0.004064       0.004064 #> sige        103.8701 23.29384 0.520866       0.566802 #>  #> 2. Quantiles for each variable: #>  #>                2.5%       25%      50%      75%      97.5% #> (Intercept) 30.6341 47.656256  56.4238  65.0877  84.808823 #> DISCBD      -9.2565 -6.160525  -4.7536  -3.3735  -0.714089 #> INC         -1.6336 -1.174123  -0.9427  -0.7090  -0.263713 #> HOVAL       -0.3719 -0.247402  -0.1791  -0.1148   0.006329 #> lag.INC     -0.8379 -0.005461   0.4129   0.8399   1.648619 #> rho         -0.2116  0.072536   0.1836   0.3067   0.535793 #> sige        67.8946 87.054945 100.9815 116.4528 161.258258 #>  print(summary(impacts(COL.D1.Bayes, tr=trMatc), short=TRUE, zstats=TRUE)) #> Impact measures (mixed, trace): #>            Direct    Indirect      Total #> DISCBD -4.8194767 -1.06169757 -5.8811743 #> INC    -0.9312352  0.29032298 -0.6409122 #> HOVAL  -0.1821150 -0.04011868 -0.2222336 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>           Direct   Indirect     Total #> DISCBD 2.1896626 1.82105239 3.3751922 #> INC    0.3494541 0.81612759 0.8914013 #> HOVAL  0.1001927 0.06787487 0.1430090 #>  #> Simulated z-values: #>           Direct   Indirect      Total #> DISCBD -2.224202 -0.7454394 -1.8451502 #> INC    -2.683306  0.3286082 -0.7510717 #> HOVAL  -1.835800 -0.7422472 -1.6384544 #>  #> Simulated p-values: #>        Direct    Indirect Total    #> DISCBD 0.0261348 0.45601  0.065016 #> INC    0.0072898 0.74245  0.452610 #> HOVAL  0.0663872 0.45794  0.101327 #data(elect80, package=\"spData\") #lw <- spdep::nb2listw(e80_queen, zero.policy=TRUE) #el_ml <- lagsarlm(log(pc_turnout) ~ log(pc_college) + log(pc_homeownership) # + log(pc_income), data=elect80, listw=lw, zero.policy=TRUE, method=\"LU\") #print(summary(el_ml)) #set.seed(1) #el_B <- spBreg_lag(log(pc_turnout) ~ log(pc_college) + log(pc_homeownership) # + log(pc_income), data=elect80, listw=lw, zero.policy=TRUE) #print(summary(el_B)) #print(el_ml$timings) #print(attr(el_B, \"timings\")) # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/SLX.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial Durbin linear (SLX, spatially lagged X) model — lmSLX","title":"Spatial Durbin linear (SLX, spatially lagged X) model — lmSLX","text":"lmSLX fits lm model augmented spatially lagged RHS variables, including lagged intercept spatial weights row-standardised. create_WX creates spatially lagged RHS variables, exposed use model fitting functions.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SLX.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial Durbin linear (SLX, spatially lagged X) model — lmSLX","text":"","code":"lmSLX(formula, data = list(), listw, na.action, weights=NULL, Durbin=TRUE,  zero.policy=NULL, return_impacts=TRUE) # S3 method for class 'SlX' print(x, digits = max(3L, getOption(\"digits\") - 3L), ...) # S3 method for class 'SlX' summary(object, correlation = FALSE, symbolic.cor = FALSE, ...) # S3 method for class 'summary.SlX' print(x, digits = max(3L, getOption(\"digits\") - 3L),  symbolic.cor = x$symbolic.cor, signif.stars = getOption(\"show.signif.stars\"), ...) # S3 method for class 'SlX' impacts(obj, ...) # S3 method for class 'WXimpact' print(x, ...) # S3 method for class 'WXimpact' summary(object, ..., adjust_k=(attr(object, \"type\") == \"SDEM\")) # S3 method for class 'SlX' predict(object, newdata, listw, zero.policy=NULL, ...) create_WX(x, listw, zero.policy=NULL, prefix=\"\")"},{"path":"https://r-spatial.github.io/spatialreg/reference/SLX.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial Durbin linear (SLX, spatially lagged X) model — lmSLX","text":"formula symbolic description model fit. details model specification given lm() data optional data frame containing variables model. default variables taken environment function called. listw listw object created example nb2listw na.action function (default options(\"na.action\")), can also na.omit na.exclude consequences residuals fitted values - cases spatial weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. weights optional vector weights used fitting process. Non-NULL weights can used indicate different observations different variances (values weights inversely proportional variances); equivalently, elements weights positive integers w_i, response y_i mean w_i unit-weight observations (including case w_i observations equal y_i data summarized) - lm Durbin default TRUE lmSLX (Durbin model including WX); TRUE, full spatial Durbin model; formula object, subset explanatory variables lag zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA return_impacts default TRUE; may set FALSE avoid problems calculating impacts aliased variables digits number significant digits use printing correlation logical; TRUE, correlation matrix estimated parameters returned printed symbolic.cor logical. TRUE, print correlations symbolic form (see 'symnum') rather numbers signif.stars logical. TRUE, 'significance stars' printed coefficient obj spatial regression object created lmSLX ... Arguments passed prefix default empty string, may “lag” cases x, object model matrix lagged; lagImpact objects created impacts methods adjust_k default TRUE SDEM else FALSE, adjust internal OLS SDEM standard errors dividing n rather (n-k) (default changed bug fixed 0.7-8; standard errors now ML SDEM summary impacts summary identical - SLX use FALSE) newdata data frame predict — NULL, predictions data model fitted. row names corresponding region.id. row names exactly ones used training, uses -sample predictors forecast.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SLX.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial Durbin linear (SLX, spatially lagged X) model — lmSLX","text":"lmSLX function returns “lm” object “mixedImps” list three impact matrixes (impacts standard errors) direct, indirect total impacts; total impacts calculated using simplified local copy estimable function gmodels package.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/SLX.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial Durbin linear (SLX, spatially lagged X) model — lmSLX","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SLX.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial Durbin linear (SLX, spatially lagged X) model — lmSLX","text":"","code":"data(oldcol, package=\"spdep\") lw <- spdep::nb2listw(COL.nb, style=\"W\") COL.SLX <- lmSLX(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw) summary(COL.SLX) #>  #> Call: #> lm(formula = formula(paste(\"y ~ \", paste(colnames(x)[-1], collapse = \"+\"))),  #>     data = as.data.frame(x), weights = weights) #>  #> Coefficients: #>              Estimate    Std. Error  t value     Pr(>|t|)   #> (Intercept)   7.503e+01   6.626e+00   1.132e+01   1.261e-14 #> INC          -1.109e+00   3.738e-01  -2.967e+00   4.854e-03 #> HOVAL        -2.897e-01   1.014e-01  -2.858e+00   6.486e-03 #> lag.INC      -1.371e+00   5.613e-01  -2.443e+00   1.867e-02 #> lag.HOVAL     1.918e-01   2.003e-01   9.572e-01   3.437e-01 #>  summary(impacts(COL.SLX)) #> Impact measures (SlX, glht, n-k): #>           Direct   Indirect       Total #> INC   -1.1089293 -1.3709725 -2.47990173 #> HOVAL -0.2897283  0.1917608 -0.09796753 #> ======================================================== #> Standard errors: #>          Direct  Indirect     Total #> INC   0.3738129 0.5612771 0.4965456 #> HOVAL 0.1013673 0.2003335 0.2028016 #> ======================================================== #> Z-values: #>          Direct   Indirect      Total #> INC   -2.966535 -2.4425945 -4.9943086 #> HOVAL -2.858202  0.9572079 -0.4830709 #>  #> p-values: #>       Direct    Indirect Total      #> INC   0.0030118 0.014582 5.9047e-07 #> HOVAL 0.0042605 0.338462 0.62905    #>  COL.SLX <- lmSLX(CRIME ~ INC + HOVAL + I(HOVAL^2), data=COL.OLD, listw=lw, Durbin=TRUE) summary(impacts(COL.SLX)) #> Impact measures (SlX, glht, n-k): #>                  Direct     Indirect       Total #> INC        -0.947594274 -1.275338647 -2.22293292 #> HOVAL      -0.777427839 -0.355048446 -1.13247628 #> I(HOVAL^2)  0.004639919  0.005608104  0.01024802 #> ======================================================== #> Standard errors: #>                 Direct   Indirect      Total #> INC        0.398832844 0.59687399 0.56325440 #> HOVAL      0.464456540 0.98213200 1.07348981 #> I(HOVAL^2) 0.004226259 0.00908385 0.01025212 #> ======================================================== #> Z-values: #>               Direct   Indirect      Total #> INC        -2.375918 -2.1366966 -3.9465877 #> HOVAL      -1.673844 -0.3615079 -1.0549483 #> I(HOVAL^2)  1.097879  0.6173709  0.9996008 #>  #> p-values: #>            Direct   Indirect Total      #> INC        0.017505 0.032623 7.9273e-05 #> HOVAL      0.094161 0.717720 0.29145    #> I(HOVAL^2) 0.272258 0.536990 0.31750    #>  summary(COL.SLX) #>  #> Call: #> lm(formula = formula(paste(\"y ~ \", paste(colnames(x)[-1], collapse = \"+\"))),  #>     data = as.data.frame(x), weights = weights) #>  #> Coefficients: #>                 Estimate    Std. Error  t value     Pr(>|t|)   #> (Intercept)      9.246e+01   1.928e+01   4.796e+00   2.058e-05 #> INC             -9.476e-01   3.988e-01  -2.376e+00   2.214e-02 #> HOVAL           -7.774e-01   4.645e-01  -1.674e+00   1.016e-01 #> I.HOVAL.2.       4.640e-03   4.226e-03   1.098e+00   2.785e-01 #> lag.INC         -1.275e+00   5.969e-01  -2.137e+00   3.849e-02 #> lag.HOVAL       -3.550e-01   9.821e-01  -3.615e-01   7.195e-01 #> lag.I.HOVAL.2.   5.608e-03   9.084e-03   6.174e-01   5.403e-01 #>  COL.SLX <- lmSLX(CRIME ~ INC + HOVAL + I(HOVAL^2), data=COL.OLD, listw=lw, Durbin=~INC) summary(impacts(COL.SLX)) #> Impact measures (SlX, glht, n-k): #>                  Direct  Indirect        Total #> INC        -1.079064628 -1.010896 -2.089960575 #> HOVAL      -0.634518755        NA -0.634518755 #> I(HOVAL^2)  0.003455273        NA  0.003455273 #> ======================================================== #> Standard errors: #>                Direct  Indirect      Total #> INC        0.38471071 0.4552667 0.44650193 #> HOVAL      0.44760078        NA 0.44760078 #> I(HOVAL^2) 0.00411036        NA 0.00411036 #> ======================================================== #> Z-values: #>                Direct  Indirect      Total #> INC        -2.8048728 -2.220448 -4.6807425 #> HOVAL      -1.4175997        NA -1.4175997 #> I(HOVAL^2)  0.8406254        NA  0.8406254 #>  #> p-values: #>            Direct    Indirect Total      #> INC        0.0050336 0.026388 2.8584e-06 #> HOVAL      0.1563077 NA       0.15631    #> I(HOVAL^2) 0.4005579 NA       0.40056    #>  summary(COL.SLX) #>  #> Call: #> lm(formula = formula(paste(\"y ~ \", paste(colnames(x)[-1], collapse = \"+\"))),  #>     data = as.data.frame(x), weights = weights) #>  #> Coefficients: #>              Estimate    Std. Error  t value     Pr(>|t|)   #> (Intercept)   8.368e+01   9.265e+00   9.032e+00   1.401e-11 #> INC          -1.079e+00   3.847e-01  -2.805e+00   7.466e-03 #> HOVAL        -6.345e-01   4.476e-01  -1.418e+00   1.634e-01 #> I.HOVAL.2.    3.455e-03   4.110e-03   8.406e-01   4.051e-01 #> lag.INC      -1.011e+00   4.553e-01  -2.220e+00   3.159e-02 #>  COL.SLX <- lmSLX(CRIME ~ INC, data=COL.OLD, listw=lw) summary(COL.SLX) #>  #> Call: #> lm(formula = formula(paste(\"y ~ \", paste(colnames(x)[-1], collapse = \"+\"))),  #>     data = as.data.frame(x), weights = weights) #>  #> Coefficients: #>              Estimate    Std. Error  t value     Pr(>|t|)   #> (Intercept)   7.398e+01   6.208e+00   1.192e+01   1.155e-15 #> INC          -1.589e+00   3.564e-01  -4.458e+00   5.276e-05 #> lag.INC      -1.086e+00   4.812e-01  -2.257e+00   2.882e-02 #>  summary(impacts(COL.SLX)) #> Impact measures (SlX, glht, n-k): #>        Direct  Indirect     Total #> INC -1.588901 -1.085867 -2.674768 #> ======================================================== #> Standard errors: #>        Direct  Indirect    Total #> INC 0.3564039 0.4811809 0.407313 #> ======================================================== #> Z-values: #>        Direct  Indirect     Total #> INC -4.458147 -2.256671 -6.566861 #>  #> p-values: #>     Direct     Indirect Total      #> INC 8.2671e-06 0.024029 5.1387e-11 #>  # \\dontrun{ crds <- cbind(COL.OLD$X, COL.OLD$Y) mdist <- sqrt(sum(diff(apply(crds, 2, range))^2)) dnb <- spdep::dnearneigh(crds, 0, mdist) dists <- spdep::nbdists(dnb, crds) f <- function(x, form, data, dnb, dists, verbose) {   glst <- lapply(dists, function(d) 1/(d^x))   lw <- spdep::nb2listw(dnb, glist=glst, style=\"B\")   res <- logLik(lmSLX(form=form, data=data, listw=lw))   if (verbose) cat(\"power:\", x, \"logLik:\", res, \"\\n\")   res } opt <- optimize(f, interval=c(0.1, 4), form=CRIME ~ INC + HOVAL,  data=COL.OLD, dnb=dnb, dists=dists, verbose=TRUE, maximum=TRUE) #> power: 1.589667 logLik: -172.6864  #> power: 2.510333 logLik: -177.741  #> power: 1.020665 logLik: -171.5379  #> power: 0.8721475 logLik: -171.7979  #> power: 1.11302 logLik: -171.4973  #> power: 1.107329 logLik: -171.497  #> power: 1.105705 logLik: -171.497  #> power: 1.105746 logLik: -171.497  #> power: 1.105664 logLik: -171.497  #> power: 1.105705 logLik: -171.497  glst <- lapply(dists, function(d) 1/(d^opt$maximum)) lw <- spdep::nb2listw(dnb, glist=glst, style=\"B\") SLX <- lmSLX(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw) summary(SLX) #>  #> Call: #> lm(formula = formula(paste(\"y ~ \", paste(colnames(x)[-1], collapse = \"+\"))),  #>     data = as.data.frame(x), weights = weights) #>  #> Coefficients: #>                  Estimate  Std. Error  t value   Pr(>|t|) #> (Intercept)      18.78498  11.23795     1.67157   0.10187 #> INC              -0.65428   0.29463    -2.22064   0.03169 #> HOVAL            -0.18244   0.08138    -2.24174   0.03019 #> lag..Intercept.   6.27790   4.44284     1.41304   0.16484 #> lag.INC          -0.12958   0.28794    -0.45002   0.65496 #> lag.HOVAL         0.02668   0.11273     0.23664   0.81406 #>  summary(impacts(SLX)) #> Impact measures (SlX, glht, n-k): #>           Direct    Indirect      Total #> INC   -0.6542760 -0.12957739 -0.7838534 #> HOVAL -0.1824383  0.02667561 -0.1557627 #> ======================================================== #> Standard errors: #>           Direct  Indirect     Total #> INC   0.29463342 0.2879383 0.3742251 #> HOVAL 0.08138257 0.1127279 0.1404591 #> ======================================================== #> Z-values: #>          Direct   Indirect     Total #> INC   -2.220644 -0.4500179 -2.094604 #> HOVAL -2.241736  0.2366371 -1.108954 #>  #> p-values: #>       Direct   Indirect Total    #> INC   0.026375 0.65270  0.036206 #> HOVAL 0.024978 0.81294  0.267450 #>  # } COL.SLX <- lmSLX(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw) pslx0 <- predict(COL.SLX) pslx1 <- predict(COL.SLX, newdata=COL.OLD, listw=lw) #> Error in predict.SlX(COL.SLX, newdata = COL.OLD, listw = lw): mismatch between newdata and spatial weights. newdata should have region.id as row.names all.equal(pslx0, pslx1) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'current' in selecting a method for function 'all.equal': object 'pslx1' not found COL.OLD1 <- COL.OLD COL.OLD1$INC <- COL.OLD1$INC + 1 pslx2 <- predict(COL.SLX, newdata=COL.OLD1, listw=lw) #> Error in predict.SlX(COL.SLX, newdata = COL.OLD1, listw = lw): mismatch between newdata and spatial weights. newdata should have region.id as row.names sum(coef(COL.SLX)[c(2,4)]) #> [1] 5.623621 mean(pslx2-pslx1) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'mean': object 'pslx2' not found"},{"path":"https://r-spatial.github.io/spatialreg/reference/SpatialFiltering.html","id":null,"dir":"Reference","previous_headings":"","what":"Semi-parametric spatial filtering — SpatialFiltering","title":"Semi-parametric spatial filtering — SpatialFiltering","text":"function selects eigenvectors semi-parametric spatial filtering approach removing spatial dependence linear models. Selection brute force finding single eigenvector reducing standard variate Moran's regression residuals , continuing candidate eigenvector reduces value tol. returns summary table selection process matrix selected eigenvectors specified model.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SpatialFiltering.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Semi-parametric spatial filtering — SpatialFiltering","text":"","code":"SpatialFiltering(formula, lagformula=NULL, data=list(), na.action=na.fail,  nb=NULL, glist = NULL,  style = \"C\", zero.policy = NULL, tol = 0.1, zerovalue = 1e-04,  ExactEV = FALSE, symmetric = TRUE, alpha=NULL, alternative=\"two.sided\",  verbose=NULL)"},{"path":"https://r-spatial.github.io/spatialreg/reference/SpatialFiltering.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Semi-parametric spatial filtering — SpatialFiltering","text":"formula symbolic description model fit, assuming spatial error representation; lagformula given, include response intercept term lagformula extra one-sided formula used spatial lag representation desired; intercept excluded within function present part formula argument, excluding explicitly lagformula argument presence factors generates collinear model matrix data optional data frame containing variables model nb object class nb glist list general weights corresponding neighbours style style can take values W, B, C, U, S na.action function (default options(\"na.action\")), can also na.omit na.exclude consequences residuals fitted values - cases spatial weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors tol tolerance value convergence spatial filtering zerovalue eigenvectors eigenvalues absolute value smaller zerovalue excluded eigenvector search ExactEV Set ExactEV=TRUE use exact expectations variances rather expectation variance Moran's previous iteration, default FALSE symmetric spatial weights matrix forced symmetry, default TRUE alpha NULL, used instead tol= argument stopping rule choose eigenvectors including one probability value exceeding alpha. alternative character string specifying alternative hypothesis, must one greater, less two.sided (default). verbose default NULL, use global option value; TRUE report eigenvectors selected","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SpatialFiltering.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Semi-parametric spatial filtering — SpatialFiltering","text":"SfResult object, : selection matrix summarising selection eigenvectors inclusion, columns: Step Step counter selection procedure SelEvec number selected eigenvector (sorted descending) Eval associated eigenvalue MinMi value Moran's residual autocorrelation ZMinMi standardized value Moran's assuming normal approximation pr(ZI) probability value permutation-based standardized deviate given value alternative argument R2 R^2 model including exogenous variables eigenvectors gamma regression coefficient selected eigenvector fit first row value start search dataset matrix selected eigenvectors order selection","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SpatialFiltering.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Semi-parametric spatial filtering — SpatialFiltering","text":"Tiefelsdorf M, Griffith DA. (2007) Semiparametric Filtering Spatial Autocorrelation: Eigenvector Approach. Environment Planning , 39 (5) 1193 - 1221.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/SpatialFiltering.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Semi-parametric spatial filtering — SpatialFiltering","text":"Yongwan Chun, Michael Tiefelsdorf, Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/SpatialFiltering.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Semi-parametric spatial filtering — SpatialFiltering","text":"","code":"require(\"sf\", quietly=TRUE) columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) #require(\"spdep\", quietly=TRUE) col.gal.nb <- spdep::read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) lmbase <- lm(CRIME ~ INC + HOVAL, data=columbus) sarcol <- SpatialFiltering(CRIME ~ INC + HOVAL, data=columbus,  nb=col.gal.nb, style=\"W\", ExactEV=TRUE) sarcol #>   Step SelEvec      Eval        MinMi      ZMinMi      Pr(ZI)        R2 #> 0    0       0 0.0000000  0.212374153  2.68100025 0.007340246 0.5524040 #> 1    1       5 0.7148326  0.121528166  1.89037770 0.058707464 0.6209393 #> 2    2       3 0.8408661  0.065848648  1.54064108 0.123404165 0.6481722 #> 3    3       1 1.0206316 -0.005424824  1.08514557 0.277857187 0.6726114 #> 4    4      10 0.3658588 -0.039356232  0.80357070 0.421644951 0.7000258 #> 5    5      14 0.1831325 -0.072949543  0.47790213 0.632719864 0.7393770 #> 6    6      11 0.3144120 -0.108332631  0.18566599 0.852706701 0.7611907 #> 7    7       2 0.9157325 -0.153675621 -0.03464097 0.972366030 0.7713163 #>       gamma #> 0   0.00000 #> 1  30.34786 #> 2  19.13010 #> 3 -18.12234 #> 4 -19.19379 #> 5 -22.99586 #> 6  17.12127 #> 7  11.66487 lmsar <- lm(CRIME ~ INC + HOVAL + fitted(sarcol), data=columbus) (x <- summary(lmsar)) #>  #> Call: #> lm(formula = CRIME ~ INC + HOVAL + fitted(sarcol), data = columbus) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -27.6527  -5.3084   0.0804   5.6844  15.6912  #>  #> Coefficients: #>                      Estimate Std. Error t value Pr(>|t|)     #> (Intercept)          68.61896    3.67609  18.666  < 2e-16 *** #> INC                  -1.59731    0.25938  -6.158 3.12e-07 *** #> HOVAL                -0.27393    0.08011  -3.419  0.00148 **  #> fitted(sarcol)vec5   30.34786    8.87679   3.419  0.00149 **  #> fitted(sarcol)vec3   19.13010    8.87679   2.155  0.03739 *   #> fitted(sarcol)vec1  -18.12234    8.87679  -2.042  0.04800 *   #> fitted(sarcol)vec10 -19.19379    8.87679  -2.162  0.03679 *   #> fitted(sarcol)vec14 -22.99586    8.87679  -2.591  0.01341 *   #> fitted(sarcol)vec11  17.12127    8.87679   1.929  0.06106 .   #> fitted(sarcol)vec2   11.66487    8.87679   1.314  0.19649     #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>  #> Residual standard error: 8.877 on 39 degrees of freedom #> Multiple R-squared:  0.7713,\tAdjusted R-squared:  0.7185  #> F-statistic: 14.62 on 9 and 39 DF,  p-value: 5.579e-10 #>  coef(x) #>                        Estimate Std. Error   t value     Pr(>|t|) #> (Intercept)          68.6189611 3.67608656 18.666307 4.802352e-21 #> INC                  -1.5973108 0.25938068 -6.158172 3.122801e-07 #> HOVAL                -0.2739315 0.08011158 -3.419374 1.483698e-03 #> fitted(sarcol)vec5   30.3478552 8.87679493  3.418785 1.486164e-03 #> fitted(sarcol)vec3   19.1300996 8.87679493  2.155068 3.738943e-02 #> fitted(sarcol)vec1  -18.1223409 8.87679493 -2.041541 4.800339e-02 #> fitted(sarcol)vec10 -19.1937947 8.87679493 -2.162244 3.679422e-02 #> fitted(sarcol)vec14 -22.9958588 8.87679493 -2.590559 1.340783e-02 #> fitted(sarcol)vec11  17.1212741 8.87679493  1.928768 6.106079e-02 #> fitted(sarcol)vec2   11.6648669 8.87679493  1.314085 1.964945e-01 anova(lmbase, lmsar) #> Analysis of Variance Table #>  #> Model 1: CRIME ~ INC + HOVAL #> Model 2: CRIME ~ INC + HOVAL + fitted(sarcol) #>   Res.Df    RSS Df Sum of Sq      F    Pr(>F)     #> 1     46 6014.9                                   #> 2     39 3073.1  7    2941.8 5.3334 0.0002445 *** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 spdep::lm.morantest(lmsar, spdep::nb2listw(col.gal.nb)) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL + fitted(sarcol), data = #> columbus) #> weights: spdep::nb2listw(col.gal.nb) #>  #> Moran I statistic standard deviate = -0.034641, p-value = 0.5138 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>     -0.153675621     -0.150918131      0.006336477  #>  lagcol <- SpatialFiltering(CRIME ~ 1, ~ INC + HOVAL - 1, data=columbus,  nb=col.gal.nb, style=\"W\") lagcol #>    Step SelEvec      Eval       MinMi      ZMinMi      Pr(ZI)        R2 #> 0     0       0 0.0000000  0.21237415  2.68100025 0.007340246 0.5524040 #> 1     1       6 0.7161123  0.11782248  1.84511963 0.065020139 0.6038801 #> 2     2       4 0.8682938  0.06242664  1.49482111 0.134961136 0.6531288 #> 3     3       1 1.0310063 -0.02066604  0.88134183 0.378132834 0.6924845 #> 4     4       5 0.7905397 -0.04619973  0.84746904 0.396733736 0.7136578 #> 5     5      15 0.1753342 -0.07609524  0.55233191 0.580720971 0.7558543 #> 6     6       9 0.5501433 -0.10190889  0.43919419 0.660520837 0.7626784 #> 7     7       8 0.5721041 -0.12232942  0.41846803 0.675604953 0.7757314 #> 8     8       3 0.9026222 -0.14991822  0.38315383 0.701605709 0.7908693 #> 9     9       2 0.9649166 -0.21756342 -0.28556733 0.775209527 0.8078727 #> 10   10       7 0.6219404 -0.22017920 -0.04856547 0.961265592 0.8082842 #>         gamma #> 0    0.000000 #> 1   19.848854 #> 2   35.542595 #> 3  -30.697851 #> 4  -24.540372 #> 5   25.227798 #> 6    7.590082 #> 7  -16.933168 #> 8  -20.556931 #> 9  -18.434534 #> 10  -2.597572 lmlag <- lm(CRIME ~ INC + HOVAL + fitted(lagcol), data=columbus) lmlag #>  #> Call: #> lm(formula = CRIME ~ INC + HOVAL + fitted(lagcol), data = columbus) #>  #> Coefficients: #>         (Intercept)                  INC                HOVAL   #>             56.7977              -0.4857              -0.3821   #>  fitted(lagcol)vec6   fitted(lagcol)vec4   fitted(lagcol)vec1   #>             19.8489              35.5426             -30.6979   #>  fitted(lagcol)vec5  fitted(lagcol)vec15   fitted(lagcol)vec9   #>            -24.5404              25.2278               7.5901   #>  fitted(lagcol)vec8   fitted(lagcol)vec3   fitted(lagcol)vec2   #>            -16.9332             -20.5569             -18.4345   #>  fitted(lagcol)vec7   #>             -2.5976   #>  anova(lmbase, lmlag) #> Analysis of Variance Table #>  #> Model 1: CRIME ~ INC + HOVAL #> Model 2: CRIME ~ INC + HOVAL + fitted(lagcol) #>   Res.Df    RSS Df Sum of Sq      F    Pr(>F)     #> 1     46 6014.9                                   #> 2     36 2576.3 10    3438.6 4.8049 0.0002165 *** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 spdep::lm.morantest(lmlag, spdep::nb2listw(col.gal.nb)) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = CRIME ~ INC + HOVAL + fitted(lagcol), data = #> columbus) #> weights: spdep::nb2listw(col.gal.nb) #>  #> Moran I statistic standard deviate = -0.048565, p-value = 0.5194 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>     -0.220179195     -0.217083975      0.004061888  #>  NA.columbus <- columbus NA.columbus$CRIME[20:25] <- NA COL.SF.NA <- SpatialFiltering(CRIME ~ INC + HOVAL, data=NA.columbus,  nb=col.gal.nb, style=\"W\", na.action=na.exclude) #> Warning: subsetting caused increase in subgraph count COL.SF.NA$na.action #> 20 21 22 23 24 25  #> 20 21 22 23 24 25  #> attr(,\"class\") #> [1] \"exclude\" summary(lm(CRIME ~ INC + HOVAL + fitted(COL.SF.NA), data=NA.columbus,  na.action=na.exclude)) #>  #> Call: #> lm(formula = CRIME ~ INC + HOVAL + fitted(COL.SF.NA), data = NA.columbus,  #>     na.action = na.exclude) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -23.6712  -4.7984   0.1761   6.7460  11.3353  #>  #> Coefficients: #>                     Estimate Std. Error t value Pr(>|t|)     #> (Intercept)         69.04674    3.91643  17.630  < 2e-16 *** #> INC                 -1.60115    0.26017  -6.154 3.88e-07 *** #> HOVAL               -0.28742    0.07716  -3.725 0.000649 *** #> fitted(COL.SF.NA)1 -39.91305    8.23597  -4.846 2.27e-05 *** #> fitted(COL.SF.NA)2  19.81805    8.23597   2.406 0.021226 *   #> fitted(COL.SF.NA)3 -35.07336    8.23597  -4.259 0.000135 *** #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>  #> Residual standard error: 8.236 on 37 degrees of freedom #>   (6 observations deleted due to missingness) #> Multiple R-squared:  0.7772,\tAdjusted R-squared:  0.7471  #> F-statistic: 25.81 on 5 and 37 DF,  p-value: 3.996e-11 #>"},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.html","id":null,"dir":"Reference","previous_headings":"","what":"Approximate profile-likelihood estimator (APLE) — aple","title":"Approximate profile-likelihood estimator (APLE) — aple","text":"Approximate profile-likelihood estimator (APLE) simultaneous autoregressive model's spatial dependence parameter introduced Li et al. (2007). employs correction term using eigenvalues spatial weights matrix, consequently used large numbers observations. also requires variable mean zero, assumed detrended. spatial weights object assumed row-standardised, using default style=\"W\" nb2listw.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Approximate profile-likelihood estimator (APLE) — aple","text":"","code":"aple(x, listw, override_similarity_check=FALSE, useTrace=TRUE)"},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Approximate profile-likelihood estimator (APLE) — aple","text":"x zero-mean detrended continuous variable listw listw object example spdep::nb2listw override_similarity_check default FALSE, TRUE - typically row-standardised weights asymmetric underlying general weights - similarity checked useTrace default TRUE, use trace sparse matrix W %*% W (Li et al. (2010)), FALSE, use crossproduct eigenvalues W Li et al. (2007)","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Approximate profile-likelihood estimator (APLE) — aple","text":"implementation checked Hongfei Li's implementation using data; help valuable.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Approximate profile-likelihood estimator (APLE) — aple","text":"scalar APLE value.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Approximate profile-likelihood estimator (APLE) — aple","text":"Li, H, Calder, C. . Cressie N. . C. (2007) Beyond Moran's : testing spatial dependence based spatial autoregressive model. Geographical Analysis 39, 357-375; Li, H, Calder, C. . Cressie N. . C. (2012) One-step estimation spatial dependence parameters: Properties extensions APLE statistic, Journal Multivariate Analysis 105, 68-84.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Approximate profile-likelihood estimator (APLE) — aple","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Approximate profile-likelihood estimator (APLE) — aple","text":"","code":"wheat <- st_read(system.file(\"shapes/wheat.gpkg\", package=\"spData\")[1], quiet=TRUE) library(spdep) #>  #> Attaching package: ‘spdep’ #> The following objects are masked from ‘package:spatialreg’: #>  #>     get.ClusterOption, get.VerboseOption, get.ZeroPolicyOption, #>     get.coresOption, get.mcOption, set.ClusterOption, #>     set.VerboseOption, set.ZeroPolicyOption, set.coresOption, #>     set.mcOption nbr1 <- spdep::poly2nb(wheat, queen=FALSE) nbrl <- spdep::nblag(nbr1, 2) #> Warning: lag 2 neighbour object has 2 sub-graphs nbr12 <- spdep::nblag_cumul(nbrl) cms0 <- with(as.data.frame(wheat), tapply(yield, c, median)) cms1 <- c(model.matrix(~ factor(c) -1, data=wheat) %*% cms0) wheat$yield_detrend <- wheat$yield - cms1 isTRUE(all.equal(c(with(as.data.frame(wheat),  tapply(yield_detrend, c, median))), rep(0.0, 25),  check.attributes=FALSE)) #> [1] TRUE spdep::moran.test(wheat$yield_detrend, spdep::nb2listw(nbr12, style=\"W\")) #>  #> \tMoran I test under randomisation #>  #> data:  wheat$yield_detrend   #> weights: spdep::nb2listw(nbr12, style = \"W\")     #>  #> Moran I statistic standard deviate = 10.305, p-value < 2.2e-16 #> alternative hypothesis: greater #> sample estimates: #> Moran I statistic       Expectation          Variance  #>      0.1935469610     -0.0020040080      0.0003600869  #>  aple(as.vector(scale(wheat$yield_detrend, scale=FALSE)), spdep::nb2listw(nbr12, style=\"W\")) #> [1] 0.6601805 # \\dontrun{ errorsarlm(yield_detrend ~ 1, wheat, spdep::nb2listw(nbr12, style=\"W\")) #>  #> Call: #> errorsarlm(formula = yield_detrend ~ 1, data = wheat, listw = spdep::nb2listw(nbr12,  #>     style = \"W\")) #> Type: error  #>  #> Coefficients: #>      lambda (Intercept)  #>  0.60189687 -0.00251772  #>  #> Log likelihood: -192.9519  # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.mc.html","id":null,"dir":"Reference","previous_headings":"","what":"Approximate profile-likelihood estimator (APLE) permutation test — aple.mc","title":"Approximate profile-likelihood estimator (APLE) permutation test — aple.mc","text":"permutation bootstrap test approximate profile-likelihood estimator (APLE).","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.mc.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Approximate profile-likelihood estimator (APLE) permutation test — aple.mc","text":"","code":"aple.mc(x, listw, nsim, override_similarity_check=FALSE, useTrace=TRUE)"},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.mc.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Approximate profile-likelihood estimator (APLE) permutation test — aple.mc","text":"x zero-mean detrended continuous variable listw listw object example spdep::nb2listw nsim number simulations override_similarity_check default FALSE, TRUE - typically row-standardised weights asymmetric underlying general weights - similarity checked useTrace default TRUE, use trace sparse matrix W %*% W (Li et al. (2010)), FALSE, use crossproduct eigenvalues W Li et al. (2007)","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.mc.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Approximate profile-likelihood estimator (APLE) permutation test — aple.mc","text":"boot object returned boot function.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.mc.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Approximate profile-likelihood estimator (APLE) permutation test — aple.mc","text":"Li, H, Calder, C. . Cressie N. . C. (2007) Beyond Moran's : testing spatial dependence based spatial autoregressive model. Geographical Analysis 39, 357-375; Li, H, Calder, C. . Cressie N. . C. (2012) One-step estimation spatial dependence parameters: Properties extensions APLE statistic, Journal Multivariate Analysis 105, 68-84.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.mc.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Approximate profile-likelihood estimator (APLE) permutation test — aple.mc","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.mc.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Approximate profile-likelihood estimator (APLE) permutation test — aple.mc","text":"","code":"# \\dontrun{ wheat <- st_read(system.file(\"shapes/wheat.gpkg\", package=\"spData\")[1], quiet=TRUE) nbr1 <- spdep::poly2nb(wheat, queen=FALSE) nbrl <- spdep::nblag(nbr1, 2) #> Warning: lag 2 neighbour object has 2 sub-graphs nbr12 <- spdep::nblag_cumul(nbrl) wheat_g <- wheat st_geometry(wheat_g) <- NULL cms0 <- with(wheat_g, tapply(yield, c, median)) cms1 <- c(model.matrix(~ factor(c) -1, data=wheat) %*% cms0) wheat$yield_detrend <- wheat$yield - cms1 oldRNG <- RNGkind() RNGkind(\"L'Ecuyer-CMRG\") set.seed(1L) boot_out_ser <- aple.mc(as.vector(scale(wheat$yield_detrend, scale=FALSE)),  spdep::nb2listw(nbr12, style=\"W\"), nsim=500) plot(boot_out_ser)  boot_out_ser #>  #> DATA PERMUTATION #>  #>  #> Call: #> boot(data = x, statistic = aple.boot, R = nsim, sim = \"permutation\",  #>     pre = pre, parallel = parallel, ncpus = ncpus, cl = cl) #>  #>  #> Bootstrap Statistics : #>      original     bias    std. error #> t1* 0.6601805 -0.6708415   0.1092922 library(parallel) oldCores <- set.coresOption(NULL) nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L # set nc to 1L here if (nc > 1L) nc <- 1L invisible(set.coresOption(nc)) set.seed(1L) if (!get.mcOption()) {   cl <- makeCluster(nc)   set.ClusterOption(cl) } else{   mc.reset.stream() } boot_out_par <- aple.mc(as.vector(scale(wheat$yield_detrend, scale=FALSE)),     spdep::nb2listw(nbr12, style=\"W\"), nsim=500) if (!get.mcOption()) {   set.ClusterOption(NULL)   stopCluster(cl) } boot_out_par #>  #> DATA PERMUTATION #>  #>  #> Call: #> boot(data = x, statistic = aple.boot, R = nsim, sim = \"permutation\",  #>     pre = pre, parallel = parallel, ncpus = ncpus, cl = cl) #>  #>  #> Bootstrap Statistics : #>      original     bias    std. error #> t1* 0.6601805 -0.6708415   0.1092922 invisible(set.coresOption(oldCores)) RNGkind(oldRNG[1], oldRNG[2]) # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.plot.html","id":null,"dir":"Reference","previous_headings":"","what":"Approximate profile-likelihood estimator (APLE) scatterplot — aple.plot","title":"Approximate profile-likelihood estimator (APLE) scatterplot — aple.plot","text":"scatterplot decomposition approximate profile-likelihood estimator, local APLE based list vectors returned scatterplot function.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.plot.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Approximate profile-likelihood estimator (APLE) scatterplot — aple.plot","text":"","code":"aple.plot(x, listw, override_similarity_check=FALSE, useTrace=TRUE, do.plot=TRUE, ...) localAple(x, listw, override_similarity_check=FALSE, useTrace=TRUE)"},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.plot.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Approximate profile-likelihood estimator (APLE) scatterplot — aple.plot","text":"x zero-mean detrended continuous variable listw listw object example spdep::nb2listw override_similarity_check default FALSE, TRUE - typically row-standardised weights asymmetric underlying general weights - similarity checked useTrace default TRUE, use trace sparse matrix W %*% W (Li et al. (2010)), FALSE, use crossproduct eigenvalues W Li et al. (2007) .plot default TRUE: scatterplot drawn ... arguments passed plot","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.plot.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Approximate profile-likelihood estimator (APLE) scatterplot — aple.plot","text":"function solves secondary eigenproblem size n internally, constructing values scatterplot quite compute memory intensive, suitable large n.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.plot.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Approximate profile-likelihood estimator (APLE) scatterplot — aple.plot","text":"aple.plot returns list components: X vector described Li et al. (2007), p. 366. Y vector described Li et al. (2007), p. 367. localAple returns vector local APLE values.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.plot.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Approximate profile-likelihood estimator (APLE) scatterplot — aple.plot","text":"Li, H, Calder, C. . Cressie N. . C. (2007) Beyond Moran's : testing spatial dependence based spatial autoregressive model. Geographical Analysis 39, pp. 357-375; Li, H, Calder, C. . Cressie N. . C. (2012) One-step estimation spatial dependence parameters: Properties extensions APLE statistic, Journal Multivariate Analysis 105, 68-84.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.plot.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Approximate profile-likelihood estimator (APLE) scatterplot — aple.plot","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/aple.plot.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Approximate profile-likelihood estimator (APLE) scatterplot — aple.plot","text":"","code":"# \\dontrun{ wheat <- st_read(system.file(\"shapes/wheat.gpkg\", package=\"spData\")[1], quiet=TRUE) nbr1 <- spdep::poly2nb(wheat, queen=FALSE) nbrl <- spdep::nblag(nbr1, 2) #> Warning: lag 2 neighbour object has 2 sub-graphs nbr12 <- spdep::nblag_cumul(nbrl) cms0 <- with(as.data.frame(wheat), tapply(yield, c, median)) cms1 <- c(model.matrix(~ factor(c) -1, data=wheat) %*% cms0) wheat$yield_detrend <- wheat$yield - cms1 plt_out <- aple.plot(as.vector(scale(wheat$yield_detrend, scale=FALSE)),  spdep::nb2listw(nbr12, style=\"W\"), cex=0.6) lm_obj <- lm(Y ~ X, plt_out) abline(lm_obj) abline(v=0, h=0, lty=2) zz <- summary(influence.measures(lm_obj)) #> Potentially influential observations of #> \t lm(formula = Y ~ X, data = plt_out) : #>  #>     dfb.1_ dfb.X dffit   cov.r   cook.d hat     #> 34  -0.12   0.01 -0.12    0.98_*  0.01   0.00   #> 50   0.10   0.01  0.11    0.98_*  0.01   0.00   #> 60   0.00   0.00  0.00    1.01_*  0.00   0.01   #> 118  0.01   0.01  0.02    1.01_*  0.00   0.01   #> 137 -0.10  -0.01 -0.10    0.98_*  0.01   0.00   #> 143 -0.02  -0.04 -0.05    1.01_*  0.00   0.01   #> 157 -0.10  -0.05 -0.11    0.99_*  0.01   0.00   #> 166  0.00   0.00  0.00    1.02_*  0.00   0.02_* #> 168  0.01   0.02  0.03    1.01_*  0.00   0.01   #> 176 -0.10   0.17 -0.20_*  0.99    0.02   0.01   #> 177  0.03  -0.07  0.08    1.01_*  0.00   0.01   #> 191  0.01   0.04  0.04    1.02_*  0.00   0.02_* #> 192  0.10   0.18  0.20_*  0.99    0.02   0.01   #> 201 -0.10   0.07 -0.12    0.99_*  0.01   0.00   #> 216  0.02   0.05  0.05    1.02_*  0.00   0.01_* #> 217  0.03   0.08  0.09    1.02_*  0.00   0.01_* #> 225 -0.11  -0.07 -0.13    0.98_*  0.01   0.00   #> 237 -0.10   0.02 -0.10    0.99_*  0.01   0.00   #> 242 -0.02  -0.04 -0.04    1.01_*  0.00   0.01   #> 287  0.14  -0.23  0.27_*  0.97_*  0.04   0.01   #> 290 -0.18  -0.35 -0.40_*  0.95_*  0.08   0.01   #> 295 -0.01  -0.01 -0.01    1.01_*  0.00   0.01   #> 322  0.00   0.00  0.00    1.01_*  0.00   0.01   #> 325 -0.10  -0.07 -0.12    0.99_*  0.01   0.00   #> 351  0.19  -0.04  0.20_*  0.94_*  0.02   0.00   #> 369  0.01  -0.03  0.03    1.01_*  0.00   0.01   #> 376 -0.05  -0.13 -0.14    1.02_*  0.01   0.02_* #> 392 -0.04   0.08 -0.09    1.01_*  0.00   0.01   #> 393 -0.03   0.06 -0.07    1.01_*  0.00   0.01   #> 394 -0.01   0.03 -0.03    1.01_*  0.00   0.01   #> 402  0.10   0.02  0.10    0.99_*  0.01   0.00   #> 429  0.13  -0.10  0.16    0.98_*  0.01   0.00   #> 430 -0.11  -0.23 -0.25_*  0.99    0.03   0.01   #> 438  0.00  -0.01 -0.01    1.01_*  0.00   0.01   #> 442 -0.01   0.04 -0.04    1.02_*  0.00   0.02_* #> 443 -0.01   0.02 -0.02    1.02_*  0.00   0.01_* #> 461  0.02   0.04  0.04    1.01_*  0.00   0.01   #> 462  0.01   0.03  0.03    1.03_*  0.00   0.02_* #> 466  0.01  -0.02  0.02    1.02_*  0.00   0.01_* #> 467 -0.03   0.08 -0.08    1.02_*  0.00   0.01_* #> 468  0.02  -0.04  0.04    1.01_*  0.00   0.01   #> 480  0.13   0.05  0.14    0.97_*  0.01   0.00   #> 488  0.16   0.09  0.18    0.96_*  0.02   0.00   #> 492 -0.13   0.12 -0.17    0.98_*  0.01   0.00   infl <- as.integer(rownames(zz)) points(plt_out$X[infl], plt_out$Y[infl], pch=3, cex=0.6, col=\"red\")  crossprod(plt_out$Y, plt_out$X)/crossprod(plt_out$X) #>           [,1] #> [1,] 0.6601805 wheat$localAple <- localAple(as.vector(scale(wheat$yield_detrend, scale=FALSE)),  spdep::nb2listw(nbr12, style=\"W\")) mean(wheat$localAple) #> [1] 0.6601805 hist(wheat$localAple)  opar <- par(no.readonly=TRUE) plot(wheat[,\"localAple\"], reset=FALSE) text(st_coordinates(st_centroid(st_geometry(wheat)))[infl,], labels=rep(\"*\", length(infl)))  par(opar) # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/do_ldet.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial regression model Jacobian computations — do_ldet","title":"Spatial regression model Jacobian computations — do_ldet","text":"functions made available package namespace developers, intended users. provide shared infrastructure setting data Jacobian computation, caclulating Jacobian, either exactly approximately, maximum likelihood fitting spatial regression models. techniques used exact eigenvalue, Cholesky decompositions (Matrix, spam), LU ones, Chebyshev Monte Carlo approximations; moments use methods due Martin Smirnov/Anselin.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/do_ldet.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial regression model Jacobian computations — do_ldet","text":"","code":"do_ldet(coef, env, which=1) jacobianSetup(method, env, con, pre_eig=NULL, trs=NULL, interval=NULL, which=1) cheb_setup(env, q=5, which=1) mcdet_setup(env, p=16, m=30, which=1) eigen_setup(env, which=1) eigen_pre_setup(env, pre_eig, which=1) spam_setup(env, pivot=\"MMD\", which=1) spam_update_setup(env, in_coef=0.1, pivot=\"MMD\", which=1) Matrix_setup(env, Imult, super=as.logical(NA), which=1) Matrix_J_setup(env, super=FALSE, which=1) LU_setup(env, which=1) LU_prepermutate_setup(env, coef=0.1, order=FALSE, which=1) moments_setup(env, trs=NULL, m, p, type=\"MC\", correct=TRUE, trunc=TRUE, eq7=TRUE, which=1) SE_classic_setup(env, SE_method=\"LU\", p=16, m=30, nrho=200, interpn=2000,  interval=c(-1,0.999), SElndet=NULL, which=1) SE_whichMin_setup(env, SE_method=\"LU\", p=16, m=30, nrho=200, interpn=2000,  interval=c(-1,0.999), SElndet=NULL, which=1) SE_interp_setup(env, SE_method=\"LU\", p=16, m=30, nrho=200,  interval=c(-1,0.999), which=1) can.be.simmed(listw)"},{"path":"https://r-spatial.github.io/spatialreg/reference/do_ldet.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial regression model Jacobian computations — do_ldet","text":"coef spatial coefficient value env environment containing pre-computed objects, fixed assignment setup functions default 1; 2, use second listw object method string value, used jacobianSetup choose method con control list passed model fitting function parsed jacobianSetup set environment variables method-specific setup pre_eig pre-computed eigenvalues length n q Chebyshev approximation order; default calling spdep functions 5, missing default p Monte Carlo approximation number random normal variables; default calling spdep functions 16, missing default m Monte Carlo approximation number series terms; default calling spdep functions 30, missing default; m serves purpose moments method pivot default “MMD”, may also “RCM” Cholesky decompisition using spam in_coef fill-initiation coefficient value, default 0.1 Imult see Cholesky; numeric scalar defaults zero. matrix decomposed +m*m value Imult identity matrix order ncol(). Default calling spdep functions 2, missing default, rescaled binary weights matrices proportion maximim row sum calling functions super see Cholesky; logical scalar indicating supernodal decomposition created.  alternative simplicial decomposition. Default calling spdep functions FALSE “Matrix_J” .logical(NA) “Matrix”.  Setting NA leaves choice CHOLMOD-internal heuristic order default FALSE; used LU_prepermutate, note warnings given lu method trs numeric vector m traces, trW type moments trace type, see trW correct default TRUE: use Smirnov correction term, see trW trunc default TRUE: truncate Smirnov correction term, see trW eq7 default TRUE; use equation 7 Smirnov Anselin (2009), FALSE unit root correction SE_method default “LU”, alternatively “MC”; underlying lndet method use generating SE toolbox emulation grid nrho default 200, number lndet values first stage SE toolbox emulation grid interval default c(-1,0.999) interval argument NULL, bounds SE toolbox emulation grid interpn default 2000, number lndet values interpolate second stage SE toolbox emulation grid SElndet default NULL, used pass pre-computed two-column matrix coefficient values corresponding interpolated lndet values listw spatial weights object","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/do_ldet.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial regression model Jacobian computations — do_ldet","text":"Since environments containers R workspace passed reference rather value, useful passing objects functions called numerical optimisation, maximum likelihood estimation spatial regression models. technique can save little time function call, balanced need access objects environment inside function. environment contain family string object either “SAR”, “CAR” “SMA” (used do_ldet choose spatial moving average spautolm, specific objects calling set-functions: eigen Classical Ord eigenvalue computations - either: listw listw spatial weights object can.sim logical scalar: can spatial weights made symmetric similarity verbose logical scalar: legacy report print control, historical reasons : pre_eig pre-computed eigenvalues assigns environment: eig vector eigenvalues eig.range search interval spatial coefficient method string: “eigen” Matrix Sparse matrix pre-computed Cholesky decomposition fast updating: listw listw spatial weights object can.sim logical scalar: can spatial weights made symmetric similarity assigns environment: csrw sparse spatial weights matrix nW negative sparse spatial weights matrix pChol “CHMfactor” factorising csrw Cholesky nChol “CHMfactor” factorising nW Cholesky method string: “Matrix” Matrix_J Standard Cholesky decomposition without updating: listw listw spatial weights object can.sim logical scalar: can spatial weights made symmetric similarity n number spatial objects assigns environment: csrw sparse spatial weights matrix sparse identity matrix super value super argument method string: “Matrix_J” spam Standard Cholesky decomposition without updating: listw listw spatial weights object can.sim logical scalar: can spatial weights made symmetric similarity n number spatial objects assigns environment: csrw sparse spatial weights matrix sparse identity matrix pivot string — pivot method method string: “spam” spam_update Pre-computed Cholesky decomposition updating: listw listw spatial weights object can.sim logical scalar: can spatial weights made symmetric similarity n number spatial objects assigns environment: csrw sparse spatial weights matrix sparse identity matrix csrwchol Cholesky decomposition updating method string: “spam” LU Standard LU decomposition without updating: listw listw spatial weights object n number spatial objects assigns environment: W sparse spatial weights matrix sparse identity matrix method string: “LU” LU_prepermutate Standard LU decomposition updating (pre-computed fill-reducing permutation): listw listw spatial weights object n number spatial objects assigns environment: W sparse spatial weights matrix lu_order order argument lu pq 2-column matrix row column permutation fill-reduction sparse identity matrix method string: “LU” MC Monte Carlo approximation: listw listw spatial weights object assigns environment: clx list Monte Carlo approximation terms  (first two simulated traces replaced analytical equivalents) W sparse spatial weights matrix method string: “MC” cheb Chebyshev approximation: listw listw spatial weights object assigns environment: trT vector Chebyshev approximation terms W sparse spatial weights matrix method string: “Chebyshev” moments moments approximation: listw listw spatial weights object can.sim logical scalar: can spatial weights made symmetric similarity assigns environment: trs vector traces, possibly approximated q12 integer vector length 2, unit roots terms, ignored 0.5-52 eq7 logical scalar: use equation 7 correct logical scalar: use Smirnov correction term trunc logical scalar: truncate Smirnov correction term method string: “moments” SE_classic : listw listw spatial weights object n number spatial objects assigns environment: detval two column matrix lndet grid values method string: “SE_classic” SE_method string: “LU” “MC” SE_whichMin : listw listw spatial weights object n number spatial objects assigns environment: detval two column matrix lndet grid values method string: “SE_whichMin” SE_method string: “LU” “MC” SE_interp : listw listw spatial weights object n number spatial objects assigns environment: fit fitted spline object predict lndet values method string: “SE_interp” SE_method string: “LU” “MC” set-functions may also assign similar environment weights made symmetric similarity. Three set-functions emulate behaviour Spatial Econometrics toolbox (March 2010) maximum likelihood lndet grid performance. toolbox lndet functions compute smaller number lndet values grid coefficient values (spacing 0.01), interpolate finer grid values (spacing 0.001). “SE_classic”, implementation SE toolbox code, example f_sar.m, appears selected row grid matrix one correct row candidate coefficient value 0.005 0.01-fuzz, always rounding row index . possible alternative choose index closest candidate coefficient value (“SE_whichMin”). Another alternative fit spline model first stage coarser grid, pass fitted model log likelihood function make point prediction using candidate coefficient value, rather finding grid index (“SE_interp”).","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/do_ldet.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial regression model Jacobian computations — do_ldet","text":"do_ldet returns value Jacobian calculation method recorded environment argument, Monte Carlo approximation, returns measure spread approximation “sd” attribute; remaining functions modify environment place side effect return nothing.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/do_ldet.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial regression model Jacobian computations — do_ldet","text":"LeSage J RK Pace (2009) Introduction Spatial Econometrics. CRC Press, Boca Raton, pp. 77–110. Bivand, R. S., Hauke, J., Kossowski, T. (2013). Computing Jacobian Gaussian spatial autoregressive models: illustrated comparison available methods. Geographical Analysis, 45(2), 150-179.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/do_ldet.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial regression model Jacobian computations — do_ldet","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/do_ldet.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial regression model Jacobian computations — do_ldet","text":"","code":"data(boston, package=\"spData\") #require(\"spdep\", quietly=TRUE) lw <- spdep::nb2listw(boston.soi) can.sim <- can.be.simmed(lw) env <- new.env(parent=globalenv()) assign(\"listw\", lw, envir=env) assign(\"can.sim\", can.sim, envir=env) assign(\"similar\", FALSE, envir=env) assign(\"verbose\", FALSE, envir=env) assign(\"family\", \"SAR\", envir=env) eigen_setup(env) get(\"similar\", envir=env) #> [1] TRUE do_ldet(0.5, env) #> [1] -18.26702 rm(env) env <- new.env(parent=globalenv()) assign(\"listw\", lw, envir=env) assign(\"can.sim\", can.sim, envir=env) assign(\"similar\", FALSE, envir=env) assign(\"verbose\", FALSE, envir=env) assign(\"family\", \"SAR\", envir=env) assign(\"n\", length(boston.soi), envir=env) eigen_pre_setup(env, pre_eig=eigenw(similar.listw(lw))) do_ldet(0.5, env) #> [1] -18.26702 rm(env) env <- new.env(parent=globalenv()) assign(\"listw\", lw, envir=env) assign(\"can.sim\", can.sim, envir=env) assign(\"similar\", FALSE, envir=env) assign(\"family\", \"SAR\", envir=env) assign(\"n\", length(boston.soi), envir=env) Matrix_setup(env, Imult=2, super=FALSE) get(\"similar\", envir=env) #> [1] TRUE do_ldet(0.5, env) #> [1] -18.26702 rm(env) env <- new.env(parent=globalenv()) assign(\"listw\", lw, envir=env) assign(\"n\", length(boston.soi), envir=env) assign(\"can.sim\", can.sim, envir=env) assign(\"similar\", FALSE, envir=env) assign(\"family\", \"SAR\", envir=env) spam_setup(env) get(\"similar\", envir=env) #> [1] TRUE do_ldet(0.5, env) #> [1] -18.26702 #> attr(,\"logarithm\") #> [1] TRUE rm(env) env <- new.env(parent=globalenv()) assign(\"listw\", lw, envir=env) assign(\"n\", length(boston.soi), envir=env) assign(\"similar\", FALSE, envir=env) assign(\"family\", \"SAR\", envir=env) LU_setup(env) get(\"similar\", envir=env) #> [1] FALSE do_ldet(0.5, env) #> [1] -18.26702 rm(env) env <- new.env(parent=globalenv()) assign(\"listw\", lw, envir=env) assign(\"n\", length(boston.soi), envir=env) assign(\"similar\", FALSE, envir=env) assign(\"family\", \"SAR\", envir=env) LU_prepermutate_setup(env) get(\"similar\", envir=env) #> [1] FALSE do_ldet(0.5, env) #> [1] -18.26702 rm(env) env <- new.env(parent=globalenv()) assign(\"listw\", lw, envir=env) assign(\"similar\", FALSE, envir=env) assign(\"family\", \"SAR\", envir=env) cheb_setup(env, q=5) get(\"similar\", envir=env) #> [1] FALSE do_ldet(0.5, env) #> [1] -18.26176 rm(env) env <- new.env(parent=globalenv()) assign(\"listw\", lw, envir=env) assign(\"n\", length(boston.soi), envir=env) assign(\"similar\", FALSE, envir=env) assign(\"family\", \"SAR\", envir=env) set.seed(12345) mcdet_setup(env, p=16, m=30) get(\"similar\", envir=env) #> [1] FALSE do_ldet(0.5, env) #> [1] -18.38606 #> attr(,\"sd\") #> [1] 0.2045107 rm(env)"},{"path":"https://r-spatial.github.io/spatialreg/reference/eigenw.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial weights matrix eigenvalues — griffith_sone","title":"Spatial weights matrix eigenvalues — griffith_sone","text":"eigenw function returns numeric vector eigenvalues weights matrix generated spatial weights object listw. eigenvalues used speed computation Jacobian spatial model estimation: $$\\log(\\det[- \\rho W]) = \\sum_{=1}^{n}\\log(1 - \\rho \\lambda_i)$$ \\(W\\) n n spatial weights matrix, \\(\\lambda_i\\) eigenvalues \\(W\\).","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/eigenw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial weights matrix eigenvalues — griffith_sone","text":"","code":"eigenw(listw, quiet=NULL) griffith_sone(P, Q, type=\"rook\") subgraph_eigenw(nb, glist=NULL, style=\"W\", zero.policy=NULL, quiet=NULL)"},{"path":"https://r-spatial.github.io/spatialreg/reference/eigenw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial weights matrix eigenvalues — griffith_sone","text":"listw listw object created example nb2listw quiet default NULL, use global !verbose option value; set FALSE short summary P number columns grid (number units horizontal axis direction) Q number rows grid (number units vertical axis direction.) type “rook” “queen” nb object class nb glist list general weights corresponding neighbours style style can take values “W”, “B”, “C”, “U”, “minmax” “S” zero.policy default NULL, use global option value; FALSE stop error empty neighbour sets, TRUE permit weights list formed zero-length weights vectors","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/eigenw.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial weights matrix eigenvalues — griffith_sone","text":"griffith_sone function function may used, following Ord Gasim (references see Griffith Sone (1995)), calculate analytical eigenvalues binary rook queen contiguous neighbours data arranged regular P times Q grid. subgraph_eigenw function may used multiple graph components, largest may handled dense matrix. eigenvalues computed subgraph turn, catenated reconstruct complete set. functions may used provide pre-computed eigenvalues spatial regression functions.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/eigenw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial weights matrix eigenvalues — griffith_sone","text":"numeric complex vector eigenvalues weights matrix generated spatial weights object.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/eigenw.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial weights matrix eigenvalues — griffith_sone","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 155; Ord, J. K. 1975 Estimation methods models spatial interaction, Journal American Statistical Association, 70, 120-126.; Griffith, D. . Sone, . (1995). Trade-offs associated normalizing constant computational simplifications estimating spatial statistical models. Journal Statistical Computation Simulation, 51, 165-183.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/eigenw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial weights matrix eigenvalues — griffith_sone","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/eigenw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial weights matrix eigenvalues — griffith_sone","text":"","code":"#require(spdep) data(oldcol, package=\"spdep\") W.eig <- eigenw(spdep::nb2listw(COL.nb, style=\"W\")) 1/range(W.eig) #> [1] -1.536177  1.000000 S.eig <- eigenw(spdep::nb2listw(COL.nb, style=\"S\")) 1/range(S.eig) #> [1] -1.7364189  0.8918997 B.eig <- eigenw(spdep::nb2listw(COL.nb, style=\"B\")) 1/range(B.eig) #> [1] -0.3229290  0.1692726 # cases for intrinsically asymmetric weights crds <- cbind(COL.OLD$X, COL.OLD$Y) k3 <- spdep::knn2nb(spdep::knearneigh(crds, k=3)) #> Warning: neighbour object has 2 sub-graphs spdep::is.symmetric.nb(k3) #> [1] FALSE k3eig <- eigenw(spdep::nb2listw(k3, style=\"W\")) is.complex(k3eig) #> [1] TRUE rho <- 0.5 Jc <- sum(log(1 - rho * k3eig)) # complex eigenvalue Jacobian Jc #> [1] -1.749705+0i # subgraphs nc <- attr(k3, \"ncomp\") if (is.null(nc)) nc <- spdep::n.comp.nb(k3) nc$nc #> [1] 2 table(nc$comp.id) #>  #>  1  2  #> 43  6  k3eigSG <- subgraph_eigenw(k3, style=\"W\") all.equal(sort(k3eig), k3eigSG) #> [1] TRUE W <- as(spdep::nb2listw(k3, style=\"W\"), \"CsparseMatrix\") I <- diag(length(k3)) Jl <- sum(log(abs(diag(slot(lu(I - rho * W), \"U\"))))) # LU Jacobian equals complex eigenvalue Jacobian Jl #> [1] -1.749705 all.equal(Re(Jc), Jl) #> [1] TRUE # wrong value if only real part used Jr <- sum(log(1 - rho * Re(k3eig))) Jr #> [1] -1.762734 all.equal(Jr, Jl) #> [1] \"Mean relative difference: 0.007391147\" # construction of Jacobian from complex conjugate pairs (Jan Hauke) Rev <- Re(k3eig)[which(Im(k3eig) == 0)] # real eigenvalues Cev <- k3eig[which(Im(k3eig) != 0)] pCev <- Cev[Im(Cev) > 0] # separate complex conjugate pairs RpCev <- Re(pCev) IpCev <- Im(pCev) # reassemble Jacobian Jc1 <- sum(log(1 - rho*Rev)) + sum(log((1 - rho * RpCev)^2 + (rho^2)*(IpCev^2))) all.equal(Re(Jc), Jc1) #> [1] TRUE # impact of omitted complex part term in real part only Jacobian Jc2 <- sum(log(1 - rho*Rev)) + sum(log((1 - rho * RpCev)^2)) all.equal(Jr, Jc2) #> [1] TRUE # trace of asymmetric (WW) and crossprod of complex eigenvalues for APLE sum(diag(W %*% W)) #> [1] 11.55556 crossprod(k3eig) #>             [,1] #> [1,] 11.55556+0i # analytical regular grid eigenvalues rg <- spdep::cell2nb(ncol=7, nrow=7, type=\"rook\") rg_eig <- eigenw(spdep::nb2listw(rg, style=\"B\")) rg_GS <- griffith_sone(P=7, Q=7, type=\"rook\") all.equal(rg_eig, rg_GS) #> [1] TRUE # \\dontrun{ run <- FALSE if (require(\"RSpectra\", quietly=TRUE)) run <- TRUE if (run) { B <- as(spdep::nb2listw(rg, style=\"B\"), \"CsparseMatrix\") res1 <- eigs(B, k=1, which=\"LR\")$values resn <- eigs(B, k=1, which=\"SR\")$values print(Re(c(resn, res1))) } #> [1] -3.695518  3.695518 if (run) { print(all.equal(range(Re(rg_eig)), c(resn, res1)))  } #> [1] TRUE if (run) { lw <- spdep::nb2listw(rg, style=\"W\") rg_eig <- eigenw(similar.listw(lw)) print(range(Re(rg_eig))) } #> [1] -1  1 if (run) { W  <- as(lw, \"CsparseMatrix\") print(Re(c(eigs(W, k=1, which=\"SR\")$values, eigs(W, k=1, which=\"LR\")$values))) }# } #> [1] -1  1"},{"path":"https://r-spatial.github.io/spatialreg/reference/gstsls.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial simultaneous autoregressive SAC model estimation by GMM — gstsls","title":"Spatial simultaneous autoregressive SAC model estimation by GMM — gstsls","text":"implementation Kelejian Prucha's generalised moments estimator autoregressive parameter spatial model   spatially lagged dependent variable.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/gstsls.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial simultaneous autoregressive SAC model estimation by GMM — gstsls","text":"","code":"gstsls(formula, data = list(), listw, listw2 = NULL, na.action = na.fail,      zero.policy = attr(listw, \"zero.policy\"), pars=NULL, scaleU=FALSE, control = list(),      verbose=NULL, method=\"nlminb\", robust=FALSE, legacy=FALSE, W2X=TRUE, sig2n_k=FALSE)  # S3 method for class 'Gmsar' impacts(obj, ..., n = NULL, tr = NULL, R = NULL,  listw = NULL, evalues=NULL, tol = 1e-06, empirical = FALSE, Q=NULL)"},{"path":"https://r-spatial.github.io/spatialreg/reference/gstsls.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial simultaneous autoregressive SAC model estimation by GMM — gstsls","text":"formula symbolic description model fit. details model specification given lm() data optional data frame containing variables model. default variables taken environment function called. listw listw object created example nb2listw listw2 listw object created example nb2listw, given, set spatial weights listw argument na.action function (default na.fail), can also na.omit na.exclude consequences residuals fitted values - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE (default) assign NA - causing GMerrorsar() terminate error pars starting values \\(\\lambda\\) \\(\\sigma^2\\) GMM optimisation,   missing (default), approximated initial 2sls model autocorrelation coefficient corrected weights style   model sigma squared scaleU Default FALSE: scale OLS residuals computing moment matrices; used pars argument missing control list control parameters. See details optim nlminb verbose default NULL, use global option value; TRUE, reports function values optimization. method default nlminb, optionally method passed optim use alternative optimizer robust see stsls legacy see stsls W2X see stsls sig2n_k see stsls obj spatial regression object created lagsarlm, lagmess lmSLX; HPDinterval.LagImpact, LagImpact object ... Arguments passed methods coda package tr vector traces powers spatial weights matrix created using trW, approximate impact measures; given, listw must given exact measures (small moderate spatial weights matrices); traces must spatial weights used fitting spatial regression, must row-standardised evalues vector eigenvalues spatial weights matrix impacts calculations R given, simulations used compute distributions impact measures, returned mcmc objects; objects used convenience output MCMC process tol Argument passed mvrnorm: tolerance (relative largest variance) numerical lack positive-definiteness coefficient covariance matrix empirical Argument passed mvrnorm (default FALSE): true, coefficients covariance matrix specify empirical population mean covariance matrix Q default NULL, else integer number cumulative power series impacts calculate tr given n defaults length(obj$residuals); method Gmsar objects may used panel settings compute impacts cross-sectional weights , suggested Angela Parenti","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/gstsls.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial simultaneous autoregressive SAC model estimation by GMM — gstsls","text":"control list set care, function converge values close ML estimator   without requiring computation Jacobian, resource-intensive part ML estimation.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/gstsls.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial simultaneous autoregressive SAC model estimation by GMM — gstsls","text":"list object class Gmsar lambda simultaneous autoregressive error coefficient coefficients GMM coefficient estimates (including spatial autocorrelation coefficient) rest.se GMM coefficient standard errors s2 GMM residual variance SSE sum squared GMM errors parameters number parameters estimated lm.model NULL call call used create object residuals GMM residuals lm.target NULL fitted.values Difference residuals response variable formula model formula aliased NULL zero.policy zero.policy model LL NULL vv list internal bigG litg components testing optimisation surface optres object returned optimizer pars start parameter values optimisation Hcov NULL na.action (possibly) named vector excluded omitted observations non-default na.action argument used","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/gstsls.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial simultaneous autoregressive SAC model estimation by GMM — gstsls","text":"Kelejian, H. H., Prucha, . R., 1999. Generalized Moments Estimator Autoregressive Parameter Spatial Model. International Economic Review, 40, pp. 509–533; Cressie, N. . C. 1993 Statistics spatial data, Wiley, New York. Roger Bivand, Gianfranco Piras (2015). Comparing Implementations Estimation Methods Spatial Econometrics. Journal Statistical Software, 63(18), 1-36. doi:10.18637/jss.v063.i18 .","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/gstsls.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial simultaneous autoregressive SAC model estimation by GMM — gstsls","text":"Gianfranco Piras Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/gstsls.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial simultaneous autoregressive SAC model estimation by GMM — gstsls","text":"","code":"#require(\"spdep\", quietly=TRUE)  data(oldcol, package=\"spdep\") COL.errW.GM <- gstsls(CRIME ~ INC + HOVAL, data=COL.OLD, spdep::nb2listw(COL.nb, style=\"W\")) summary(COL.errW.GM) #>  #> Call: #> gstsls(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,  #>     style = \"W\")) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.87710  -5.74981  -0.21447   6.19490  22.85527  #>  #> Type: GM SARAR estimator #> Coefficients: (GM standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> Rho_Wy       0.454171   0.177939  2.5524  0.010699 #> (Intercept) 43.782818  10.467857  4.1826 2.882e-05 #> INC         -0.994831   0.366818 -2.7121  0.006687 #> HOVAL       -0.267076   0.088149 -3.0298  0.002447 #>  #> Lambda: 0.016647 #> Residual variance (sigma squared): 94.921, (sigma: 9.7427) #> GM argmin sigma squared: 93.729 #> Number of observations: 49  #> Number of parameters estimated: 6  #>  aa <- GMargminImage(COL.errW.GM) levs <- quantile(aa$z, seq(0, 1, 1/12)) image(aa, breaks=levs, xlab=\"lambda\", ylab=\"s2\") points(COL.errW.GM$lambda, COL.errW.GM$s2, pch=3, lwd=2) contour(aa, levels=signif(levs, 4), add=TRUE)  COL.errW.GM <- gstsls(CRIME ~ INC + HOVAL, data=COL.OLD,  spdep::nb2listw(COL.nb, style=\"W\"), scaleU=TRUE) summary(COL.errW.GM) #>  #> Call: #> gstsls(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,  #>     style = \"W\"), scaleU = TRUE) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.87710  -5.74981  -0.21447   6.19490  22.85527  #>  #> Type: GM SARAR estimator #> Coefficients: (GM standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> Rho_Wy       0.454171   0.177939  2.5524  0.010699 #> (Intercept) 43.782818  10.467857  4.1826 2.882e-05 #> INC         -0.994831   0.366818 -2.7121  0.006687 #> HOVAL       -0.267076   0.088149 -3.0298  0.002447 #>  #> Lambda: 0.016647 #> Residual variance (sigma squared): 94.921, (sigma: 9.7427) #> (scaled) GM argmin sigma squared: 0.96653 #> Number of observations: 49  #> Number of parameters estimated: 6  #>  listw <- spdep::nb2listw(COL.nb) W <- as(listw, \"CsparseMatrix\") trMat <- trW(W, type=\"mult\") impacts(COL.errW.GM, tr=trMat) #> Impact measures (lag, trace): #>           Direct   Indirect      Total #> INC   -1.0543769 -0.7682309 -1.8226078 #> HOVAL -0.2830618 -0.2062420 -0.4893038"},{"path":"https://r-spatial.github.io/spatialreg/reference/impacts.html","id":null,"dir":"Reference","previous_headings":"","what":"Impacts in spatial lag models — impacts","title":"Impacts in spatial lag models — impacts","text":"calculation impacts spatial lag spatial Durbin models needed order interpret regression coefficients correctly, spillovers terms data generation processes (unlike spatial error model). Methods “SLX” Bayesian fitted models also provided, former need MC simulations, latter pass MCMC draws.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/impacts.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Impacts in spatial lag models — impacts","text":"","code":"#\\method{impacts}{sarlm}(obj, \\dots, tr, R = NULL, listw = NULL, evalues=NULL, # useHESS = NULL, tol = 1e-06, empirical = FALSE, Q=NULL) #\\method{impacts}{lagmess}(obj, ..., R=NULL, listw=NULL, tol=1e-6, # empirical=FALSE) #\\method{impacts}{SLX}(obj, ...) #\\method{impacts}{MCMC_sar_g}(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL) #\\method{impacts}{MCMC_sem_g}(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL) #\\method{impacts}{MCMC_sac_g}(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL) # S3 method for class 'LagImpact' plot(x, ..., choice=\"direct\", trace=FALSE, density=TRUE) # S3 method for class 'LagImpact' print(x, ..., reportQ=NULL) # S3 method for class 'LagImpact' summary(object, ..., zstats=FALSE, short=FALSE, reportQ=NULL) #\\method{print}{WXImpact}(x, ...) #\\method{summary}{WXImpact}(object, ..., adjust_k=(attr(object, \"type\") == \"SDEM\")) # S3 method for class 'LagImpact' HPDinterval(obj, prob = 0.95, ..., choice=\"direct\") intImpacts(rho, beta, P, n, mu, Sigma, irho, drop2beta, bnames, interval,  type, tr, R, listw, evalues, tol, empirical, Q, icept, iicept, p, mess=FALSE,  samples=NULL, zero_fill = NULL, dvars = NULL)"},{"path":"https://r-spatial.github.io/spatialreg/reference/impacts.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Impacts in spatial lag models — impacts","text":"obj spatial regression object created lagsarlm lmSLX; HPDinterval.LagImpact, LagImpact object ... Arguments passed methods coda package tr vector traces powers spatial weights matrix created using trW, approximate impact measures; given, listw must given exact measures (small moderate spatial weights matrices); traces must spatial weights used fitting spatial regression, must row-standardised listw tr given, spatial weights object created nb2listw; must spatial weights used fitting spatial regression, row-standardised evalues vector eigenvalues spatial weights matrix impacts calculations n defaults length(obj$residuals); method gmsar objects may used panel settings compute impacts cross-sectional weights , suggested Angela Parenti R given, simulations used compute distributions impact measures, returned mcmc objects; objects used convenience output MCMC process useHESS Use Hessian approximation (available) even asymptotic coefficient covariance matrix available; used comparing methods tol Argument passed mvrnorm: tolerance (relative largest variance) numerical lack positive-definiteness coefficient covariance matrix empirical Argument passed mvrnorm (default FALSE): true, coefficients covariance matrix specify empirical population mean covariance matrix Q default NULL, else integer number cumulative power series impacts calculate tr given reportQ default NULL; TRUE Q given argument impacts, report impact components x, object LagImpact objects created impacts methods zstats default FALSE, TRUE, also return z-values p-values impacts based simulations short default FALSE, TRUE passed print summary method omit printing mcmc summaries choice One three impacts: direct, indirect, total trace Argument passed plot.mcmc: plot trace plots density Argument passed plot.mcmc: plot density plots prob Argument passed HPDinterval.mcmc: numeric scalar interval (0,1) giving target probability content intervals adjust_k default TRUE SDEM else FALSE, adjust internal OLS SDEM standard errors dividing n rather (n-k) (default changed bug fixed 0.7-8; standard errors now ML SDEM summary impacts summary identical - SLX use FALSE) rho, beta, P, mu, Sigma, irho, drop2beta, bnames,     interval, type, icept, iicept, p, mess, samples, zero_fill, dvars internal arguments shared inside impacts methods","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/impacts.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Impacts in spatial lag models — impacts","text":"called without R set, method returns direct, indirect total impacts variables model, variables tha spatial lag model case, variables spatial lags spatial Durbin (mixed) model case. spatial lag impact measures computed using eq. 2.46 (LeSage Pace, 2009, p. 38), either using exact dense matrix (listw given), traces powers weights matrix (tr given). traces created powering sparse matrices, exact trace methods give similar results, unless number powers used small, spatial coefficient close bounds. R given, simulations used create distributions impact measures, provided fitted model object contains coefficient covariance matrix. simulations made using mvrnorm coefficients covariance matrix fitted model. simulations stored mcmc objects defined coda package; objects used convenience output MCMC process. simulated values coefficients checked see spatial coefficient remains within valid interval — draws outside interval discarded. model fitted “Durbin=” set formula subsetting explanatory variables, impacts object returned reports Durbin impacts variables included formula lag impacts variables. Q tr given, addition impact component results provided step traces powers weights matrix including Q'th power. increases computing time output object substantially increased size proportion size Q. method gmsar objects type SARAR output gstsls, assume spatial error coefficient fixed, thus omitted coefficients covariance matrix used simulation.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/impacts.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Impacts in spatial lag models — impacts","text":"object class LagImpact. simulation carried , object returned list : direct numeric vector indirect numeric vector total numeric vector matching Qres list attribute Q given. simulation carried , object returned list : res list three components non-simulation case, matching Qres list attribute Q given sres list three mcmc matrices, direct, indirect total impacts matching Qmcmc list attribute Q given","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/impacts.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Impacts in spatial lag models — impacts","text":"LeSage J RK Pace (2009) Introduction Spatial Econometrics. CRC Press, Boca Raton, pp. 33–42, 114–115; LeSage J MM Fischer (2008) Spatial growth regressions: model specification, estimation interpretation. Spatial Economic Analysis 3 (3), pp. 275–304. Roger Bivand, Gianfranco Piras (2015). Comparing Implementations Estimation Methods Spatial Econometrics. Journal Statistical Software, 63(18), 1-36. doi:10.18637/jss.v063.i18 .","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/impacts.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Impacts in spatial lag models — impacts","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/impacts.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Impacts in spatial lag models — impacts","text":"","code":"require(\"sf\", quietly=TRUE) columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) #require(\"spdep\", quietly=TRUE) col.gal.nb <- spdep::read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) listw <- spdep::nb2listw(col.gal.nb) ev <- eigenw(listw) lobj <- lagsarlm(CRIME ~ INC + HOVAL, columbus, listw,  control=list(pre_eig=ev)) summary(lobj) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = columbus, listw = listw,  #>     control = list(pre_eig = ev)) #>  #> Residuals: #>         Min          1Q      Median          3Q         Max  #> -37.4497093  -5.4565567   0.0016387   6.7159553  24.7107978  #>  #> Type: lag  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 46.851431   7.314754  6.4051 1.503e-10 #> INC         -1.073533   0.310872 -3.4533 0.0005538 #> HOVAL       -0.269997   0.090128 -2.9957 0.0027381 #>  #> Rho: 0.40389, LR test value: 8.4179, p-value: 0.0037154 #> Asymptotic standard error: 0.12071 #>     z-value: 3.3459, p-value: 0.00082027 #> Wald statistic: 11.195, p-value: 0.00082027 #>  #> Log likelihood: -183.1683 for lag model #> ML residual variance (sigma squared): 99.164, (sigma: 9.9581) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 376.34, (AIC for lm: 382.75) #> LM test for residual autocorrelation #> test value: 0.19184, p-value: 0.66139 #>  mobj <- lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, Durbin=TRUE,  control=list(pre_eig=ev)) summary(mobj) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = columbus, listw = listw,  #>     Durbin = TRUE, control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.15904  -6.62594  -0.39823   6.57561  23.62757  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 45.592896  13.128680  3.4728 0.0005151 #> INC         -0.939088   0.338229 -2.7765 0.0054950 #> HOVAL       -0.299605   0.090843 -3.2980 0.0009736 #> lag.INC     -0.618375   0.577052 -1.0716 0.2838954 #> lag.HOVAL    0.266615   0.183971  1.4492 0.1472760 #>  #> Rho: 0.38251, LR test value: 4.1648, p-value: 0.041272 #> Asymptotic standard error: 0.16237 #>     z-value: 2.3557, p-value: 0.018488 #> Wald statistic: 5.5493, p-value: 0.018488 #>  #> Log likelihood: -182.0161 for mixed model #> ML residual variance (sigma squared): 95.051, (sigma: 9.7494) #> Number of observations: 49  #> Number of parameters estimated: 7  #> AIC: 378.03, (AIC for lm: 380.2) #> LM test for residual autocorrelation #> test value: 0.101, p-value: 0.75063 #>  mobj1 <- lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, Durbin= ~ INC,  control=list(pre_eig=ev)) summary(mobj1) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = columbus, listw = listw,  #>     Durbin = ~INC, control = list(pre_eig = ev)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.62163  -6.13108   0.11211   6.70682  24.76777  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 51.951213  12.577339  4.1305 3.619e-05 #> INC         -1.038812   0.337656 -3.0765  0.002094 #> HOVAL       -0.269345   0.090406 -2.9793  0.002889 #> lag.INC     -0.254653   0.544298 -0.4679  0.639887 #>  #> Rho: 0.35028, LR test value: 3.4351, p-value: 0.063823 #> Asymptotic standard error: 0.1617 #>     z-value: 2.1662, p-value: 0.030293 #> Wald statistic: 4.6926, p-value: 0.030293 #>  #> Log likelihood: -183.065 for mixed model #> ML residual variance (sigma squared): 99.846, (sigma: 9.9923) #> Number of observations: 49  #> Number of parameters estimated: 6  #> AIC: 378.13, (AIC for lm: 379.57) #> LM test for residual autocorrelation #> test value: 2.5646, p-value: 0.10928 #>  W <- as(listw, \"CsparseMatrix\") trMatc <- trW(W, type=\"mult\") trMC <- trW(W, type=\"MC\") set.seed(1) impacts(lobj, listw=listw) #> Impact measures (lag, exact): #>           Direct   Indirect      Total #> INC   -1.1225156 -0.6783818 -1.8008973 #> HOVAL -0.2823163 -0.1706152 -0.4529315 impacts(lobj, tr=trMatc) #> Impact measures (lag, trace): #>           Direct   Indirect      Total #> INC   -1.1225156 -0.6783818 -1.8008973 #> HOVAL -0.2823163 -0.1706152 -0.4529315 impacts(lobj, tr=trMC) #> Impact measures (lag, trace): #>           Direct   Indirect      Total #> INC   -1.1247738 -0.6761235 -1.8008973 #> HOVAL -0.2828842 -0.1700472 -0.4529315 impacts(lobj, evalues=ev) #> Impact measures (lag, evalues): #>           Direct   Indirect      Total #> INC   -1.1225156 -0.6783818 -1.8008973 #> HOVAL -0.2823163 -0.1706152 -0.4529315 library(coda) lobjIQ5 <- impacts(lobj, tr=trMatc, R=200, Q=5) summary(lobjIQ5, zstats=TRUE, short=TRUE) #> Impact measures (lag, trace): #>           Direct   Indirect      Total #> INC   -1.1225156 -0.6783818 -1.8008973 #> HOVAL -0.2823163 -0.1706152 -0.4529315 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3298544 0.3834114 0.5945946 #> HOVAL 0.1014420 0.1261509 0.2033617 #>  #> Simulated z-values: #>          Direct  Indirect     Total #> INC   -3.417467 -1.886887 -3.112575 #> HOVAL -2.895853 -1.551116 -2.406724 #>  #> Simulated p-values: #>       Direct     Indirect Total     #> INC   0.00063207 0.059176 0.0018546 #> HOVAL 0.00378129 0.120874 0.0160963 summary(lobjIQ5, zstats=TRUE, short=TRUE, reportQ=TRUE) #> Impact measures (lag, trace): #>           Direct   Indirect      Total #> INC   -1.1225156 -0.6783818 -1.8008973 #> HOVAL -0.2823163 -0.1706152 -0.4529315 #> ================================= #> Impact components #> $direct #>             INC         HOVAL #> Q1 -1.073533466 -0.2699971236 #> Q2  0.000000000  0.0000000000 #> Q3 -0.038985415 -0.0098049573 #> Q4 -0.005269654 -0.0013253350 #> Q5 -0.003276079 -0.0008239444 #>  #> $indirect #>            INC        HOVAL #> Q1  0.00000000  0.000000000 #> Q2 -0.43358910 -0.109049054 #> Q3 -0.13613675 -0.034238831 #> Q4 -0.06546038 -0.016463497 #> Q5 -0.02529105 -0.006360781 #>  #> $total #>            INC        HOVAL #> Q1 -1.07353347 -0.269997124 #> Q2 -0.43358910 -0.109049054 #> Q3 -0.17512216 -0.044043788 #> Q4 -0.07073004 -0.017788832 #> Q5 -0.02856713 -0.007184726 #>  #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3298544 0.3834114 0.5945946 #> HOVAL 0.1014420 0.1261509 0.2033617 #>  #> Simulated z-values: #>          Direct  Indirect     Total #> INC   -3.417467 -1.886887 -3.112575 #> HOVAL -2.895853 -1.551116 -2.406724 #>  #> Simulated p-values: #>       Direct     Indirect Total     #> INC   0.00063207 0.059176 0.0018546 #> HOVAL 0.00378129 0.120874 0.0160963 #> ======================================================== #> Simulated impact components z-values: #> $Direct #>           INC      HOVAL #> Q1 -3.3247602 -2.9008692 #> Q2        NaN        NaN #> Q3 -1.7540115 -1.4638039 #> Q4 -1.2444388 -1.0830402 #> Q5 -0.9405222 -0.8474166 #>  #> $Indirect #>           INC      HOVAL #> Q1        NaN        NaN #> Q2 -2.6977076 -2.1475985 #> Q3 -1.7540115 -1.4638039 #> Q4 -1.2444388 -1.0830402 #> Q5 -0.9405222 -0.8474166 #>  #> $Total #>           INC      HOVAL #> Q1 -3.3247602 -2.9008692 #> Q2 -2.6977076 -2.1475985 #> Q3 -1.7540115 -1.4638039 #> Q4 -1.2444388 -1.0830402 #> Q5 -0.9405222 -0.8474166 #>  #>  #> Simulated impact components p-values: #> $Direct #>    INC        HOVAL     #> Q1 0.00088495 0.0037213 #> Q2 NA         NA        #> Q3 0.07942853 0.1432475 #> Q4 0.21333812 0.2787906 #> Q5 0.34694975 0.3967630 #>  #> $Indirect #>    INC       HOVAL    #> Q1 NA        NA       #> Q2 0.0069819 0.031746 #> Q3 0.0794285 0.143248 #> Q4 0.2133381 0.278791 #> Q5 0.3469497 0.396763 #>  #> $Total #>    INC        HOVAL     #> Q1 0.00088495 0.0037213 #> Q2 0.00698187 0.0317457 #> Q3 0.07942853 0.1432475 #> Q4 0.21333812 0.2787906 #> Q5 0.34694975 0.3967630 #>  impacts(mobj, listw=listw) #> Impact measures (mixed, exact): #>           Direct   Indirect       Total #> INC   -1.0418080 -1.4804246 -2.52223255 #> HOVAL -0.2836325  0.2302055 -0.05342697 impacts(mobj, tr=trMatc) #> Impact measures (mixed, trace): #>           Direct   Indirect       Total #> INC   -1.0418080 -1.4804246 -2.52223255 #> HOVAL -0.2836325  0.2302055 -0.05342697 impacts(mobj, tr=trMC) #> Impact measures (mixed, trace): #>           Direct   Indirect       Total #> INC   -1.0462717 -1.4759609 -2.52223255 #> HOVAL -0.2829384  0.2295114 -0.05342697 impacts(mobj1, tr=trMatc) #> Impact measures (mixed, trace): #>           Direct   Indirect      Total #> INC   -1.0968247 -0.8939687 -1.9907934 #> HOVAL -0.2781941 -0.1363596 -0.4145537 impacts(mobj1, listw=listw) #> Impact measures (mixed, exact): #>           Direct   Indirect      Total #> INC   -1.0968247 -0.8939687 -1.9907934 #> HOVAL -0.2781941 -0.1363596 -0.4145537 # \\dontrun{ try(impacts(mobj, evalues=ev), silent=TRUE) #> Impact measures (mixed, evalues): #>           Direct   Indirect       Total #> INC   -1.0418080 -1.4804246 -2.52223255 #> HOVAL -0.2836325  0.2302055 -0.05342697 # } summary(impacts(mobj, tr=trMatc, R=200), short=TRUE, zstats=TRUE) #> Impact measures (mixed, trace): #>           Direct   Indirect       Total #> INC   -1.0418080 -1.4804246 -2.52223255 #> HOVAL -0.2836325  0.2302055 -0.05342697 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3407851 0.8610832 0.9221567 #> HOVAL 0.0980867 0.3285062 0.3625254 #>  #> Simulated z-values: #>          Direct   Indirect      Total #> INC   -3.017200 -1.7533600 -2.7522499 #> HOVAL -2.931757  0.6507956 -0.2035056 #>  #> Simulated p-values: #>       Direct    Indirect Total     #> INC   0.0025512 0.07954  0.0059187 #> HOVAL 0.0033705 0.51518  0.8387399 summary(impacts(mobj1, tr=trMatc, R=200), short=TRUE, zstats=TRUE) #> Impact measures (mixed, trace): #>           Direct   Indirect      Total #> INC   -1.0968247 -0.8939687 -1.9907934 #> HOVAL -0.2781941 -0.1363596 -0.4145537 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3752297 0.6525338 0.7183806 #> HOVAL 0.1078220 0.1277117 0.1990840 #>  #> Simulated z-values: #>          Direct  Indirect     Total #> INC   -2.902700 -1.247249 -2.649084 #> HOVAL -2.637881 -1.168002 -2.177921 #>  #> Simulated p-values: #>       Direct    Indirect Total    #> INC   0.0036996 0.21231  0.008071 #> HOVAL 0.0083426 0.24281  0.029412 xobj <- lmSLX(CRIME ~ INC + HOVAL, columbus, listw) summary(impacts(xobj)) #> Impact measures (SlX, glht, n-k): #>           Direct   Indirect       Total #> INC   -1.1081273 -1.3834468 -2.49157410 #> HOVAL -0.2949095  0.2261538 -0.06875574 #> ======================================================== #> Standard errors: #>          Direct  Indirect     Total #> INC   0.3749956 0.5591789 0.4928197 #> HOVAL 0.1013524 0.2026169 0.2049626 #> ======================================================== #> Z-values: #>          Direct  Indirect      Total #> INC   -2.955041 -2.474068 -5.0557523 #> HOVAL -2.909744  1.116164 -0.3354551 #>  #> p-values: #>       Direct    Indirect Total     #> INC   0.0031263 0.013358 4.287e-07 #> HOVAL 0.0036172 0.264352 0.73728   #>  eobj <- errorsarlm(CRIME ~ INC + HOVAL, columbus, listw, etype=\"emixed\") summary(impacts(eobj), adjust_k=TRUE) #> Impact measures (SDEM, glht, n): #>           Direct   Indirect      Total #> INC   -1.0695301 -1.1967736 -2.2663036 #> HOVAL -0.2803441  0.1467585 -0.1335856 #> ======================================================== #> Standard errors: #>           Direct  Indirect     Total #> INC   0.32471853 0.5689676 0.6209448 #> HOVAL 0.09180929 0.2008722 0.2323518 #> ======================================================== #> Z-values: #>          Direct   Indirect      Total #> INC   -3.293714 -2.1034124 -3.6497665 #> HOVAL -3.053548  0.7306064 -0.5749284 #>  #> p-values: #>       Direct     Indirect Total      #> INC   0.00098873 0.03543  0.00026248 #> HOVAL 0.00226152 0.46502  0.56533971 #>  # \\dontrun{ mobj1 <- lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, type=\"mixed\",  method=\"Matrix\", control=list(fdHess=TRUE)) summary(mobj1) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = columbus, listw = listw,  #>     type = \"mixed\", method = \"Matrix\", control = list(fdHess = TRUE)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.15904  -6.62594  -0.39823   6.57561  23.62757  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 45.592896  14.240041  3.2017 0.0013660 #> INC         -0.939088   0.343069 -2.7373 0.0061942 #> HOVAL       -0.299605   0.090393 -3.3145 0.0009182 #> lag.INC     -0.618375   0.607708 -1.0176 0.3088903 #> lag.HOVAL    0.266615   0.181524  1.4688 0.1418998 #>  #> Rho: 0.38251, LR test value: 4.1648, p-value: 0.041272 #> Asymptotic standard error: 0.17375 #>     z-value: 2.2015, p-value: 0.027702 #> Wald statistic: 4.8465, p-value: 0.027702 #>  #> Log likelihood: -182.0161 for mixed model #> ML residual variance (sigma squared): 95.051, (sigma: 9.7494) #> Number of observations: 49  #> Number of parameters estimated: 7  #> AIC: 378.03, (AIC for lm: 380.2) #> LM test for residual autocorrelation #> test value: 0.101, p-value: 0.75063 #>  set.seed(1) summary(impacts(mobj1, tr=trMatc, R=1000), zstats=TRUE, short=TRUE) #> Impact measures (mixed, trace): #>           Direct   Indirect       Total #> INC   -1.0418080 -1.4804246 -2.52223255 #> HOVAL -0.2836325  0.2302055 -0.05342697 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>           Direct  Indirect     Total #> INC   0.34686331 0.8324743 0.8959688 #> HOVAL 0.09085583 0.3131242 0.3483785 #>  #> Simulated z-values: #>          Direct   Indirect      Total #> INC   -3.023902 -1.8284275 -2.8695190 #> HOVAL -3.120537  0.7910739 -0.1028036 #>  #> Simulated p-values: #>       Direct    Indirect Total    #> INC   0.0024954 0.067485 0.004111 #> HOVAL 0.0018052 0.428901 0.918119 summary(impacts(mobj, tr=trMatc, R=1000), zstats=TRUE, short=TRUE) #> Impact measures (mixed, trace): #>           Direct   Indirect       Total #> INC   -1.0418080 -1.4804246 -2.52223255 #> HOVAL -0.2836325  0.2302055 -0.05342697 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3123750 0.8291512 0.8821167 #> HOVAL 0.0922758 0.2961092 0.3267773 #>  #> Simulated z-values: #>          Direct   Indirect      Total #> INC   -3.330304 -1.8060414 -2.8769263 #> HOVAL -3.099811  0.8140556 -0.1376722 #>  #> Simulated p-values: #>       Direct     Indirect Total     #> INC   0.00086751 0.070912 0.0040157 #> HOVAL 0.00193644 0.415613 0.8904995 mobj2 <- lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, type=\"mixed\",  method=\"Matrix\", control=list(fdHess=TRUE, optimHess=TRUE)) summary(impacts(mobj2, tr=trMatc, R=1000), zstats=TRUE, short=TRUE) #> Impact measures (mixed, trace): #>           Direct   Indirect       Total #> INC   -1.0418080 -1.4804246 -2.52223255 #> HOVAL -0.2836325  0.2302055 -0.05342697 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>           Direct  Indirect     Total #> INC   0.32853332 0.8044059 0.8615603 #> HOVAL 0.09291975 0.3169361 0.3571304 #>  #> Simulated z-values: #>          Direct   Indirect      Total #> INC   -3.231204 -1.8690203 -2.9771674 #> HOVAL -3.026494  0.7323897 -0.1374858 #>  #> Simulated p-values: #>       Direct    Indirect Total     #> INC   0.0012327 0.06162  0.0029093 #> HOVAL 0.0024741 0.46393  0.8906468 mobj3 <- lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, type=\"mixed\",  method=\"spam\", control=list(fdHess=TRUE)) summary(impacts(mobj3, tr=trMatc, R=1000), zstats=TRUE, short=TRUE) #> Impact measures (mixed, trace): #>           Direct   Indirect       Total #> INC   -1.0418080 -1.4804246 -2.52223255 #> HOVAL -0.2836325  0.2302055 -0.05342697 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>           Direct  Indirect     Total #> INC   0.32866009 0.8664620 0.9215792 #> HOVAL 0.09837849 0.3110899 0.3492674 #>  #> Simulated z-values: #>          Direct   Indirect     Total #> INC   -3.190433 -1.7325351 -2.766712 #> HOVAL -2.890221  0.7694814 -0.128720 #>  #> Simulated p-values: #>       Direct    Indirect Total     #> INC   0.0014206 0.083178 0.0056625 #> HOVAL 0.0038497 0.441608 0.8975792 # } # \\dontrun{ data(boston, package=\"spData\") Wb <- as(spdep::nb2listw(boston.soi), \"CsparseMatrix\") trMatb <- trW(Wb, type=\"mult\") gp2mMi <- lagsarlm(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +  I(RM^2) +  AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),  data=boston.c, spdep::nb2listw(boston.soi), type=\"mixed\", method=\"Matrix\",  control=list(fdHess=TRUE), trs=trMatb) summary(gp2mMi) #>  #> Call:lagsarlm(formula = log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +  #>     I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B +  #>     log(LSTAT), data = boston.c, listw = spdep::nb2listw(boston.soi),  #>     type = \"mixed\", method = \"Matrix\", trs = trMatb, control = list(fdHess = TRUE)) #>  #> Residuals: #>        Min         1Q     Median         3Q        Max  #> -0.6316833 -0.0629790 -0.0090776  0.0682421  0.6991072  #>  #> Type: mixed  #> Coefficients: (asymptotic standard errors)  #>                   Estimate  Std. Error  z value  Pr(>|z|) #> (Intercept)     1.89816225  0.24400203   7.7793 7.327e-15 #> CRIM           -0.00571021  0.00093857  -6.0839 1.173e-09 #> ZN              0.00069091  0.00051874   1.3319 0.1828931 #> INDUS          -0.00111343  0.00307380  -0.3622 0.7171778 #> CHAS1          -0.04163225  0.02738839  -1.5201 0.1284937 #> I(NOX^2)       -0.01034950  0.19358633  -0.0535 0.9573639 #> I(RM^2)         0.00794979  0.00102109   7.7856 6.883e-15 #> AGE            -0.00128789  0.00048929  -2.6322 0.0084838 #> log(DIS)       -0.12404108  0.09510145  -1.3043 0.1921304 #> log(RAD)        0.05863502  0.02257529   2.5973 0.0093957 #> TAX            -0.00049084  0.00012146  -4.0412 5.317e-05 #> PTRATIO        -0.01319853  0.00595331  -2.2170 0.0266227 #> B               0.00056383  0.00011084   5.0867 3.643e-07 #> log(LSTAT)     -0.24724454  0.02265149 -10.9152 < 2.2e-16 #> lag.CRIM       -0.00464215  0.00173900  -2.6694 0.0075978 #> lag.ZN         -0.00037937  0.00070703  -0.5366 0.5915659 #> lag.INDUS       0.00025064  0.00385911   0.0649 0.9482165 #> lag.CHAS1       0.12518252  0.04083949   3.0652 0.0021750 #> lag.I(NOX^2)   -0.38640403  0.22253428  -1.7364 0.0824967 #> lag.I(RM^2)    -0.00451252  0.00148919  -3.0302 0.0024440 #> lag.AGE         0.00149678  0.00068470   2.1860 0.0288128 #> lag.log(DIS)   -0.00453785  0.10056961  -0.0451 0.9640104 #> lag.log(RAD)   -0.00940702  0.03127787  -0.3008 0.7636002 #> lag.TAX         0.00041083  0.00017859   2.3004 0.0214237 #> lag.PTRATIO     0.00060355  0.00789994   0.0764 0.9391011 #> lag.B          -0.00050781  0.00014107  -3.5996 0.0003187 #> lag.log(LSTAT)  0.09846781  0.03574183   2.7550 0.0058697 #>  #> Rho: 0.59578, LR test value: 181.68, p-value: < 2.22e-16 #> Asymptotic standard error: 0.037474 #>     z-value: 15.899, p-value: < 2.22e-16 #> Wald statistic: 252.76, p-value: < 2.22e-16 #>  #> Log likelihood: 300.6131 for mixed model #> ML residual variance (sigma squared): 0.016011, (sigma: 0.12654) #> Number of observations: 506  #> Number of parameters estimated: 29  #> AIC: -543.23, (AIC for lm: -363.55) #> LM test for residual autocorrelation #> test value: 29.772, p-value: 4.8604e-08 #>  summary(impacts(gp2mMi, tr=trMatb, R=1000), zstats=TRUE, short=TRUE) #> Impact measures (mixed, trace): #>                   Direct      Indirect         Total #> CRIM       -0.0074555753 -0.0181548470 -0.0256104223 #> ZN          0.0006979073  0.0000727985  0.0007707058 #> INDUS      -0.0012029822 -0.0009314672 -0.0021344494 #> CHAS1      -0.0198526431  0.2265453879  0.2066927447 #> I(NOX^2)   -0.0955268252 -0.8859909283 -0.9815177535 #> I(RM^2)     0.0079983430  0.0005050175  0.0085033605 #> AGE        -0.0011296134  0.0016463650  0.0005167515 #> log(DIS)   -0.1410601685 -0.1770277708 -0.3180879393 #> log(RAD)    0.0641735546  0.0576102594  0.1217838140 #> TAX        -0.0004651543  0.0002672119 -0.0001979424 #> PTRATIO    -0.0147737151 -0.0163846522 -0.0311583673 #> B           0.0005265343 -0.0003879424  0.0001385920 #> log(LSTAT) -0.2578403220 -0.1102143882 -0.3680547101 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>                  Direct     Indirect        Total #> CRIM       0.0010076566 0.0036285971 0.0040401747 #> ZN         0.0004896474 0.0012385892 0.0012617113 #> INDUS      0.0028820705 0.0060789543 0.0057788737 #> CHAS1      0.0271174416 0.0816948950 0.0902306553 #> I(NOX^2)   0.1798525319 0.2954129272 0.2426994629 #> I(RM^2)    0.0010995238 0.0031443424 0.0036252679 #> AGE        0.0004766510 0.0012848631 0.0013546129 #> log(DIS)   0.0884514383 0.1106832550 0.0757291955 #> log(RAD)   0.0197637995 0.0513249209 0.0502885515 #> TAX        0.0001172963 0.0003281755 0.0003385766 #> PTRATIO    0.0054150426 0.0127887825 0.0122251822 #> B          0.0001051363 0.0002388721 0.0002375770 #> log(LSTAT) 0.0224736420 0.0610706224 0.0660453166 #>  #> Simulated z-values: #>                 Direct    Indirect      Total #> CRIM        -7.4242633 -5.04782172 -6.3852730 #> ZN           1.4302178  0.09961643  0.6528326 #> INDUS       -0.4184439 -0.10883366 -0.3231737 #> CHAS1       -0.7260661  2.79074703  2.3085362 #> I(NOX^2)    -0.5230875 -3.05728030 -4.1089450 #> I(RM^2)      7.3426845  0.17905211  2.3822949 #> AGE         -2.4149822  1.25401260  0.3396769 #> log(DIS)    -1.5778895 -1.66514935 -4.2766960 #> log(RAD)     3.2376719  1.17611638  2.4727850 #> TAX         -3.9726814  0.78133925 -0.6189573 #> PTRATIO     -2.7323855 -1.29137856 -2.5612005 #> B            5.0000793 -1.62377140  0.5800914 #> log(LSTAT) -11.4429357 -1.77731839 -5.5372039 #>  #> Simulated p-values: #>            Direct     Indirect   Total      #> CRIM       1.1346e-13 4.4688e-07 1.7109e-10 #> ZN         0.1526545  0.9206489  0.513864   #> INDUS      0.6756226  0.9133344  0.746564   #> CHAS1      0.4677982  0.0052587  0.020969   #> I(NOX^2)   0.6009133  0.0022336  3.9747e-05 #> I(RM^2)    2.0939e-13 0.8578968  0.017205   #> AGE        0.0157360  0.2098374  0.734100   #> log(DIS)   0.1145910  0.0958830  1.8969e-05 #> log(RAD)   0.0012051  0.2395484  0.013406   #> TAX        7.1068e-05 0.4346030  0.535944   #> PTRATIO    0.0062878  0.1965724  0.010431   #> B          5.7307e-07 0.1044246  0.561853   #> log(LSTAT) < 2.22e-16 0.0755159  3.0734e-08 #data(house, package=\"spData\") #lw <- spdep::nb2listw(LO_nb) #form <- formula(log(price) ~ age + I(age^2) + I(age^3) + log(lotsize) + #   rooms + log(TLA) + beds + syear) #lobj <- lagsarlm(form, house, lw, method=\"Matrix\", # control=list(fdHess=TRUE), trs=trMat) #summary(lobj) #loobj <- impacts(lobj, tr=trMat, R=1000) #summary(loobj, zstats=TRUE, short=TRUE) #lobj1 <- stsls(form, house, lw) #loobj1 <- impacts(lobj1, tr=trMat, R=1000) #summary(loobj1, zstats=TRUE, short=TRUE) #mobj <- lagsarlm(form, house, lw, type=\"mixed\", # method=\"Matrix\", control=list(fdHess=TRUE), trs=trMat) #summary(mobj) #moobj <- impacts(mobj, tr=trMat, R=1000) #summary(moobj, zstats=TRUE, short=TRUE) # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/invIrM.html","id":null,"dir":"Reference","previous_headings":"","what":"Compute SAR generating operator — invIrM","title":"Compute SAR generating operator — invIrM","text":"Computes matrix used generating simultaneous autoregressive random variables, given value rho, neighbours list object matrix, chosen coding scheme style, optionally list general weights corresponding neighbours.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/invIrM.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Compute SAR generating operator — invIrM","text":"","code":"invIrM(neighbours, rho, glist=NULL, style=\"W\", method=\"solve\",  feasible=NULL) invIrW(x, rho, method=\"solve\", feasible=NULL)"},{"path":"https://r-spatial.github.io/spatialreg/reference/invIrM.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Compute SAR generating operator — invIrM","text":"neighbours object class nb rho autoregressive parameter glist list general weights corresponding neighbours style style can take values W, B, C, S method default solve, can also take value chol feasible NULL, given value rho checked see lies within feasible range, TRUE, test conducted x either listw object example nb2listw square spatial weights matrix, optionally sparse matrix","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/invIrM.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Compute SAR generating operator — invIrM","text":"invIrW function generates full weights matrix V, checks rho lies feasible range 1/min(eigen(V)) 1/max(eigen(V)), returns nxn inverted matrix $$(- \\rho V)^{-1}$$. method=“chol” (listw object), Cholesky decomposition used, thanks contributed code Markus Reder Werner Mueller. Note , situations simulation, may matter random vector rnorm similar exactly N(0, 1), also contain random amounts spatial autocorrelection , mix spatial autocorrelection injected process operator $$(- \\rho V)^{-1}$$. addition, follow stipulated distribution exactly either, several steps may needed scale random vector, remove artefacts coming deviance distributional parameters, remove random spatial autocorrelation - see examples . Thanks Rune Østergaard Pedersen bring question. powerWeights function uses power series summation cumulate product $$(- \\rho V)^{-1} \\%*\\% X$$ $$(+ \\rho V + (\\rho V)^2 + \\dots) \\%*\\% X$$, can done storing sparse V several matrices dimensions X. makes possible handle larger spatial weights matrices, sensitive power weights order tolerance arguments spatial coefficient close bounds, leading incorrect estimates implied inverse matrix.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/invIrM.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Compute SAR generating operator — invIrM","text":"nxn matrix \"call\" attribute; powerWeights function returns matrix dimensions X multipled power series equivalent dense matrix $$(- \\rho V)^{-1}$$.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/invIrM.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Compute SAR generating operator — invIrM","text":"version 0.6-10, powerWeights worked correctly positive rho, differences true values increasing rho approached -1, exploding -1 true negative bound.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/invIrM.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Compute SAR generating operator — invIrM","text":"Tiefelsdorf, M., Griffith, D. ., Boots, B. 1999 variance-stabilizing coding scheme spatial link matrices, Environment Planning , 31, pp. 165-180; Tiefelsdorf, M. 2000 Modelling spatial processes, Lecture notes earth sciences, Springer, p. 76; Haining, R. 1990 Spatial data analysis social environmental sciences, Cambridge University Press, p. 117; Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion, p. 152; Reder, M. Mueller, W. (2007) Improvement invIrM Routine Geostatistical R-package spdep Cholesky Inversion, Statistical Projects, LV : 238.205, SS 2006, Department Applied Statistics, Johannes Kepler University, Linz","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/invIrM.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Compute SAR generating operator — invIrM","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/invIrM.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Compute SAR generating operator — invIrM","text":"","code":"library(spdep) nb7rt <- cell2nb(7, 7, torus=TRUE) lw <- nb2listw(nb7rt, style=\"W\") set.seed(1) x <- matrix(sample(rnorm(500*length(nb7rt))), nrow=length(nb7rt)) if (requireNamespace(\"spatialreg\", quietly=TRUE)) { # Only needed in some simulation settings where the input and # output distributions must agree in all but autocorrelation if (FALSE) { e <- spatialreg::eigenw(lw) x <- apply(x, 2, scale) st <- apply(x, 2, function(x) shapiro.test(x)$p.value) x <- x[, (st > 0.2 & st < 0.8)] x <- apply(x, 2, function(v) spatialreg::residuals.spautolm(  spatialreg::spautolm(v ~ 1, listw=lw, method=\"eigen\",  control=list(pre_eig=e, fdHess=FALSE)))) x <- apply(x, 2, scale) } res0 <- apply(invIrM(nb7rt, rho=0.0, method=\"chol\",  feasible=TRUE) %*% x, 2, function(x) var(x)/length(x)) res2 <- apply(invIrM(nb7rt, rho=0.2, method=\"chol\",  feasible=TRUE) %*% x, 2, function(x) var(x)/length(x)) res4 <- apply(invIrM(nb7rt, rho=0.4, method=\"chol\",  feasible=TRUE) %*% x, 2, function(x) var(x)/length(x)) res6 <- apply(invIrM(nb7rt, rho=0.6, method=\"chol\",  feasible=TRUE) %*% x, 2, function(x) var(x)/length(x)) res8 <- apply(invIrM(nb7rt, rho=0.8, method=\"chol\",  feasible=TRUE) %*% x, 2, function(x) var(x)/length(x)) res9 <- apply(invIrM(nb7rt, rho=0.9, method=\"chol\",  feasible=TRUE) %*% x, 2, function(x) var(x)/length(x)) plot(density(res9), col=\"red\", xlim=c(-0.01, max(density(res9)$x)),   ylim=range(density(res0)$y),   xlab=\"estimated variance of the mean\",   main=expression(paste(\"Effects of spatial autocorrelation for different \",     rho, \" values\"))) lines(density(res0), col=\"black\") lines(density(res2), col=\"brown\") lines(density(res4), col=\"green\") lines(density(res6), col=\"orange\") lines(density(res8), col=\"pink\") legend(c(-0.02, 0.01), c(7, 25),  legend=c(\"0.0\", \"0.2\", \"0.4\", \"0.6\", \"0.8\", \"0.9\"),  col=c(\"black\", \"brown\", \"green\", \"orange\", \"pink\", \"red\"), lty=1, bty=\"n\") }  # \\dontrun{ x <- matrix(rnorm(length(nb7rt)), ncol=1) system.time(e <- invIrM(nb7rt, rho=0.9, method=\"chol\", feasible=TRUE) %*% x) #>    user  system elapsed  #>   0.003   0.000   0.002  system.time(e <- invIrM(nb7rt, rho=0.9, method=\"chol\", feasible=NULL) %*% x) #>    user  system elapsed  #>   0.002   0.000   0.002  system.time(e <- invIrM(nb7rt, rho=0.9, method=\"solve\", feasible=TRUE) %*% x) #>    user  system elapsed  #>   0.001   0.000   0.001  system.time(e <- invIrM(nb7rt, rho=0.9, method=\"solve\", feasible=NULL) %*% x) #>    user  system elapsed  #>   0.002   0.000   0.002  # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/lagmess.html","id":null,"dir":"Reference","previous_headings":"","what":"Matrix exponential spatial lag model — lagmess","title":"Matrix exponential spatial lag model — lagmess","text":"function fits matrix exponential spatial lag model, using optim find value alpha, spatial coefficient.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lagmess.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Matrix exponential spatial lag model — lagmess","text":"","code":"lagmess(formula, data = list(), listw, zero.policy = NULL, na.action = na.fail,  q = 10, start = -2.5, control=list(), method=\"BFGS\", verbose=NULL,  use_expm=FALSE)"},{"path":"https://r-spatial.github.io/spatialreg/reference/lagmess.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Matrix exponential spatial lag model — lagmess","text":"formula symbolic description model fit. details model specification given lm() data optional data frame containing variables model. default variables taken environment function called. listw listw object created example spdep::nb2listw() zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA - causing lagmess() terminate error na.action function (default options(\"na.action\")), can also na.omit na.exclude consequences residuals fitted values - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. q default 10; number powers spatial weights use start starting value numerical optimization, small negative number control control parameters passed optim method default BFGS, method passed optim verbose default NULL, use global option value; TRUE report function values optimization use_expm default FALSE; TRUE use expm::expAtv instead truncated power series W","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lagmess.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Matrix exponential spatial lag model — lagmess","text":"underlying spatial lag model: $$y = \\rho W y + X \\beta + \\varepsilon$$ \\(\\rho\\) spatial parameter may fitted maximum likelihood. case, log likelihood function includes logarithm cumbersome Jacobian term \\(|- \\rho W|\\). rewrite model : $$S y = X \\beta + \\varepsilon$$ see ML case \\(S y = (- \\rho W) y\\). W row-stochastic, S may expressed linear combination row-stochastic matrices. pre-computing matrix \\([y, Wy, W^2y, ..., W^{q-1}y]\\), term \\(S y (\\alpha)\\) can readily found numerical optimization using matrix exponential approach. \\(\\alpha\\) \\(\\rho\\) related \\(\\rho = 1 - \\exp{\\alpha}\\), conditional number matrix power terms taken q.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lagmess.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Matrix exponential spatial lag model — lagmess","text":"function returns object class Lagmess components: lmobj lm object returned fitting alpha alpha spatial coefficient alphase standard error spatial coefficient using numerical Hessian rho value rho implied alpha bestmess object returned optim q number powers spatial weights used start starting value numerical optimization used na.action (possibly) named vector excluded omitted observations non-default na.action argument used nullLL log likelihood aspatial model data","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lagmess.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Matrix exponential spatial lag model — lagmess","text":"J. P. LeSage R. K. Pace (2007) matrix exponential specification. Journal Econometrics, 140, 190-214; J. P. LeSage R. K. Pace (2009) Introduction Spatial Econometrics. CRC Press, Chapter 9.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lagmess.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Matrix exponential spatial lag model — lagmess","text":"Roger Bivand Roger.Bivand@nhh.Eric Blankmeyer","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/lagmess.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Matrix exponential spatial lag model — lagmess","text":"","code":"#require(spdep, quietly=TRUE) data(baltimore, package=\"spData\") baltimore$AGE <- ifelse(baltimore$AGE < 1, 1, baltimore$AGE) lw <- spdep::nb2listw(spdep::knn2nb(spdep::knearneigh(cbind(baltimore$X, baltimore$Y), k=7))) obj1 <- lm(log(PRICE) ~ PATIO + log(AGE) + log(SQFT),  data=baltimore) spdep::lm.morantest(obj1, lw) #>  #> \tGlobal Moran I for regression residuals #>  #> data:   #> model: lm(formula = log(PRICE) ~ PATIO + log(AGE) + log(SQFT), data = #> baltimore) #> weights: lw #>  #> Moran I statistic standard deviate = 7.4648, p-value = 4.171e-14 #> alternative hypothesis: greater #> sample estimates: #> Observed Moran I      Expectation         Variance  #>      0.245149959     -0.007853660      0.001148722  #>  spdep::lm.LMtests(obj1, lw, test=\"all\") #> Please update scripts to use lm.RStests in place of lm.LMtests #>  #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #>  #> data:   #> model: lm(formula = log(PRICE) ~ PATIO + log(AGE) + log(SQFT), data = #> baltimore) #> test weights: listw #>  #> RSerr = 48.648, df = 1, p-value = 3.063e-12 #>  #>  #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #>  #> data:   #> model: lm(formula = log(PRICE) ~ PATIO + log(AGE) + log(SQFT), data = #> baltimore) #> test weights: listw #>  #> RSlag = 83.091, df = 1, p-value < 2.2e-16 #>  #>  #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #>  #> data:   #> model: lm(formula = log(PRICE) ~ PATIO + log(AGE) + log(SQFT), data = #> baltimore) #> test weights: listw #>  #> adjRSerr = 1.2535, df = 1, p-value = 0.2629 #>  #>  #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #>  #> data:   #> model: lm(formula = log(PRICE) ~ PATIO + log(AGE) + log(SQFT), data = #> baltimore) #> test weights: listw #>  #> adjRSlag = 35.696, df = 1, p-value = 2.306e-09 #>  #>  #> \tRao's score (a.k.a Lagrange multiplier) diagnostics for spatial #> \tdependence #>  #> data:   #> model: lm(formula = log(PRICE) ~ PATIO + log(AGE) + log(SQFT), data = #> baltimore) #> test weights: listw #>  #> SARMA = 84.344, df = 2, p-value < 2.2e-16 #>  system.time(obj2 <- lagmess(log(PRICE) ~ PATIO + log(AGE) + log(SQFT), data=baltimore, listw=lw)) #>    user  system elapsed  #>    0.03    0.00    0.03  (x <- summary(obj2)) #> Matrix exponential spatial lag model: #>  #> Call: #> lagmess(formula = log(PRICE) ~ PATIO + log(AGE) + log(SQFT),  #>     data = baltimore, listw = lw) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -2.026722 -0.141191  0.050831  0.223830  1.073114  #>  #> Coefficients: #>              Estimate Std. Error t value  Pr(>|t|) #> (Intercept)  1.546376   0.214513  7.2088 1.039e-11 #> PATIO        0.258287   0.086891  2.9726  0.003303 #> log(AGE)    -0.148174   0.035252 -4.2033 3.912e-05 #> log(SQFT)    0.300966   0.071598  4.2036 3.908e-05 #>  #> Residual standard error: 0.41658 on 207 degrees of freedom #> Multiple R-squared:  0.22373,\tAdjusted R-squared:  0.21248  #> F-statistic: 19.887 on 3 and 207 DF,  p-value: 2.2881e-11 #>  #> Alpha: -0.64302, standard error: 0.1043 #>     z-value: -6.1649, p-value: 7.0511e-10 #> LR test value: 48.296, p-value: 3.6644e-12 #> Implied rho: 0.4742995  #>  coef(x) #>               Estimate Std. Error   t value     Pr(>|t|) #> (Intercept)  1.5463761 0.21451319  7.208769 1.038762e-11 #> PATIO        0.2582874 0.08689079  2.972552 3.303312e-03 #> log(AGE)    -0.1481738 0.03525174 -4.203305 3.912250e-05 #> log(SQFT)    0.3009659 0.07159771  4.203569 3.908038e-05 has_expm <- require(\"expm\", quietly=TRUE) #>  #> Attaching package: ‘expm’ #> The following object is masked from ‘package:Matrix’: #>  #>     expm if (has_expm) { system.time( obj2a <- lagmess(log(PRICE) ~ PATIO + log(AGE) + log(SQFT), data=baltimore, listw=lw, use_expm=TRUE) ) summary(obj2a) } #> Matrix exponential spatial lag model: #> (calculated with expm) #>  #> Call: #> lagmess(formula = log(PRICE) ~ PATIO + log(AGE) + log(SQFT),  #>     data = baltimore, listw = lw, use_expm = TRUE) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -2.026722 -0.141191  0.050831  0.223830  1.073114  #>  #> Coefficients: #>              Estimate Std. Error t value  Pr(>|t|) #> (Intercept)  1.546376   0.214513  7.2088 1.039e-11 #> PATIO        0.258287   0.086891  2.9726  0.003303 #> log(AGE)    -0.148174   0.035252 -4.2033 3.912e-05 #> log(SQFT)    0.300966   0.071598  4.2036 3.908e-05 #>  #> Residual standard error: 0.41658 on 207 degrees of freedom #> Multiple R-squared:  0.22373,\tAdjusted R-squared:  0.21248  #> F-statistic: 19.887 on 3 and 207 DF,  p-value: 2.2881e-11 #>  #> Alpha: -0.64302, standard error: 0.1043 #>     z-value: -6.1649, p-value: 7.0511e-10 #> LR test value: 48.296, p-value: 3.6644e-12 #> Implied rho: 0.4742995  #>  obj3 <- lagsarlm(log(PRICE) ~ PATIO + log(AGE) + log(SQFT), data=baltimore, listw=lw) summary(obj3) #>  #> Call:lagsarlm(formula = log(PRICE) ~ PATIO + log(AGE) + log(SQFT),  #>     data = baltimore, listw = lw) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -1.969554 -0.147514  0.042581  0.199567  1.076181  #>  #> Type: lag  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept)  1.255885   0.320679  3.9163 8.991e-05 #> PATIO        0.244225   0.083448  2.9267 0.0034262 #> log(AGE)    -0.131947   0.034510 -3.8235 0.0001316 #> log(SQFT)    0.278888   0.070259  3.9694 7.205e-05 #>  #> Rho: 0.55765, LR test value: 52.661, p-value: 3.9635e-13 #> Asymptotic standard error: 0.072749 #>     z-value: 7.6653, p-value: 1.7764e-14 #> Wald statistic: 58.757, p-value: 1.7875e-14 #>  #> Log likelihood: -110.4248 for lag model #> ML residual variance (sigma squared): 0.1589, (sigma: 0.39862) #> Number of observations: 211  #> Number of parameters estimated: 6  #> AIC: 232.85, (AIC for lm: 283.51) #> LM test for residual autocorrelation #> test value: 8.7942, p-value: 0.0030219 #>  # \\donttest{ data(boston, package=\"spData\") lw <- spdep::nb2listw(boston.soi) gp2 <- lagsarlm(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) + I(RM^2)  +  AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),  data=boston.c, lw, method=\"Matrix\") summary(gp2) #>  #> Call:lagsarlm(formula = log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +  #>     I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B +  #>     log(LSTAT), data = boston.c, listw = lw, method = \"Matrix\") #>  #> Residuals: #>        Min         1Q     Median         3Q        Max  #> -0.5262308 -0.0749699 -0.0044237  0.0713409  0.7122121  #>  #> Type: lag  #> Coefficients: (asymptotic standard errors)  #>                Estimate  Std. Error  z value  Pr(>|z|) #> (Intercept)  2.2796e+00  1.7495e-01  13.0302 < 2.2e-16 #> CRIM        -7.1045e-03  9.6236e-04  -7.3824 1.554e-13 #> ZN           3.7985e-04  3.8510e-04   0.9864 0.3239507 #> INDUS        1.2572e-03  1.7986e-03   0.6990 0.4845472 #> CHAS1        7.3677e-03  2.5416e-02   0.2899 0.7719057 #> I(NOX^2)    -2.6892e-01  8.8026e-02  -3.0550 0.0022508 #> I(RM^2)      6.7243e-03  1.0039e-03   6.6985 2.106e-11 #> AGE         -2.7682e-04  4.0062e-04  -0.6910 0.4895829 #> log(DIS)    -1.5830e-01  2.5554e-02  -6.1947 5.841e-10 #> log(RAD)     7.0689e-02  1.4616e-02   4.8363 1.323e-06 #> TAX         -3.6569e-04  9.3744e-05  -3.9009 9.582e-05 #> PTRATIO     -1.2011e-02  3.9599e-03  -3.0330 0.0024211 #> B            2.8432e-04  7.9402e-05   3.5807 0.0003427 #> log(LSTAT)  -2.3216e-01  2.0425e-02 -11.3663 < 2.2e-16 #>  #> Rho: 0.48537, LR test value: 214.06, p-value: < 2.22e-16 #> Asymptotic standard error: 0.029426 #>     z-value: 16.494, p-value: < 2.22e-16 #> Wald statistic: 272.06, p-value: < 2.22e-16 #>  #> Log likelihood: 264.0089 for lag model #> ML residual variance (sigma squared): 0.019276, (sigma: 0.13884) #> Number of observations: 506  #> Number of parameters estimated: 16  #> AIC: -496.02, (AIC for lm: -283.96) #> LM test for residual autocorrelation #> test value: 10.74, p-value: 0.0010486 #>  gp2a <- lagmess(CMEDV ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) + I(RM^2)  +  AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),  data=boston.c, lw) summary(gp2a) #> Matrix exponential spatial lag model: #>  #> Call: #> lagmess(formula = CMEDV ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +  #>     I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B +  #>     log(LSTAT), data = boston.c, listw = lw) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -17.03755  -2.05386  -0.30295   1.67710  21.82120  #>  #> Coefficients: #>               Estimate Std. Error  t value  Pr(>|t|) #> (Intercept) 35.3206850  3.0128759  11.7232 < 2.2e-16 #> CRIM        -0.0986056  0.0242819  -4.0609 5.688e-05 #> ZN           0.0198500  0.0098638   2.0124 0.0447222 #> INDUS        0.0071211  0.0461104   0.1544 0.8773301 #> CHAS1        0.8158059  0.6477224   1.2595 0.2084473 #> I(NOX^2)    -9.2592911  2.2072427  -4.1950 3.238e-05 #> I(RM^2)      0.2434745  0.0256001   9.5107 < 2.2e-16 #> AGE         -0.0040683  0.0102667  -0.3963 0.6920816 #> log(DIS)    -5.3974116  0.6514323  -8.2855 1.125e-15 #> log(RAD)     1.7142905  0.3732772   4.5925 5.569e-06 #> TAX         -0.0087053  0.0023933  -3.6373 0.0003046 #> PTRATIO     -0.4118524  0.0977997  -4.2112 3.021e-05 #> B            0.0056141  0.0020116   2.7908 0.0054614 #> log(LSTAT)  -6.1484203  0.4878957 -12.6019 < 2.2e-16 #>  #> Residual standard error: 3.5594 on 492 degrees of freedom #> Multiple R-squared:  0.76221,\tAdjusted R-squared:  0.75593  #> F-statistic: 121.31 on 13 and 492 DF,  p-value: < 2.22e-16 #>  #> Alpha: -0.41361, standard error: 0.038521 #>     z-value: -10.737, p-value: < 2.22e-16 #> LR test value: 121.4, p-value: < 2.22e-16 #> Implied rho: 0.3387434  #>  # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/lextrB.html","id":null,"dir":"Reference","previous_headings":"","what":"Find extreme eigenvalues of binary symmetric spatial weights — lextrB","title":"Find extreme eigenvalues of binary symmetric spatial weights — lextrB","text":"functions find extreme eigenvalues binary symmetric spatial weights, form planar graphs; general weights permiited. l_max finds largest eigenvalue using Rayleigh quotient methods “listw” object. lextrB first calls l_max, uses output find smallest eigenvalue addition binary symmetric spatial weights. lextrW extends find smallest eigenvalue intrinsically symmetric row-standardized binary weights matrices (transformed symmetric similarity internally). lextrS variance-stabilized (“S” style) intrinsically symmetric binary weights matrices (transformed symmetric similarity internally).","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lextrB.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Find extreme eigenvalues of binary symmetric spatial weights — lextrB","text":"","code":"lextrB(lw, zero.policy = TRUE, control = list()) lextrW(lw, zero.policy=TRUE, control=list()) lextrS(lw, zero.policy=TRUE, control=list()) l_max(lw, zero.policy=TRUE, control=list())"},{"path":"https://r-spatial.github.io/spatialreg/reference/lextrB.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Find extreme eigenvalues of binary symmetric spatial weights — lextrB","text":"lw binary symmetric listw object , example, nb2listw style “B” lextrB, style “W” lextrW style “S” lextrS; l_max, object may asymmetric binary zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE assign NA control list control arguments","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lextrB.html","id":"control-arguments","dir":"Reference","previous_headings":"","what":"Control arguments","title":"Find extreme eigenvalues of binary symmetric spatial weights — lextrB","text":"trace report values loops, default NULL assuming FALSE; logical tol tolerance breaking loops, default .Machine$double.eps^(1/2); numeric maxiter maximum number iterations loops, default 6 * (length(lw$neighbours) - 2; integer useC use C code, default TRUE, logical (l_max)","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lextrB.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Find extreme eigenvalues of binary symmetric spatial weights — lextrB","text":"functions return approximations extreme eigenvalues eigenvectors returned attributes object.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lextrB.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Find extreme eigenvalues of binary symmetric spatial weights — lextrB","text":"Griffith, D. . (2004). Extreme eigenfunctions adjacency matrices planar graphs employed spatial analyses. Linear Algebra Applications, 388:201–219.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lextrB.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Find extreme eigenvalues of binary symmetric spatial weights — lextrB","text":"Roger Bivand, Yongwan Chun, Daniel Griffith","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lextrB.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Find extreme eigenvalues of binary symmetric spatial weights — lextrB","text":"may necessary modify control arguments warnings lack convergence seen.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/lextrB.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Find extreme eigenvalues of binary symmetric spatial weights — lextrB","text":"","code":"data(boston, package=\"spData\") #require(spdep, quietly=TRUE) ab.listb <- spdep::nb2listw(boston.soi, style=\"B\") er <- range(eigenw(ab.listb)) er #> [1] -3.039465  5.306204 res_1 <- lextrB(ab.listb) c(res_1) #>  lambda_n  lambda_1  #> -3.039374  5.306203  run <- FALSE if (require(\"RSpectra\", quietly=TRUE)) run <- TRUE if (run) { B <- as(ab.listb, \"CsparseMatrix\") eigs(B, k=1, which=\"SR\")$values } #> [1] -3.039465 if (run) { eigs(B, k=1, which=\"LR\")$values } #> [1] 5.306204 k5 <- spdep::knn2nb(spdep::knearneigh(boston.utm, k=5)) c(l_max(spdep::nb2listw(k5, style=\"B\"))) #> [1] 5 max(Re(eigenw(spdep::nb2listw(k5, style=\"B\")))) #> [1] 5 c(l_max(spdep::nb2listw(k5, style=\"C\"))) #> [1] 1 max(Re(eigenw(spdep::nb2listw(k5, style=\"C\")))) #> [1] 1 ab.listw <- spdep::nb2listw(boston.soi, style=\"W\") er <- range(eigenw(similar.listw(ab.listw))) er #> [1] -0.9708644  1.0000000 res_1 <- lextrW(ab.listw) c(res_1) #>   lambda_n   lambda_1  #> -0.9708644  0.9999991  if (run) { B <- as(similar.listw(ab.listw), \"CsparseMatrix\") eigs(B, k=1, which=\"SR\")$values } #> [1] -0.9708644 if (run) { eigs(B, k=1, which=\"LR\")$values } #> [1] 1 # \\dontrun{ ab.listw <- spdep::nb2listw(boston.soi, style=\"S\") er <- range(eigenw(similar.listw(ab.listw))) er #> [1] -0.723495  1.110373 res_1 <- lextrS(ab.listw) c(res_1) #>   lambda_n   lambda_1  #> -0.7230376  1.1103694  # } if (run) { B <- as(similar.listw(ab.listw), \"CsparseMatrix\") eigs(B, k=1, which=\"SR\")$values } #> [1] -0.723495 if (run) { eigs(B, k=1, which=\"LR\")$values } #> [1] 1.110373"},{"path":"https://r-spatial.github.io/spatialreg/reference/predict.sarlm.html","id":null,"dir":"Reference","previous_headings":"","what":"Prediction for spatial simultaneous autoregressive linear model objects — predict.Sarlm","title":"Prediction for spatial simultaneous autoregressive linear model objects — predict.Sarlm","text":"predict.Sarlm() calculates predictions far present possible spatial simultaneous autoregressive linear model objects, using Haining's terminology decomposition trend, signal, noise, types predictors — see references.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/predict.sarlm.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Prediction for spatial simultaneous autoregressive linear model objects — predict.Sarlm","text":"","code":"# S3 method for class 'Sarlm' predict(object, newdata = NULL, listw = NULL, pred.type = \"TS\", all.data = FALSE,  zero.policy = NULL, legacy = TRUE, legacy.mixed = FALSE, power = NULL, order = 250,  tol = .Machine$double.eps^(3/5), spChk = NULL, ...) #\\method{predict}{SLX}(object, newdata, listw, zero.policy=NULL, ...) # S3 method for class 'Sarlm.pred' print(x, ...) # S3 method for class 'Sarlm.pred' as.data.frame(x, ...)"},{"path":"https://r-spatial.github.io/spatialreg/reference/predict.sarlm.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Prediction for spatial simultaneous autoregressive linear model objects — predict.Sarlm","text":"object Sarlm object returned lagsarlm, errorsarlm sacsarlm, method SLX objects takes output lmSLX newdata data frame predict — NULL, predictions data model fitted. row names corresponding region.id. row names exactly ones used training, uses -sample predictors forecast.  See ‘Details’ listw listw object created example nb2listw. --sample prediction case (ie. newdata NULL), legacy.mixed=FALSE pred.type!=\"TS\", include -sample --sample spatial units. case, regions listw correct order, reordered.  See ‘Details’ pred.type predictor type — default “TS”, use decomposition trend, signal, noise ; types available depending newdata. newdata=NULL (-sample prediction), “TS”, “trend”, “TC” “BP” available. newdata NULL row names data used fit model (forecast case), “TS”, “trend” “TC” available. cases (--sample prediction), “TS”, “trend”, “KP1”, “KP2”, “KP3”, “KP4”, “KP5”, “TC”, “BP”, “BPW”, “BPN”, “TS1”, “TC1”, “BP1”, “BPW1” “BPN1” available.  See ‘Details’ references .data (applies pred.type=\"TC\" newdata NULL) default FALSE: return predictions newdata units, TRUE return predictions data units.  See ‘Details’ zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE (default) assign NA - causing function terminate error legacy (applies lag Durbin (mixed) models pred.type=\"TS\") default TRUE: use ad-hoc predictor, FALSE use DGP-based predictor legacy.mixed (applies mixed models newdata NULL) default FALSE: compute lagged variables -sample --sample units \\([W X]_O\\) \\([W X]_S\\) X=cbind(Xs, Xo), TRUE compute lagged variables independantly -sample --sample units \\(W_{OO} X_O\\) \\(W_{SS} X_S\\) power (applies lag Durbin (mixed) models “TS”, “KP1”, “KP2”, “KP3”, “TC”, “TC1”, “BP”, “BP1”, “BPN”, “BPN1”, “BPW” “BPW1” types) use powerWeights, default NULL, set FALSE object$method “eigen”, otherwise TRUE order power series maximum limit power TRUE tol tolerance convergence power series power TRUE spChk row names data frames checked spatial objects identity integrity, TRUE, FALSE, default NULL use get.spChkOption() x object printed  ... arguments passed ","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/predict.sarlm.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Prediction for spatial simultaneous autoregressive linear model objects — predict.Sarlm","text":"function supports three types prediction.  -sample prediction computation predictors data used fit model (newdata=NULL).  Prevision, also called forecast, computation predictors (“trend”, -sample “TC” --sample “TS”) spatial units ones used fit model, different observations variables model (row names newdata row names data frame used fit model).  --sample prediction computation predictors spatial units ones used fit model (newdata different row names).  extensive definitions, see Goulard et al. (2017). pred.type predictors available according model object type prediction.  two following tables, “yes” means predictor can used model, “” means predict.Sarlm() stop error, “yes*” means predictor designed specified model, can used predict.Sarlm().  last case, careful computation inappropriate predictor. -sample predictors models Note “trend” “TC” available prevision. --sample predictors models Values pred.type= include “TS1”, “TC”, “TC1”, “BP”, “BP1”, “BPW”, “BPW1”, “BPN”, “BPN1”, following notation Goulard et al. (2017), pred.type= “KP1”, “KP2”, “KP3”, “KP4”, “KP5”, following notation Kelejian et al. (2007).  pred.type=\"TS\" described bellow Bivand (2002). following, trend non-spatial smooth, signal spatial smooth, noise residual.  fit returned pred.type=\"TS\" sum trend signal. pred.type=\"TS\", function approaches prediction first dividing invocations without newdata.  newdata present, response variable may reconstructed sum trend, signal, noise (residuals).  Since values response variable known, spatial lags used calculate signal components (Cressie 1993, p. 564).  error model, trend = \\(X \\beta\\), signal = \\(\\lambda W y - \\lambda W X \\beta\\). lag mixed models, trend = \\(X \\beta\\), signal = \\(\\rho W y\\). approach differs design choices made software, example GeoDa, use observations response variable, corresponds newdata situation described . however newdata used prediction, observations response variable predicted available.  Consequently, trend components , signal take full account spatial smooth.  error model Durbin error model, signal set zero, since spatial smooth expressed terms error: \\((- \\lambda W)^{-1} \\varepsilon\\). lag model, signal can expressed following way (legacy=TRUE): $$(- \\rho W) y = X \\beta + \\varepsilon$$ $$y = (- \\rho W)^{-1} X \\beta + (- \\rho W)^{-1} \\varepsilon$$ giving feasible signal component : $$\\rho W y = \\rho W (- \\rho W)^{-1} X \\beta$$ legacy=FALSE, trend computed first : $$X \\beta$$ next prediction using DGP: $$(- \\rho W)^{-1} X \\beta$$ signal found difference prediction trend. numerical results legacy DGP methods identical. setting error term zero.  also means predictions signal component lag mixed models require inversion n--n matrix. outcomes spatial smooth error term unobservable, means signal values newdata incomplete.  mixed model, spatially lagged RHS variables influence trend signal, root mean square prediction error examples case newdata smallest, although model best fit. newdata one row, leave-one-predictors (pred.type= include “TS1”, “TC1”, “BP1”, “BPW1”, “BPN1”, “KP1”, “KP2”, “KP3”, “KP4”, “KP5”) computed separatly --sample unit. listw provided except newdata=NULL pred.type= include “TS”, “trend”, newdata NULL, pred.type=\"trend\" object mixed model. .data useful --sample predictors return different predictions -sample units, predictor type computed -sample data.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/predict.sarlm.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Prediction for spatial simultaneous autoregressive linear model objects — predict.Sarlm","text":"predict.Sarlm() returns vector predictions three attribute vectors trend, signal (pred.type=\"TS\") region.id values two attributes pred.type call class Sarlm.pred. print.Sarlm.pred() print function class, printing returning data frame columns: \"fit\", \"trend\" \"signal\" (available) region.id row names.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/predict.sarlm.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Prediction for spatial simultaneous autoregressive linear model objects — predict.Sarlm","text":"Haining, R. 1990 Spatial data analysis social environmental sciences, Cambridge: Cambridge University Press, p. 258; Cressie, N. . C. 1993 Statistics spatial data, Wiley, New York; Michel Goulard, Thibault Laurent & Christine Thomas-Agnan, 2017 predictions spatial autoregressive models: optimal almost optimal strategies,  Spatial Economic Analysis Volume 12, Issue 2–3, 304–325 doi:10.1080/17421772.2017.1300679 , ; Kelejian, H. H. Prucha, . R. 2007 relative efficiencies various predictors spatial econometric models containing spatial lags, Regional Science Urban Economics, Volume 37, Issue 3, 363–374; Bivand, R. 2002 Spatial econometrics functions R: Classes methods, Journal Geographical Systems, Volume 4, . 4, 405–421","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/predict.sarlm.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Prediction for spatial simultaneous autoregressive linear model objects — predict.Sarlm","text":"Roger Bivand Roger.Bivand@nhh.Martin Gubri","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/predict.sarlm.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Prediction for spatial simultaneous autoregressive linear model objects — predict.Sarlm","text":"","code":"data(oldcol, package=\"spdep\") lw <- spdep::nb2listw(COL.nb) COL.lag.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, lw)  COL.mix.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, lw,   type=\"mixed\") print(p1 <- predict(COL.mix.eig)) #> This method assumes the response is known - see manual page #>            fit     trend    signal #> 1001 26.044310 14.854350 11.189960 #> 1002 44.034234 29.263210 14.771023 #> 1003 43.511934 25.819381 17.692554 #> 1004 37.656561 16.455557 21.201004 #> 1005 10.902976  0.366406 10.536570 #> 1006 36.829798 24.290524 12.539274 #> 1007 44.290467 27.038660 17.251807 #> 1008 38.853571 21.534238 17.319332 #> 1009 50.870854 29.509277 21.361577 #> 1010 16.401300  5.602910 10.798390 #> 1011 36.354390 28.641535  7.712855 #> 1012 20.452836 12.460727  7.992109 #> 1013 20.324088 14.417343  5.906745 #> 1014 19.243496 10.260642  8.982854 #> 1015 19.747775 12.255686  7.492089 #> 1016  6.962527 -2.013749  8.976277 #> 1017  7.452143 -6.380893 13.833037 #> 1018 28.481587 14.212559 14.269028 #> 1019 43.351392 28.044206 15.307187 #> 1020 50.359682 30.660814 19.698868 #> 1021 38.905226 24.749097 14.156129 #> 1022 44.724478 28.831429 15.893049 #> 1023 37.888974 23.777886 14.111088 #> 1024 45.527017 26.916318 18.610699 #> 1025 32.429571 17.189239 15.240332 #> 1026 26.490842 14.889397 11.601445 #> 1027 35.629157 23.457720 12.171437 #> 1028 35.574326 21.900100 13.674226 #> 1029 38.598639 23.181843 15.416796 #> 1030 36.602053 14.861406 21.740647 #> 1031 50.320031 30.101397 20.218634 #> 1032 53.698863 31.209416 22.489448 #> 1033 49.364208 26.515119 22.849089 #> 1034 46.262357 25.553822 20.708535 #> 1035 39.177121 15.768932 23.408190 #> 1036 54.984344 32.659083 22.325261 #> 1037 51.611458 33.129019 18.482439 #> 1038 51.998831 30.742830 21.256001 #> 1039 43.651605 27.410787 16.240818 #> 1040 44.196841 25.940924 18.255917 #> 1041 49.310593 29.510649 19.799944 #> 1042 37.995310 15.703901 22.291409 #> 1043 46.908709 28.268759 18.639949 #> 1044 28.976789 19.538922  9.437868 #> 1045 25.343793 17.183819  8.159973 #> 1046 24.006252 16.010370  7.995883 #> 1047 25.034907 18.461647  6.573260 #> 1048 10.478529  3.357357  7.121172 #> 1049 13.495623  5.335650  8.159973 print(p2 <- predict(COL.mix.eig, newdata=COL.OLD, listw=lw, pred.type = \"TS\",  legacy.mixed = TRUE)) #>            fit     trend    signal #> 1001 29.038788 14.854350 14.184438 #> 1002 46.227075 29.263210 16.963865 #> 1003 45.640479 25.819381 19.821099 #> 1004 36.643520 16.455557 20.187963 #> 1005 14.819940  0.366406 14.453534 #> 1006 38.764777 24.290524 14.474253 #> 1007 45.715716 27.038660 18.677056 #> 1008 37.514611 21.534238 15.980372 #> 1009 49.324228 29.509277 19.814951 #> 1010 17.510606  5.602910 11.907697 #> 1011 34.973607 28.641535  6.332073 #> 1012 21.079100 12.460727  8.618373 #> 1013 19.704134 14.417343  5.286791 #> 1014 16.365521 10.260642  6.104879 #> 1015 17.063856 12.255686  4.808170 #> 1016  6.190282 -2.013749  8.204032 #> 1017  5.967260 -6.380893 12.348154 #> 1018 29.250462 14.212559 15.037903 #> 1019 41.530036 28.044206 13.485830 #> 1020 49.344769 30.660814 18.683955 #> 1021 39.508818 24.749097 14.759721 #> 1022 42.772692 28.831429 13.941263 #> 1023 37.114901 23.777886 13.337016 #> 1024 43.622499 26.916318 16.706181 #> 1025 33.247197 17.189239 16.057958 #> 1026 30.301331 14.889397 15.411934 #> 1027 38.316063 23.457720 14.858343 #> 1028 36.886068 21.900100 14.985968 #> 1029 38.970564 23.181843 15.788721 #> 1030 33.014615 14.861406 18.153209 #> 1031 48.209875 30.101397 18.108478 #> 1032 50.808064 31.209416 19.598648 #> 1033 44.555996 26.515119 18.040877 #> 1034 43.232773 25.553822 17.678952 #> 1035 35.009061 15.768932 19.240129 #> 1036 52.113364 32.659083 19.454281 #> 1037 52.189015 33.129019 19.059996 #> 1038 51.631805 30.742830 20.888974 #> 1039 46.543564 27.410787 19.132778 #> 1040 45.036095 25.940924 19.095171 #> 1041 45.907835 29.510649 16.397186 #> 1042 35.337110 15.703901 19.633209 #> 1043 43.948398 28.268759 15.679639 #> 1044 32.091257 19.538922 12.552335 #> 1045 29.647005 17.183819 12.463186 #> 1046 26.375304 16.010370 10.364935 #> 1047 27.235807 18.461647  8.774160 #> 1048 14.785518  3.357357 11.428161 #> 1049 17.798836  5.335650 12.463186 AIC(COL.mix.eig) #> [1] 376.787 sqrt(deviance(COL.mix.eig)/length(COL.nb)) #> [1] 9.580773 sqrt(sum((COL.OLD$CRIME - as.vector(p1))^2)/length(COL.nb)) #> [1] 9.580773 sqrt(sum((COL.OLD$CRIME - as.vector(p2))^2)/length(COL.nb)) #> [1] 10.35029  COL.err.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, lw) AIC(COL.err.eig) #> [1] 376.7609 sqrt(deviance(COL.err.eig)/length(COL.nb)) #> [1] 9.776221 sqrt(sum((COL.OLD$CRIME - as.vector(predict(COL.err.eig)))^2)/length(COL.nb)) #> This method assumes the response is known - see manual page #> [1] 9.776221 sqrt(sum((COL.OLD$CRIME - as.vector(predict(COL.err.eig, newdata=COL.OLD,   listw=lw, pred.type = \"TS\")))^2)/length(COL.nb)) #> [1] 11.61744  COL.SDerr.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, lw,  etype=\"emixed\") AIC(COL.SDerr.eig) #> [1] 377.1693 sqrt(deviance(COL.SDerr.eig)/length(COL.nb)) #> [1] 9.619298 sqrt(sum((COL.OLD$CRIME - as.vector(predict(COL.SDerr.eig)))^2)/length(COL.nb)) #> This method assumes the response is known - see manual page #> [1] 9.619298 sqrt(sum((COL.OLD$CRIME - as.vector(predict(COL.SDerr.eig, newdata=COL.OLD,   listw=lw, pred.type = \"TS\")))^2)/length(COL.nb)) #> Warning: only legacy.mixed=TRUE is supported for pred.type='TS' and mixed models. legacy.mixed is forced #> [1] 10.40472  AIC(COL.lag.eig) #> [1] 374.7809 sqrt(deviance(COL.lag.eig)/length(COL.nb)) #> [1] 9.772129 sqrt(sum((COL.OLD$CRIME - as.vector(predict(COL.lag.eig)))^2)/length(COL.nb)) #> This method assumes the response is known - see manual page #> [1] 9.772129 sqrt(sum((COL.OLD$CRIME - as.vector(predict(COL.lag.eig, newdata=COL.OLD,   listw=lw, pred.type = \"TS\")))^2)/length(COL.nb)) #> [1] 10.72654  p3 <- predict(COL.mix.eig, newdata=COL.OLD, listw=lw, pred.type = \"TS\",  legacy=FALSE, legacy.mixed = TRUE) all.equal(p2, p3, check.attributes=FALSE) #> [1] TRUE p4 <- predict(COL.mix.eig, newdata=COL.OLD, listw=lw, pred.type = \"TS\",  legacy=FALSE, power=TRUE, legacy.mixed = TRUE) all.equal(p2, p4, check.attributes=FALSE) #> [1] TRUE p5 <- predict(COL.mix.eig, newdata=COL.OLD, listw=lw, pred.type = \"TS\",  legacy=TRUE, power=TRUE, legacy.mixed = TRUE) all.equal(p2, p5, check.attributes=FALSE) #> [1] TRUE"},{"path":"https://r-spatial.github.io/spatialreg/reference/sarlm_tests.html","id":null,"dir":"Reference","previous_headings":"","what":"Likelihood ratio test — LR.Sarlm","title":"Likelihood ratio test — LR.Sarlm","text":"LR.Sarlm() function provides likelihood ratio test objects logLik() function exists class, objects class logLik. LR1.Sarlm() Wald1.Sarlm() used internally summary.Sarlm(), may accessed directly; report values respectively LR Wald tests absence spatial dependence spatial lag error models. spatial Hausman test available models fitted errorSarlm GMerrorsar.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/sarlm_tests.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Likelihood ratio test — LR.Sarlm","text":"","code":"LR.Sarlm(x, y) # S3 method for class 'Sarlm' logLik(object, ...) LR1.Sarlm(object) Wald1.Sarlm(object) # S3 method for class 'Sarlm' Hausman.test(object, ..., tol=NULL) # S3 method for class 'Sarlm' anova(object, ...) bptest.Sarlm(object, varformula=NULL, studentize = TRUE, data=list()) # S3 method for class 'Sarlm' impacts(obj, ..., tr, R = NULL, listw = NULL, evalues=NULL,  useHESS = NULL, tol = 1e-06, empirical = FALSE, Q=NULL)"},{"path":"https://r-spatial.github.io/spatialreg/reference/sarlm_tests.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Likelihood ratio test — LR.Sarlm","text":"x logLik object object logLik() function exists y logLik object object logLik() function exists object, obj Sarlm object ... arguments passed methods  varformula formula describing potential explanatory variables variance (dependent variable needed). default explanatory variables taken main regression model studentize logical. set TRUE Koenker's studentized    version test statistic used. data optional data frame containing variables varformula tr vector traces powers spatial weights matrix created using trW, approximate impact measures; given, listw must given exact measures (small moderate spatial weights matrices); traces must spatial weights used fitting spatial regression, must row-standardised listw tr given, spatial weights object created nb2listw; must spatial weights used fitting spatial regression, row-standardised evalues vector eigenvalues spatial weights matrix impacts calculations R given, simulations used compute distributions impact measures, returned mcmc objects; objects used convenience output MCMC process useHESS Use Hessian approximation (available) even asymptotic coefficient covariance matrix available; used comparing methods tol Argument passed mvrnorm solve: tolerance (relative largest variance) numerical lack positive-definiteness coefficient covariance matrix empirical Argument passed mvrnorm (default FALSE): true, coefficients covariance matrix specify empirical population mean covariance matrix Q default NULL, else integer number cumulative power series impacts calculate tr given","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/sarlm_tests.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Likelihood ratio test — LR.Sarlm","text":"tests return objects class htest : statistic value statistic parameter degrees freedom p.value Probability value estimate varies test method description test method logLik.Sarlm() returns object class logLik   LR1.Sarlm, Hausman.Sarlm Wald1.Sarlm returm objects class htest","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/sarlm_tests.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Likelihood ratio test — LR.Sarlm","text":"numbers degrees freedom returned logLik.Sarlm() include nuisance parameters, number regression coefficients, plus sigma, plus spatial parameter esitmate(s).","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/sarlm_tests.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Likelihood ratio test — LR.Sarlm","text":"LeSage J RK Pace (2009) Introduction Spatial Econometrics. CRC Press, Boca Raton, pp. 61–63; Pace RK LeSage J (2008) spatial Hausman test. Economics Letters 101, 282–284. T.S. Breusch & .R. Pagan (1979), Simple Test Heteroscedasticity Random Coefficient Variation. Econometrica 47, 1287–1294 W. Krämer & H. Sonnberger (1986), Linear Regression Model Test. Heidelberg: Physica. L. Anselin (1988) Spatial econometrics: methods models. Dordrecht: Kluwer, pp. 121–122.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/sarlm_tests.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Likelihood ratio test — LR.Sarlm","text":"Roger Bivand Roger.Bivand@nhh., bptest: Torsten Hothorn Achim Zeileis, modified Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/sarlm_tests.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Likelihood ratio test — LR.Sarlm","text":"","code":"require(\"sf\", quietly=TRUE) columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) #require(\"spdep\", quietly=TRUE) col.gal.nb <- spdep::read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) lm.mod <- lm(CRIME ~ HOVAL + INC, data=columbus) lag <- lagsarlm(CRIME ~ HOVAL + INC, data=columbus, spdep::nb2listw(col.gal.nb)) mixed <- lagsarlm(CRIME ~ HOVAL + INC, data=columbus, spdep::nb2listw(col.gal.nb), type=\"mixed\") error <- errorsarlm(CRIME ~ HOVAL + INC, data=columbus, spdep::nb2listw(col.gal.nb)) Hausman.test(error) #>  #> \tSpatial Hausman test (asymptotic) #>  #> data:  NULL #> Hausman test = 6.4729, df = 3, p-value = 0.09074 #>  LR.Sarlm(mixed, error) #>  #> \tLikelihood ratio for spatial linear models #>  #> data:   #> Likelihood ratio = 4.2782, df = 2, p-value = 0.1178 #> sample estimates: #> Log likelihood of mixed Log likelihood of error  #>               -182.0161               -184.1552  #>  anova(lag, lm.mod) #>        Model df    AIC  logLik Test L.Ratio   p-value #> lag        1  5 376.34 -183.17    1                   #> lm.mod     2  4 382.75 -187.38    2  8.4179 0.0037154 anova(lag, error, mixed) #>       Model df    AIC  logLik Test L.Ratio p-value #> lag       1  5 376.34 -183.17    1                 #> error     2  5 378.31 -184.16    1                 #> mixed     3  7 378.03 -182.02    2  4.2782 0.11776 AIC(lag, error, mixed) #>       df      AIC #> lag    5 376.3366 #> error  5 378.3104 #> mixed  7 378.0322 bptest.Sarlm(error) #>  #> \tstudentized Breusch-Pagan test #>  #> data:   #> BP = 9.3694, df = 2, p-value = 0.009235 #>  bptest.Sarlm(error, studentize=FALSE) #>  #> \tBreusch-Pagan test #>  #> data:   #> BP = 16.285, df = 2, p-value = 0.0002908 #>"},{"path":"https://r-spatial.github.io/spatialreg/reference/set.mcOption.html","id":null,"dir":"Reference","previous_headings":"","what":"Options for parallel support — set.mcOption","title":"Options for parallel support — set.mcOption","text":"Provides support use parallel computation parallel package.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/set.mcOption.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Options for parallel support — set.mcOption","text":"","code":"set.mcOption(value) get.mcOption() set.coresOption(value) get.coresOption() set.ClusterOption(cl) get.ClusterOption()"},{"path":"https://r-spatial.github.io/spatialreg/reference/set.mcOption.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Options for parallel support — set.mcOption","text":"value valid replacement value cl cluster object created makeCluster parallel","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/set.mcOption.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Options for parallel support — set.mcOption","text":"Options spatialreg package held environment local package namespace exported. Option values set retrieved pairs access functions, get set. mc option set default FALSE Windows systems, fork R session; default TRUE systems, may set FALSE. mc FALSE, Cluster option used: mc FALSE Cluster option NULL parallel computing done, Cluster option passed “cluster” object created parallel snow package access without passed argument. cores option set NULL default, can used store number cores use integer. cores NULL, facilities parallel package used.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/set.mcOption.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Options for parallel support — set.mcOption","text":"option access functions return current settings, assignment functions usually return previous value option.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/set.mcOption.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Options for parallel support — set.mcOption","text":"extended example shown documentation mom_calc, including treatment seeding RNG multicore/cluster.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/set.mcOption.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Options for parallel support — set.mcOption","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/set.mcOption.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Options for parallel support — set.mcOption","text":"","code":"ls(envir=spatialreg:::.spatialregOptions) #> [1] \"cluster\"      \"cores\"        \"mc\"           \"rlecuyerSeed\" \"verbose\"      #> [6] \"zeroPolicy\"   library(parallel) nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L nc #> [1] 5 # set nc to 1L here if (nc > 1L) nc <- 1L #nc <- ifelse(nc > 2L, 2L, nc) coresOpt <- get.coresOption() coresOpt #> NULL if (!is.na(nc)) {  invisible(set.coresOption(nc))  print(exists(\"mom_calc\"))  if(.Platform$OS.type == \"windows\") { # forking not permitted on Windows - start cluster # removed for Github actions 210502 # \\dontrun{   print(get.mcOption())   cl <- makeCluster(get.coresOption())   print(clusterEvalQ(cl, exists(\"mom_calc\")))   set.ClusterOption(cl)   clusterEvalQ(get.ClusterOption(), library(spatialreg))   print(clusterEvalQ(cl, exists(\"mom_calc\")))   clusterEvalQ(get.ClusterOption(), detach(package:spatialreg))   set.ClusterOption(NULL)   print(clusterEvalQ(cl, exists(\"mom_calc\")))   stopCluster(cl) # }  } else {   mcOpt <- get.mcOption()   print(mcOpt)   print(mclapply(1:get.coresOption(), function(i) exists(\"mom_calc\"),    mc.cores=get.coresOption()))   invisible(set.mcOption(FALSE))   cl <- makeCluster(nc)   print(clusterEvalQ(cl, exists(\"mom_calc\")))   set.ClusterOption(cl)   clusterEvalQ(get.ClusterOption(), library(spatialreg))   print(clusterEvalQ(cl, exists(\"mom_calc\")))   clusterEvalQ(get.ClusterOption(), detach(package:spatialreg))   set.ClusterOption(NULL)   print(clusterEvalQ(cl, exists(\"mom_calc\")))   stopCluster(cl)   invisible(set.mcOption(mcOpt))  }  invisible(set.coresOption(coresOpt)) } #> [1] TRUE #> [1] TRUE #> [[1]] #> [1] TRUE #>  #> [[1]] #> [1] FALSE #>  #> [[1]] #> [1] TRUE #>  #> [[1]] #> [1] FALSE #>"},{"path":"https://r-spatial.github.io/spatialreg/reference/set.spChkOption.html","id":null,"dir":"Reference","previous_headings":"","what":"Control checking of spatial object IDs — set.ZeroPolicyOption","title":"Control checking of spatial object IDs — set.ZeroPolicyOption","text":"Provides support checking mutual integrity spatial neighbour weights spatial data; similar mechanisms used passing global verbose zero.policy options, providing access running cluster embarrassingly parallel tasks.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/set.spChkOption.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Control checking of spatial object IDs — set.ZeroPolicyOption","text":"","code":"set.VerboseOption(check) get.VerboseOption() set.ZeroPolicyOption(check) get.ZeroPolicyOption() #set.listw_is_CsparseMatrix_Option(check) #get.listw_is_CsparseMatrix_Option()"},{"path":"https://r-spatial.github.io/spatialreg/reference/set.spChkOption.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Control checking of spatial object IDs — set.ZeroPolicyOption","text":"check logical value, TRUE FALSE","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/set.spChkOption.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Control checking of spatial object IDs — set.ZeroPolicyOption","text":"Analysis functions spChk argument default set NULL, call get.spChkOption() get global spatial option whether check — initialised FALSE, consequently break anything. can changed TRUE using set.spChkOption(TRUE), spChk argument can assigned analysis functions. spNamedVec() provided ensure rownames passed single columns taken two-dimensional arrays data frames.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/set.spChkOption.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Control checking of spatial object IDs — set.ZeroPolicyOption","text":"set.spChkOption() returns old logical value, get.spChkOption() returns current logical value, chkIDs() returns logical value test lack difference. spNamedVec() returns selected column names set row names object extracted.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/set.spChkOption.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Control checking of spatial object IDs — set.ZeroPolicyOption","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/set.spChkOption.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Control checking of spatial object IDs — set.ZeroPolicyOption","text":"","code":"get.VerboseOption() #> [1] FALSE get.ZeroPolicyOption() #> [1] FALSE"},{"path":"https://r-spatial.github.io/spatialreg/reference/similar.listw.html","id":null,"dir":"Reference","previous_headings":"","what":"Create symmetric similar weights lists — similar.listw","title":"Create symmetric similar weights lists — similar.listw","text":"Ord's 1975 paper, known Jacobian SAR models may found \"symmetrizing\" similarity (eigenvalues similar matrices identical, Jacobian ). applies styles \"W\" \"S\" underlying symmetric binary neighbour relations symmetric general neighbour relations (k-nearest neighbour relations). function invoked automatically within SAR fitting functions, call eigen symmetric matrix default eigen method, make possible use Matrix method weights can \"symmetrized\" way.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/similar.listw.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Create symmetric similar weights lists — similar.listw","text":"","code":"similar.listw(listw)"},{"path":"https://r-spatial.github.io/spatialreg/reference/similar.listw.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Create symmetric similar weights lists — similar.listw","text":"listw listw object created example spdep::nb2listw","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/similar.listw.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Create symmetric similar weights lists — similar.listw","text":"listw object","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/similar.listw.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Create symmetric similar weights lists — similar.listw","text":"Ord, J. K. 1975 Estimation methods models spatial interaction, Journal American Statistical Association, 70, 120-126","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/similar.listw.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Create symmetric similar weights lists — similar.listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/similar.listw.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Create symmetric similar weights lists — similar.listw","text":"","code":"#require(\"spdep\", quietly=TRUE) data(oldcol, package=\"spdep\") COL.W <- spdep::nb2listw(COL.nb, style=\"W\") COL.S <- spdep::nb2listw(COL.nb, style=\"S\") sum(log(1 - 0.5 * eigenw(COL.W))) #> [1] -1.62766 sum(log(1 - 0.5 * eigenw(similar.listw(COL.W)))) #> [1] -1.62766 W_J <- as(as_dsTMatrix_listw(similar.listw(COL.W)), \"CsparseMatrix\") I <- as_dsCMatrix_I(dim(W_J)[1]) c(determinant(I - 0.5 * W_J, logarithm=TRUE)$modulus) #> [1] -1.62766 sum(log(1 - 0.5 * eigenw(COL.S))) #> [1] -1.602757 sum(log(1 - 0.5 * eigenw(similar.listw(COL.S)))) #> [1] -1.602757 W_J <- as(as_dsTMatrix_listw(similar.listw(COL.S)), \"CsparseMatrix\") c(determinant(I - 0.5 * W_J, logarithm=TRUE)$modulus) #> [1] -1.602757"},{"path":"https://r-spatial.github.io/spatialreg/reference/sparse_mat.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial neighbour sparse representation — as.spam.listw","title":"Spatial neighbour sparse representation — as.spam.listw","text":"Interface Matrix class objects weights lists. .spam.listw method converts \"listw\" object sparse matrix defined spam package.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/sparse_mat.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial neighbour sparse representation — as.spam.listw","text":"","code":"as.spam.listw(listw) listw2U_spam(lw) listw2U_Matrix(lw) as_dgRMatrix_listw(listw) as_dsTMatrix_listw(listw) as_dsCMatrix_I(n) as_dsCMatrix_IrW(W, rho) Jacobian_W(W, rho) powerWeights(W, rho, order=250, X, tol=.Machine$double.eps^(3/5))"},{"path":"https://r-spatial.github.io/spatialreg/reference/sparse_mat.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial neighbour sparse representation — as.spam.listw","text":"listw, lw listw object example nb2listw W dsTMatrix object created using as_dsTMatrix_listw symmetric listw object rho spatial regression coefficient n length diagonal identity matrix order Power series maximum limit X numerical matrix tol Tolerance convergence power series","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/sparse_mat.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial neighbour sparse representation — as.spam.listw","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/sparse_mat.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial neighbour sparse representation — as.spam.listw","text":"","code":"# \\dontrun{ require(sf, quietly=TRUE) columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) #require(spdep, quietly=TRUE) col.gal.nb <- spdep::read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) col.listw <- spdep::nb2listw(col.gal.nb) if (require(\"spam\", quietly=TRUE)) {   col.sp <- as.spam.listw(col.listw)   str(col.sp) } #> Spam version 2.11-0 (2024-10-03) is loaded. #> Type 'help( Spam)' or 'demo( spam)' for a short introduction  #> and overview of this package. #> Help for individual functions is also obtained by adding the #> suffix '.spam' to the function name, e.g. 'help( chol.spam)'. #>  #> Attaching package: ‘spam’ #> The following object is masked from ‘package:Matrix’: #>  #>     det #> The following objects are masked from ‘package:base’: #>  #>     backsolve, forwardsolve #> Formal class 'spam' [package \"spam\"] with 4 slots #>   ..@ entries    : num [1:230] 0.5 0.5 0.333 0.333 0.333 ... #>   ..@ colindices : int [1:230] 2 3 1 3 4 1 2 4 5 2 ... #>   ..@ rowpointers: int [1:50] 1 3 6 10 14 21 23 27 33 41 ... #>   ..@ dimension  : int [1:2] 49 49 suppressMessages(nyadjmat <- as.matrix(foreign::read.dbf(system.file(  \"misc/nyadjwts.dbf\", package=\"spData\")[1])[-1])) nyadjlw <- spdep::mat2listw(nyadjmat) #> Warning: style is M (missing); style should be set to a valid value listw_NY <- spdep::nb2listw(nyadjlw$neighbours, style=\"B\") W_C <- as(listw_NY, \"CsparseMatrix\") W_R <- as(listw_NY, \"RsparseMatrix\") W_S <- as(listw_NY, \"symmetricMatrix\") n <- nrow(W_S) I <- Diagonal(n) rho <- 0.1 c(determinant(I - rho * W_S, logarithm=TRUE)$modulus) #> [1] -9.587255 sum(log(1 - rho * eigenw(listw_NY))) #> [1] -9.587255 nW <- - W_S nChol <- Cholesky(nW, Imult=8) n * log(rho) + (2 * c(determinant(update(nChol, nW, 1/rho))$modulus)) #> [1] 99.8069 # } nb7rt <- spdep::cell2nb(7, 7, torus=TRUE) x <- matrix(sample(rnorm(500*length(nb7rt))), nrow=length(nb7rt)) lw <- spdep::nb2listw(nb7rt) if (FALSE) { # Only needed in some simulation settings where the input and # output distributions must agree in all but autocorrelation e <- eigenw(lw) x <- apply(x, 2, scale) st <- apply(x, 2, function(x) shapiro.test(x)$p.value) x <- x[, (st > 0.2 & st < 0.8)] x <- apply(x, 2, function(v) residuals(spautolm(v ~ 1, listw=lw,  method=\"eigen\", control=list(pre_eig=e, fdHess=FALSE)))) x <- apply(x, 2, scale) } W <- as(lw, \"CsparseMatrix\") system.time(e <- invIrM(nb7rt, rho=0.98, method=\"solve\", feasible=NULL) %*% x) #>    user  system elapsed  #>   0.002   0.000   0.003  system.time(ee <- powerWeights(W, rho=0.98, X=x)) #> Warning: not converged within order iterations #>    user  system elapsed  #>   0.173   0.006   0.180  str(attr(ee, \"internal\")) #> List of 5 #>  $ series: num [1:250] 0.287 0.234 0.201 0.178 0.16 ... #>  $ order : num 250 #>  $ tol   : num 4.05e-10 #>  $ iter  : num 250 #>  $ conv  : logi FALSE all.equal(e, as(ee, \"matrix\"), check.attributes=FALSE) #> [1] \"Mean relative difference: 0.0060747\" # \\dontrun{ system.time(ee <- powerWeights(W, rho=0.9, X=x)) #>    user  system elapsed  #>   0.130   0.002   0.133  system.time(ee <- powerWeights(W, rho=0.98, order=1000, X=x)) #>    user  system elapsed  #>   0.662   0.011   0.675  all.equal(e, as(ee, \"matrix\"), check.attributes=FALSE) #> [1] TRUE nb60rt <- spdep::cell2nb(60, 60, torus=TRUE) W <- as(spdep::nb2listw(nb60rt), \"CsparseMatrix\") set.seed(1) x <- matrix(rnorm(dim(W)[1]), ncol=1) system.time(ee <- powerWeights(W, rho=0.3, X=x)) #>    user  system elapsed  #>   0.009   0.000   0.009  str(as(ee, \"matrix\")) #>  num [1:3600, 1] -0.383 0.207 -0.731 1.552 0.32 ... #>  - attr(*, \"dimnames\")=List of 2 #>   ..$ : chr [1:3600] \"1:1\" \"2:1\" \"3:1\" \"4:1\" ... #>   ..$ : NULL obj <- errorsarlm(as(ee, \"matrix\")[,1] ~ 1, listw=spdep::nb2listw(nb60rt), method=\"Matrix\") coefficients(obj) #>      lambda (Intercept)  #>  0.30639880  0.01380415  # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/spautolm.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial conditional and simultaneous autoregression model estimation — spautolm","title":"Spatial conditional and simultaneous autoregression model estimation — spautolm","text":"Function taking family weights arguments spatial autoregression model estimation Maximum Likelihood, using dense matrix methods, suited large data sets thousands observations. one sparse matrix methods, larger numbers observations can handled, interval= argument set. implementation GLS using single spatial coefficient value, termed lambda, found line search using optimize maximise log likelihood.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/spautolm.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial conditional and simultaneous autoregression model estimation — spautolm","text":"","code":"spautolm(formula, data = list(), listw, weights,  na.action, family = \"SAR\", method=\"eigen\", verbose = NULL, trs=NULL,  interval=NULL, zero.policy = NULL, tol.solve=.Machine$double.eps,  llprof=NULL, control=list()) # S3 method for class 'Spautolm' summary(object, correlation = FALSE, adj.se=FALSE,  Nagelkerke=FALSE, ...)"},{"path":"https://r-spatial.github.io/spatialreg/reference/spautolm.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial conditional and simultaneous autoregression model estimation — spautolm","text":"formula symbolic description model fit. details model specification given lm() data optional data frame containing variables model. default variables taken environment function called. listw listw object created example nb2listw weights optional vector weights used fitting process na.action function (default options(\"na.action\")), can also na.omit na.exclude consequences residuals fitted values - cases weights list subsetted remove NAs data. Note weights lists created without using glist argument nb2listw may subsetted. family character string: either \"SAR\" \"CAR\" simultaneous conditional autoregressions; \"SMA\" spatial moving average added thanks Jielai Ma - \"SMA\" implemented method=\"eigen\" necessarily involves dense matrices method character string: default \"eigen\" use dense matrices, \"Matrix_J\" sparse matrices (restricted spatial weights symmetric similar symmetric) using methods Matrix package; “Matrix” provides updating Cholesky decomposition methods. Values method may also include \"LU\", provides alternative sparse matrix decomposition approach, \"Chebyshev\" Monte Carlo \"MC\" approximate log-determinant methods. verbose default NULL, use global option value; TRUE, reports function values optimization. trs default NULL, given, vector powered spatial weights matrix traces output trW; given, used Jacobian methods interval search interval autoregressive parameter using method=\"eigen\"; default c(-1,0.999), optimize reset NA/NaN bound gives warning interval poorly set; method=\"Matrix\" attempt search appropriate interval, find_interval=TRUE (fails platforms) zero.policy default NULL, use global option value; Include list -neighbour observations output TRUE — otherwise zero.policy handled within listw argument tol.solve tolerance detecting linear dependencies columns matrices inverted - passed solve() (default=double precision machine tolerance). Errors solve() may constitute indications poorly scaled variables: variables scales differing much autoregressive coefficient, values matrix may different scale, inverting matrix analytically possible definition, numerically unstable; rescaling RHS variables alleviates better setting tol.solve small value llprof default NULL, can either integer, divide feasible range llprof points, sequence spatial coefficient values, evaluate likelihood function control list extra control arguments - see section object Spautolm object spautolm correlation logical; 'TRUE', correlation matrix estimated parameters returned printed (default=FALSE) adj.se TRUE, adjust coefficient standard errors number fitted coefficients Nagelkerke TRUE, Nagelkerke pseudo R-squared reported ... arguments passed methods","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/spautolm.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Spatial conditional and simultaneous autoregression model estimation — spautolm","text":"implementation based lm.gls errorsarlm. particular, function (yet) prevent asymmetric spatial weights used \"CAR\" family models. appears numerical issues (convergence particular) uncertainties exact spatial weights matrix used make difficult reproduce Cressie Chan's 1989 results, also given Cressie 1993. Note fitted() function output object assumes response variable may reconstructed sum trend, signal, noise (residuals). Since values response variable known, spatial lags used calculate signal components (Cressie 1993, p. 564). differs software, including GeoDa, use knowledge response variable making predictions fitting data.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/spautolm.html","id":"control-arguments","dir":"Reference","previous_headings":"","what":"Control arguments","title":"Spatial conditional and simultaneous autoregression model estimation — spautolm","text":"tol.opt: desired accuracy optimization - passed optimize() (default=.Machine$double.eps^(2/3)) fdHess: default NULL, set (method != \"eigen\") internally; use fdHess compute approximate Hessian using finite differences using sparse matrix methods; used make coefficient covariance matrix number observations large; may turned save resources need optimHess: default FALSE, use fdHess nlme, TRUE, use optim calculate Hessian optimum optimHessMethod: default “optimHess”, may “nlm” one optim methods Imult: default 2; used preparing Cholesky decompositions updating Jacobian function super: NULL (default), set FALSE use simplicial decomposition sparse Cholesky decomposition method “Matrix_J”, set  .logical(NA) method “Matrix”, TRUE, use supernodal decomposition cheb_q: default 5; highest power approximating polynomial Chebyshev approximation MC_p: default 16; number random variates MC_m: default 30; number products random variates matrix spatial weights matrix type default “MC”, used method “moments”; alternatives “mult” “moments”, use trs missing, trW correct default TRUE, used method “moments” compute Smirnov/Anselin correction term trunc default TRUE, used method “moments” truncate Smirnov/Anselin correction term SE_method default “LU”, may “MC” nrho default 200, SE toolbox; size first stage lndet grid; may reduced example 40 interpn default 2000, SE toolbox; size second stage lndet grid small_asy default TRUE; method “eigen”, use asymmetric covariances rather numerical Hessian ones n <= small small default 1500; threshold number observations asymmetric covariances method “eigen” SElndet default NULL, may used pass pre-computed SE toolbox style matrix coefficients lndet values \"SE_classic\" \"SE_whichMin\" methods LU_order default FALSE; used “LU_prepermutate”, note warnings given lu method pre_eig default NULL; may used pass pre-computed vector eigenvalues","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/spautolm.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial conditional and simultaneous autoregression model estimation — spautolm","text":"list object class Spautolm: fit list, items: coefficients ML coefficient estimates SSE ML sum squared errors s2 ML residual variance imat ML coefficient covariance matrix (multiplying s2) signal_trend non-spatial component fitted.values signal_stochastic spatial component fitted.values fitted.values sum non-spatial spatial components fitted.values residuals difference observed fitted values lambda ML autoregressive coefficient LL log likelihood fitted model LL0 log likelihood model lambda=0 call call used create object parameters number parameters estimated aliased NULL, details aliased variables method Jacobian method chosen family family chosen zero.policy zero.policy used weights case weights used interval line search interval used timings processing timings na.action (possibly) named vector excluded omitted observations non-default na.action argument used llprof NULL, list components lambda ll equal length lambda.se Numerical Hessian-based standard error lambda fdHess Numerical Hessian-based variance-covariance matrix X covariates used model fitting Y response used model fitting weights weights used model fitting","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/spautolm.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial conditional and simultaneous autoregression model estimation — spautolm","text":"Cliff, . D., Ord, J. K. 1981 Spatial processes, Pion; Ord, J. K. 1975 Estimation methods models spatial interaction, Journal American Statistical Association, 70, 120-126; Waller, L. ., Gotway, C. . 2004 Applied spatial statistics public health, Wiley, Hoboken, NJ, 325-380; Cressie, N. . C. 1993 Statistics spatial data, Wiley, New York, 548-568; Ripley, B. D. 1981 Spatial statistics, Wiley, New York, 88-95; LeSage J RK Pace (2009) Introduction Spatial Econometrics. CRC Press, Boca Raton.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/spautolm.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial conditional and simultaneous autoregression model estimation — spautolm","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/spautolm.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Spatial conditional and simultaneous autoregression model estimation — spautolm","text":"standard errors given Waller Gotway (2004) adjusted numbers parameters estimated, may reproduced using additional argument adj.se=TRUE summary method. addition, function returns fitted values residuals given Cressie (1993) p. 564.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/spautolm.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial conditional and simultaneous autoregression model estimation — spautolm","text":"","code":"require(\"sf\", quietly=TRUE) nydata <- st_read(system.file(\"shapes/NY8_bna_utm18.gpkg\", package=\"spData\")[1], quiet=TRUE) # \\dontrun{ lm0 <- lm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata) summary(lm0) #>  #> Call: #> lm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata) #>  #> Residuals: #>     Min      1Q  Median      3Q     Max  #> -1.7417 -0.3957 -0.0326  0.3353  4.1398  #>  #> Coefficients: #>             Estimate Std. Error t value Pr(>|t|)     #> (Intercept) -0.51728    0.15856  -3.262  0.00124 **  #> PEXPOSURE    0.04884    0.03506   1.393  0.16480     #> PCTAGE65P    3.95089    0.60550   6.525 3.22e-10 *** #> PCTOWNHOME  -0.56004    0.17031  -3.288  0.00114 **  #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>  #> Residual standard error: 0.6571 on 277 degrees of freedom #> Multiple R-squared:  0.1932,\tAdjusted R-squared:  0.1844  #> F-statistic:  22.1 on 3 and 277 DF,  p-value: 7.306e-13 #>  lm0w <- lm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, weights=POP8) summary(lm0w) #>  #> Call: #> lm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     weights = POP8) #>  #> Weighted Residuals: #>      Min       1Q   Median       3Q      Max  #> -129.067  -14.714    5.817   25.624   70.723  #>  #> Coefficients: #>             Estimate Std. Error t value Pr(>|t|)     #> (Intercept) -0.77837    0.14116  -5.514 8.03e-08 *** #> PEXPOSURE    0.07626    0.02731   2.792  0.00560 **  #> PCTAGE65P    3.85656    0.57126   6.751 8.60e-11 *** #> PCTOWNHOME  -0.39869    0.15305  -2.605  0.00968 **  #> --- #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #>  #> Residual standard error: 33.5 on 277 degrees of freedom #> Multiple R-squared:  0.1977,\tAdjusted R-squared:  0.189  #> F-statistic: 22.75 on 3 and 277 DF,  p-value: 3.382e-13 #>  # } suppressMessages(nyadjmat <- as.matrix(foreign::read.dbf(system.file(  \"misc/nyadjwts.dbf\", package=\"spData\")[1])[-1])) suppressMessages(ID <- as.character(names(foreign::read.dbf(system.file(  \"misc/nyadjwts.dbf\", package=\"spData\")[1]))[-1])) identical(substring(ID, 2, 10), substring(as.character(nydata$AREAKEY), 2, 10)) #> [1] TRUE #require(\"spdep\", quietly=TRUE) listw_NY <- spdep::mat2listw(nyadjmat, as.character(nydata$AREAKEY), style=\"B\") eigs <- eigenw(listw_NY) # \\dontrun{ esar0 <- errorsarlm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY) summary(esar0) #>  #> Call:errorsarlm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  #>     data = nydata, listw = listw_NY) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.56754 -0.38239 -0.02643  0.33109  4.01219  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.618193   0.176784 -3.4969 0.0004707 #> PEXPOSURE    0.071014   0.042051  1.6888 0.0912635 #> PCTAGE65P    3.754200   0.624722  6.0094 1.862e-09 #> PCTOWNHOME  -0.419890   0.191329 -2.1946 0.0281930 #>  #> Lambda: 0.040487, LR test value: 5.2438, p-value: 0.022026 #> Asymptotic standard error: 0.016214 #>     z-value: 2.4971, p-value: 0.01252 #> Wald statistic: 6.2356, p-value: 0.01252 #>  #> Log likelihood: -276.1069 for error model #> ML residual variance (sigma squared): 0.41388, (sigma: 0.64333) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 564.21, (AIC for lm: 567.46) #>  system.time(esar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  data=nydata, listw=listw_NY, family=\"SAR\", method=\"eigen\",  control=list(pre_eig=eigs))) #>    user  system elapsed  #>     0.2     0.0     0.2  res <- summary(esar1f) print(res) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, family = \"SAR\", method = \"eigen\", control = list(pre_eig = eigs)) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.56754 -0.38239 -0.02643  0.33109  4.01219  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.618193   0.176784 -3.4969 0.0004707 #> PEXPOSURE    0.071014   0.042051  1.6888 0.0912635 #> PCTAGE65P    3.754200   0.624722  6.0094 1.862e-09 #> PCTOWNHOME  -0.419890   0.191329 -2.1946 0.0281930 #>  #> Lambda: 0.040487 LR test value: 5.2438 p-value: 0.022026  #> Numerical Hessian standard error of lambda: 0.017201  #>  #> Log likelihood: -276.1069  #> ML residual variance (sigma squared): 0.41388, (sigma: 0.64333) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 564.21 #>  coef(res) #>                Estimate Std. Error   z value     Pr(>|z|) #> (Intercept) -0.61819272 0.17678351 -3.496891 4.707136e-04 #> PEXPOSURE    0.07101384 0.04205063  1.688770 9.126350e-02 #> PCTAGE65P    3.75419996 0.62472153  6.009397 1.862142e-09 #> PCTOWNHOME  -0.41988960 0.19132936 -2.194591 2.819298e-02 sqrt(diag(res$resvar)) #> (Intercept)   PEXPOSURE   PCTAGE65P  PCTOWNHOME  #>  0.17678351  0.04205063  0.62472153  0.19132936  sqrt(diag(esar1f$fit$imat)*esar1f$fit$s2) #> (Intercept)   PEXPOSURE   PCTAGE65P  PCTOWNHOME  #>  0.17678351  0.04205063  0.62472153  0.19132936  sqrt(diag(esar1f$fdHess)) #> [1] 0.01720109 0.18504698 0.04378056 0.62990270 0.20343911 system.time(esar1M <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  data=nydata, listw=listw_NY, family=\"SAR\", method=\"Matrix\")) #>    user  system elapsed  #>   0.227   0.000   0.227  summary(esar1M) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, family = \"SAR\", method = \"Matrix\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -3.406132 -0.561646 -0.092662  0.474796  5.384405  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.414826   0.102166 -4.0603 4.901e-05 #> PEXPOSURE    0.015081   0.017772  0.8486    0.3961 #> PCTAGE65P    5.159749   0.476498 10.8285 < 2.2e-16 #> PCTOWNHOME  -0.892387   0.099241 -8.9921 < 2.2e-16 #>  #> Lambda: -0.38889 LR test value: 254.73 p-value: < 2.22e-16  #> Numerical Hessian standard error of lambda: 0.044857  #>  #> Log likelihood: -151.3662  #> ML residual variance (sigma squared): 0.95111, (sigma: 0.97525) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 314.73 #>  system.time(esar1M <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  data=nydata, listw=listw_NY, family=\"SAR\", method=\"Matrix\",  control=list(super=TRUE))) #>    user  system elapsed  #>   0.203   0.000   0.204  summary(esar1M) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, family = \"SAR\", method = \"Matrix\", control = list(super = TRUE)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -3.178535 -0.521860 -0.074421  0.414212  5.184465  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.411041   0.104426 -3.9362 8.279e-05 #> PEXPOSURE    0.015768   0.018366  0.8585    0.3906 #> PCTAGE65P    5.070130   0.483332 10.4900 < 2.2e-16 #> PCTOWNHOME  -0.880883   0.102093 -8.6282 < 2.2e-16 #>  #> Lambda: -0.33146 LR test value: 247.44 p-value: < 2.22e-16  #> Numerical Hessian standard error of lambda: 0.030659  #>  #> Log likelihood: -155.0108  #> ML residual variance (sigma squared): 0.82436, (sigma: 0.90795) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 322.02 #>  esar1wf <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, weights=POP8, family=\"SAR\", method=\"eigen\",  control=list(pre_eig=eigs)) summary(esar1wf) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, weights = POP8, family = \"SAR\", method = \"eigen\",  #>     control = list(pre_eig = eigs)) #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.48488 -0.26823  0.09489  0.46552  4.28343  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.797063   0.144054 -5.5331 3.146e-08 #> PEXPOSURE    0.080545   0.028334  2.8428  0.004473 #> PCTAGE65P    3.816731   0.576037  6.6258 3.453e-11 #> PCTOWNHOME  -0.380778   0.156507 -2.4330  0.014975 #>  #> Lambda: 0.0095636 LR test value: 0.32665 p-value: 0.56764  #> Numerical Hessian standard error of lambda: 0.016522  #>  #> Log likelihood: -251.6017  #> ML residual variance (sigma squared): 1104.1, (sigma: 33.229) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: NA (not available for weighted model) #>  system.time(esar1wM <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  data=nydata, listw=listw_NY, weights=POP8, family=\"SAR\", method=\"Matrix\")) #>    user  system elapsed  #>    0.22    0.00    0.22  summary(esar1wM) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, weights = POP8, family = \"SAR\", method = \"Matrix\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -2.561100 -0.374524  0.057405  0.591094  5.700142  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.578546   0.090006 -6.4279 1.294e-10 #> PEXPOSURE    0.035402   0.013959  2.5361   0.01121 #> PCTAGE65P    4.651137   0.421285 11.0404 < 2.2e-16 #> PCTOWNHOME  -0.666898   0.091443 -7.2931 3.029e-13 #>  #> Lambda: -0.34423 LR test value: 264.24 p-value: < 2.22e-16  #> Numerical Hessian standard error of lambda: 0.036776  #>  #> Log likelihood: -119.6468  #> ML residual variance (sigma squared): 2129.1, (sigma: 46.142) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: NA (not available for weighted model) #>  esar1wlu <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, weights=POP8, family=\"SAR\", method=\"LU\") summary(esar1wlu) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, weights = POP8, family = \"SAR\", method = \"LU\") #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.48488 -0.26823  0.09489  0.46552  4.28343  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.797063   0.144054 -5.5331 3.146e-08 #> PEXPOSURE    0.080545   0.028334  2.8428  0.004473 #> PCTAGE65P    3.816731   0.576037  6.6258 3.453e-11 #> PCTOWNHOME  -0.380778   0.156507 -2.4330  0.014975 #>  #> Lambda: 0.0095636 LR test value: 0.32665 p-value: 0.56764  #> Numerical Hessian standard error of lambda: 0.016522  #>  #> Log likelihood: -251.6017  #> ML residual variance (sigma squared): 1104.1, (sigma: 33.229) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: NA (not available for weighted model) #>  esar1wch <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, weights=POP8, family=\"SAR\", method=\"Chebyshev\") summary(esar1wch) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, weights = POP8, family = \"SAR\", method = \"Chebyshev\") #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -4.39831 -0.86303  0.12117  1.09320  8.78570  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.538555   0.087573 -6.1498  7.76e-10 #> PEXPOSURE    0.029782   0.013074  2.2780   0.02273 #> PCTAGE65P    4.896346   0.419359 11.6758 < 2.2e-16 #> PCTOWNHOME  -0.737829   0.087569 -8.4257 < 2.2e-16 #>  #> Lambda: -1 LR test value: 236970 p-value: < 2.22e-16  #> Numerical Hessian standard error of lambda: NaN  #>  #> Log likelihood: 118232.5  #> ML residual variance (sigma squared): 9336.4, (sigma: 96.625) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: NA (not available for weighted model) #>  # } ecar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, family=\"CAR\", method=\"eigen\",  control=list(pre_eig=eigs)) summary(ecar1f) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, family = \"CAR\", method = \"eigen\", control = list(pre_eig = eigs)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -1.539732 -0.384311 -0.030646  0.335126  3.808848  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.648362   0.181129 -3.5796 0.0003442 #> PEXPOSURE    0.077899   0.043692  1.7829 0.0745986 #> PCTAGE65P    3.703830   0.627185  5.9055 3.516e-09 #> PCTOWNHOME  -0.382789   0.195564 -1.9574 0.0503053 #>  #> Lambda: 0.084123 LR test value: 5.8009 p-value: 0.016018  #> Numerical Hessian standard error of lambda: 0.030872  #>  #> Log likelihood: -275.8283  #> ML residual variance (sigma squared): 0.40758, (sigma: 0.63842) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 563.66 #>  # \\dontrun{ system.time(ecar1M <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  data=nydata, listw=listw_NY, family=\"CAR\", method=\"Matrix\")) #>    user  system elapsed  #>   0.311   0.000   0.313  summary(ecar1M) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, family = \"CAR\", method = \"Matrix\") #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -3.449951 -0.633777 -0.072436  0.550248  6.039594  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.402788   0.112612 -3.5768 0.0003479 #> PEXPOSURE    0.020131   0.020783  0.9686 0.3327222 #> PCTAGE65P    4.632644   0.500526  9.2555 < 2.2e-16 #> PCTOWNHOME  -0.812981   0.112867 -7.2030 5.891e-13 #>  #> Lambda: -0.5 LR test value: 228.48 p-value: < 2.22e-16  #> Numerical Hessian standard error of lambda: NaN  #>  #> Log likelihood: -164.4897  #> ML residual variance (sigma squared): 0.50386, (sigma: 0.70983) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: 340.98 #>  # } ecar1wf <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,  listw=listw_NY, weights=POP8, family=\"CAR\", method=\"eigen\",  control=list(pre_eig=eigs)) summary(ecar1wf) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, weights = POP8, family = \"CAR\", method = \"eigen\",  #>     control = list(pre_eig = eigs)) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -1.491042 -0.270906  0.081435  0.451556  4.198134  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.790154   0.144862 -5.4545 4.910e-08 #> PEXPOSURE    0.081922   0.028593  2.8651  0.004169 #> PCTAGE65P    3.825858   0.577720  6.6223 3.536e-11 #> PCTOWNHOME  -0.386820   0.157436 -2.4570  0.014010 #>  #> Lambda: 0.022419 LR test value: 0.38785 p-value: 0.53343  #> Numerical Hessian standard error of lambda: 0.038977  #>  #> Log likelihood: -251.5711  #> ML residual variance (sigma squared): 1102.9, (sigma: 33.21) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: NA (not available for weighted model) #>  # \\dontrun{ system.time(ecar1wM <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,  data=nydata, listw=listw_NY, weights=POP8, family=\"CAR\", method=\"Matrix\")) #>    user  system elapsed  #>   0.260   0.000   0.262  summary(ecar1wM) #>  #> Call:  #> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,  #>     listw = listw_NY, weights = POP8, family = \"CAR\", method = \"Matrix\") #>  #> Residuals: #>      Min       1Q   Median       3Q      Max  #> -1.98144 -0.15716  0.37342  1.08857  7.10495  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) -0.714952   0.093905 -7.6136 2.665e-14 #> PEXPOSURE    0.041467   0.015279  2.7139   0.00665 #> PCTAGE65P    4.149207   0.425446  9.7526 < 2.2e-16 #> PCTOWNHOME  -0.478396   0.097030 -4.9304 8.205e-07 #>  #> Lambda: -0.5 LR test value: 262.65 p-value: < 2.22e-16  #> Numerical Hessian standard error of lambda: NaN  #>  #> Log likelihood: -120.4395  #> ML residual variance (sigma squared): 1159.2, (sigma: 34.046) #> Number of observations: 281  #> Number of parameters estimated: 6  #> AIC: NA (not available for weighted model) #>  # } # \\dontrun{ require(\"sf\", quietly=TRUE) nc.sids <- st_read(system.file(\"shapes/sids.gpkg\", package=\"spData\")[1], quiet=TRUE) ft.SID74 <- sqrt(1000)*(sqrt(nc.sids$SID74/nc.sids$BIR74) +  sqrt((nc.sids$SID74+1)/nc.sids$BIR74)) lm_nc <- lm(ft.SID74 ~ 1) sids.nhbr30 <- spdep::dnearneigh(cbind(nc.sids$east, nc.sids$north), 0, 30,  row.names=row.names(nc.sids)) #> Warning: neighbour object has 3 sub-graphs sids.nhbr30.dist <- spdep::nbdists(sids.nhbr30, cbind(nc.sids$east, nc.sids$north)) sids.nhbr <- spdep::listw2sn(spdep::nb2listw(sids.nhbr30,  glist=sids.nhbr30.dist, style=\"B\", zero.policy=TRUE)) dij <- sids.nhbr[,3] n <- nc.sids$BIR74 el1 <- min(dij)/dij el2 <- sqrt(n[sids.nhbr$to]/n[sids.nhbr$from]) sids.nhbr$weights <- el1*el2 sids.nhbr.listw <- spdep::sn2listw(sids.nhbr) #> Warning: style is M (missing); style should be set to a valid value #> Warning: 56, 87 are not origins #> Error in spdep::sn2listw(sids.nhbr): no-neighbour observations found, set zero.policy to TRUE both <- factor(paste(nc.sids$L_id, nc.sids$M_id, sep=\":\")) ft.NWBIR74 <- sqrt(1000)*(sqrt(nc.sids$NWBIR74/nc.sids$BIR74) +  sqrt((nc.sids$NWBIR74+1)/nc.sids$BIR74)) mdata <- data.frame(both, ft.NWBIR74, ft.SID74, BIR74=nc.sids$BIR74) outl <- which.max(rstandard(lm_nc)) as.character(nc.sids$NAME[outl]) #> [1] \"Anson\" mdata.4 <- mdata[-outl,] W <- spdep::listw2mat(sids.nhbr.listw) #> Error: object 'sids.nhbr.listw' not found W.4 <- W[-outl, -outl] #> Error: object 'W' not found sids.nhbr.listw.4 <- spdep::mat2listw(W.4) #> Error: object 'W.4' not found esarI <- errorsarlm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw,  zero.policy=TRUE) #> Error: object 'sids.nhbr.listw' not found summary(esarI) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarI' not found esarIa <- spautolm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw,  family=\"SAR\") #> Error: object 'sids.nhbr.listw' not found summary(esarIa) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIa' not found esarIV <- errorsarlm(ft.SID74 ~ ft.NWBIR74, data=mdata, listw=sids.nhbr.listw,  zero.policy=TRUE) #> Error: object 'sids.nhbr.listw' not found summary(esarIV) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIV' not found esarIVa <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata, listw=sids.nhbr.listw,  family=\"SAR\") #> Error: object 'sids.nhbr.listw' not found summary(esarIVa) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIVa' not found esarIaw <- spautolm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw,  weights=BIR74, family=\"SAR\") #> Error: object 'sids.nhbr.listw' not found summary(esarIaw) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIaw' not found esarIIaw <- spautolm(ft.SID74 ~ both - 1, data=mdata, listw=sids.nhbr.listw,  weights=BIR74, family=\"SAR\") #> Error: object 'sids.nhbr.listw' not found summary(esarIIaw) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIIaw' not found esarIVaw <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata,  listw=sids.nhbr.listw, weights=BIR74, family=\"SAR\") #> Error: object 'sids.nhbr.listw' not found summary(esarIVaw) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIVaw' not found ecarIaw <- spautolm(ft.SID74 ~ 1, data=mdata.4, listw=sids.nhbr.listw.4,  weights=BIR74, family=\"CAR\") #> Error: object 'sids.nhbr.listw.4' not found summary(ecarIaw) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'ecarIaw' not found ecarIIaw <- spautolm(ft.SID74 ~ both - 1, data=mdata.4,  listw=sids.nhbr.listw.4, weights=BIR74, family=\"CAR\") #> Error: object 'sids.nhbr.listw.4' not found summary(ecarIIaw) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'ecarIIaw' not found ecarIVaw <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata.4,  listw=sids.nhbr.listw.4, weights=BIR74, family=\"CAR\") #> Error: object 'sids.nhbr.listw.4' not found summary(ecarIVaw) #> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'ecarIVaw' not found nc.sids$fitIV <- append(fitted.values(ecarIVaw), NA, outl-1) #> Error: object 'ecarIVaw' not found plot(nc.sids[,\"fitIV\"], nbreaks=12) # Cressie 1993, p. 565 #> Error in `[.data.frame`(x, i, j, drop = drop): undefined columns selected # } # \\dontrun{ data(oldcol, package=\"spdep\") COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,  spdep::nb2listw(COL.nb, style=\"W\")) summary(COL.errW.eig) #>  #> Call: #> errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,  #>     style = \"W\")) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -34.81174  -6.44031  -0.72142   7.61476  23.33626  #>  #> Type: error  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 59.893219   5.366163 11.1613 < 2.2e-16 #> INC         -0.941312   0.330569 -2.8476 0.0044057 #> HOVAL       -0.302250   0.090476 -3.3407 0.0008358 #>  #> Lambda: 0.56179, LR test value: 7.9935, p-value: 0.0046945 #> Asymptotic standard error: 0.13387 #>     z-value: 4.1966, p-value: 2.7098e-05 #> Wald statistic: 17.611, p-value: 2.7098e-05 #>  #> Log likelihood: -183.3805 for error model #> ML residual variance (sigma squared): 95.575, (sigma: 9.7762) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 376.76, (AIC for lm: 382.75) #>  COL.errW.sar <- spautolm(CRIME ~ INC + HOVAL, data=COL.OLD,  spdep::nb2listw(COL.nb, style=\"W\")) summary(COL.errW.sar) #>  #> Call:  #> spautolm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,  #>     style = \"W\")) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -34.81174  -6.44031  -0.72142   7.61476  23.33626  #>  #> Coefficients:  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 59.893219   5.366162 11.1613 < 2.2e-16 #> INC         -0.941312   0.330569 -2.8476 0.0044057 #> HOVAL       -0.302250   0.090476 -3.3407 0.0008358 #>  #> Lambda: 0.56179 LR test value: 7.9935 p-value: 0.0046945  #> Numerical Hessian standard error of lambda: 0.15241  #>  #> Log likelihood: -183.3805  #> ML residual variance (sigma squared): 95.575, (sigma: 9.7762) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 376.76 #>  data(boston, package=\"spData\") gp1 <- spautolm(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2)  + I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),   data=boston.c, spdep::nb2listw(boston.soi), family=\"SMA\") summary(gp1) #>  #> Call: spautolm(formula = log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +  #>     I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B +  #>     log(LSTAT), data = boston.c, listw = spdep::nb2listw(boston.soi),  #>     family = \"SMA\") #>  #> Residuals: #>        Min         1Q     Median         3Q        Max  #> -0.5847694 -0.0713881  0.0012284  0.0827517  0.6071219  #>  #> Coefficients:  #>                Estimate  Std. Error  z value  Pr(>|z|) #> (Intercept)  4.28501607  0.15367176  27.8842 < 2.2e-16 #> CRIM        -0.00718807  0.00106298  -6.7622 1.359e-11 #> ZN           0.00023008  0.00051897   0.4433 0.6575185 #> INDUS        0.00047300  0.00263339   0.1796 0.8574551 #> CHAS1        0.01020698  0.02872047   0.3554 0.7222970 #> I(NOX^2)    -0.44885530  0.13675913  -3.2821 0.0010304 #> I(RM^2)      0.00638094  0.00110330   5.7835 7.316e-09 #> AGE         -0.00043973  0.00051336  -0.8566 0.3916862 #> log(DIS)    -0.15650578  0.03856337  -4.0584 4.941e-05 #> log(RAD)     0.07583760  0.02016468   3.7609 0.0001693 #> TAX         -0.00049364  0.00012162  -4.0588 4.933e-05 #> PTRATIO     -0.02494959  0.00538791  -4.6307 3.645e-06 #> B            0.00048517  0.00010944   4.4334 9.277e-06 #> log(LSTAT)  -0.32961379  0.02353891 -14.0029 < 2.2e-16 #>  #> Lambda: 0.61991 LR test value: 144.28 p-value: < 2.22e-16  #> Numerical Hessian standard error of lambda: 0.044296  #>  #> Log likelihood: 229.1208  #> ML residual variance (sigma squared): 0.02596, (sigma: 0.16112) #> Number of observations: 506  #> Number of parameters estimated: 16  #> AIC: -426.24 #>  # }"},{"path":"https://r-spatial.github.io/spatialreg/reference/stsls.html","id":null,"dir":"Reference","previous_headings":"","what":"Generalized spatial two stage least squares — stsls","title":"Generalized spatial two stage least squares — stsls","text":"function fits spatial lag model two stage least squares, option adjusting results heteroskedasticity.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/stsls.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generalized spatial two stage least squares — stsls","text":"","code":"stsls(formula, data = list(), listw, zero.policy = NULL,  na.action = na.fail, robust = FALSE, HC=NULL, legacy=FALSE, W2X = TRUE,  sig2n_k=TRUE, adjust.n=FALSE) # S3 method for class 'Stsls' impacts(obj, ..., tr, R = NULL, listw = NULL, evalues=NULL,  tol = 1e-06, empirical = FALSE, Q=NULL)"},{"path":"https://r-spatial.github.io/spatialreg/reference/stsls.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generalized spatial two stage least squares — stsls","text":"formula symbolic description model fit. details model specification given lm() data optional data frame containing variables model. default variables taken environment function called. listw listw object created example nb2listw zero.policy default NULL, use global option value; TRUE assign zero lagged value zones without neighbours, FALSE (default) assign NA - causing lagsarlm() terminate error na.action function (default na.fail), can also na.omit na.exclude consequences residuals fitted values - cases weights list subsetted remove NAs data. may necessary set zero.policy TRUE subsetting may create -neighbour observations. Note weights lists created without using glist argument nb2listw may subsetted. robust default FALSE, TRUE, apply heteroskedasticity correction coefficients covariances HC default NULL, robust TRUE, assigned “HC0”, may take values “HC0” “HC1” White estimates MacKinnon-White estimates respectively legacy argument chooses two implementations robustness correction: default FALSE - use estimate Omega White consistent estimator variance-covariance matrix, TRUE, use original implementation runs GLS using estimate Omega, overrides sig2n_k, yields different coefficient estimates well - see example W2X default TRUE, FALSE WX used instruments spatial two stage least squares; release 0.4-60, WX used - see example ; Python spreg::GM_Lag default FALSE sig2n_k default TRUE - use n-k calculate sigma^2, FALSE use n; Python spreg::GM_Lag default FALSE adjust.n default FALSE, used creating spatial weights constants Anselin-Kelejian (1997) test obj spatial regression object created lagsarlm, lagmess lmSLX; HPDinterval.LagImpact, LagImpact object ... Arguments passed methods coda package tr vector traces powers spatial weights matrix created using trW, approximate impact measures; given, listw must given exact measures (small moderate spatial weights matrices); traces must spatial weights used fitting spatial regression, must row-standardised evalues vector eigenvalues spatial weights matrix impacts calculations R given, simulations used compute distributions impact measures, returned mcmc objects; objects used convenience output MCMC process tol Argument passed mvrnorm: tolerance (relative largest variance) numerical lack positive-definiteness coefficient covariance matrix empirical Argument passed mvrnorm (default FALSE): true, coefficients covariance matrix specify empirical population mean covariance matrix Q default NULL, else integer number cumulative power series impacts calculate tr given","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/stsls.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Generalized spatial two stage least squares — stsls","text":"fitting implementation fits spatial lag model: $$y = \\rho W y + X \\beta + \\varepsilon$$ using spatially lagged X variables instruments spatially lagged dependent variable. version 1.3-6, general Anselin-Kelejian (1997) test residual spatial autocorrelation added.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/stsls.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generalized spatial two stage least squares — stsls","text":"object class \"Stsls\" containing: coefficients coefficient estimates var coefficient covariance matrix sse sum squared errors residuals model residuals df degrees freedom","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/stsls.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Generalized spatial two stage least squares — stsls","text":"Kelejian, H.H. .R. Prucha (1998). generalized spatial two stage least squares procedure estimating spatial autoregressive model autoregressive disturbances. Journal Real Estate Finance Economics 17, 99-121. doi:10.1023/:1007707430416 . Anselin, L., & Kelejian, H. H. (1997). Testing Spatial Error Autocorrelation Presence Endogenous Regressors. International Regional Science Review, 20(1-2), 153-182. doi:10.1177/016001769702000109 . Roger Bivand, Gianfranco Piras (2015). Comparing Implementations Estimation Methods Spatial Econometrics. Journal Statistical Software, 63(18), 1-36. doi:10.18637/jss.v063.i18 .","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/stsls.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Generalized spatial two stage least squares — stsls","text":"Luc Anselin, Gianfranco Piras Roger Bivand","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/stsls.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generalized spatial two stage least squares — stsls","text":"","code":"data(oldcol, package=\"spdep\") #require(spdep, quietly=TRUE) lw <- spdep::nb2listw(COL.nb) COL.lag.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, lw) summary(COL.lag.eig, correlation=TRUE) #>  #> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = lw) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.68585  -5.35636   0.05421   6.02013  23.20555  #>  #> Type: lag  #> Coefficients: (asymptotic standard errors)  #>              Estimate Std. Error z value  Pr(>|z|) #> (Intercept) 45.079250   7.177347  6.2808 3.369e-10 #> INC         -1.031616   0.305143 -3.3808 0.0007229 #> HOVAL       -0.265926   0.088499 -3.0049 0.0026570 #>  #> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588 #> Asymptotic standard error: 0.11768 #>     z-value: 3.6626, p-value: 0.00024962 #> Wald statistic: 13.415, p-value: 0.00024962 #>  #> Log likelihood: -182.3904 for lag model #> ML residual variance (sigma squared): 95.494, (sigma: 9.7721) #> Number of observations: 49  #> Number of parameters estimated: 5  #> AIC: 374.78, (AIC for lm: 382.75) #> LM test for residual autocorrelation #> test value: 0.31954, p-value: 0.57188 #>  #>  Correlation of coefficients  #>             sigma rho   (Intercept) INC   #> rho         -0.14                         #> (Intercept)  0.12 -0.83                   #> INC         -0.05  0.35 -0.61             #> HOVAL       -0.01  0.08 -0.25       -0.44 #>  COL.lag.stsls <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, lw) (x <- summary(COL.lag.stsls, correlation=TRUE)) #>  #> Call:stsls(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = lw) #>  #> Residuals: #>       Min        1Q    Median        3Q       Max  #> -37.86437  -5.65096  -0.13669   6.23315  22.90823  #>  #> Coefficients:  #>              Estimate Std. Error t value  Pr(>|t|) #> Rho          0.454567   0.185118  2.4555  0.014067 #> (Intercept) 43.793442  10.952229  3.9986 6.372e-05 #> INC         -1.000716   0.383858 -2.6070  0.009134 #> HOVAL       -0.265489   0.091852 -2.8904  0.003847 #>  #> Residual variance (sigma squared): 103.44, (sigma: 10.171) #> Anselin-Kelejian (1997) test for residual autocorrelation #> test value: 0.043401, p-value: 0.83497 #>  #> Correlation of Coefficients: #>             Rho   (Intercept) INC   #> (Intercept) -0.92                   #> INC          0.63 -0.76             #> HOVAL        0.04 -0.16       -0.36 #>  coef(x) #>               Estimate  Std. Error   t value     Pr(>|t|) #> Rho          0.4545669  0.18511845  2.455546 1.406706e-02 #> (Intercept) 43.7934425 10.95222944  3.998587 6.372175e-05 #> INC         -1.0007158  0.38385778 -2.606996 9.134037e-03 #> HOVAL       -0.2654890  0.09185167 -2.890410 3.847398e-03 W <- as(lw, \"CsparseMatrix\") trMatc <- trW(W, type=\"mult\") loobj1 <- impacts(COL.lag.stsls, R=200, tr=trMatc) summary(loobj1, zstats=TRUE, short=TRUE) #> Impact measures (lag, trace): #>           Direct   Indirect     Total #> INC   -1.0607411 -0.7739768 -1.834718 #> HOVAL -0.2814136 -0.2053354 -0.486749 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>           Direct  Indirect     Total #> INC   0.39668006 0.9695180 1.0529050 #> HOVAL 0.09757127 0.3123932 0.3649017 #>  #> Simulated z-values: #>          Direct   Indirect     Total #> INC   -2.768354 -0.8583926 -1.833383 #> HOVAL -2.954457 -0.8425926 -1.511339 #>  #> Simulated p-values: #>       Direct    Indirect Total    #> INC   0.0056340 0.39068  0.066746 #> HOVAL 0.0031322 0.39946  0.130702 ev <- eigenw(lw) loobj2 <- impacts(COL.lag.stsls, R=200, evalues=ev) summary(loobj2, zstats=TRUE, short=TRUE) #> Impact measures (lag, evalues): #>           Direct   Indirect     Total #> INC   -1.0607411 -0.7739768 -1.834718 #> HOVAL -0.2814136 -0.2053354 -0.486749 #> ======================================================== #> Simulation results ( variance matrix): #> ======================================================== #> Simulated standard errors #>          Direct  Indirect     Total #> INC   0.3841092 0.7160775 0.8241613 #> HOVAL 0.1008357 0.4126274 0.4698167 #>  #> Simulated z-values: #>          Direct   Indirect     Total #> INC   -2.895776 -1.1602746 -2.357719 #> HOVAL -2.743940 -0.6064747 -1.121576 #>  #> Simulated p-values: #>       Direct    Indirect Total    #> INC   0.0037822 0.24594  0.018388 #> HOVAL 0.0060707 0.54420  0.262043 require(coda) HPDinterval(loobj1) #>            lower       upper #> INC   -1.7799556 -0.35225230 #> HOVAL -0.4587508 -0.09515137 #> attr(,\"Probability\") #> [1] 0.95 COL.lag.stslsW <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, lw, W2X=FALSE) summary(COL.lag.stslsW, correlation=TRUE) #>  #> Call:stsls(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = lw,  #>     W2X = FALSE) #>  #> Residuals: #>        Min         1Q     Median         3Q        Max  #> -37.785778  -5.442414  -0.052649   6.170104  23.039123  #>  #> Coefficients:  #>              Estimate Std. Error t value  Pr(>|t|) #> Rho          0.444202   0.189141  2.3485  0.018848 #> (Intercept) 44.359512  11.157079  3.9759 7.011e-05 #> INC         -1.014319   0.387469 -2.6178  0.008850 #> HOVAL       -0.265681   0.091954 -2.8893  0.003861 #>  #> Residual variance (sigma squared): 103.67, (sigma: 10.182) #> Anselin-Kelejian (1997) test for residual autocorrelation #> test value: 0.058156, p-value: 0.80943 #>  #> Correlation of Coefficients: #>             Rho   (Intercept) INC   #> (Intercept) -0.93                   #> INC          0.64 -0.77             #> HOVAL        0.04 -0.16       -0.36 #>  COL.lag.stslsWn <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, lw, W2X=FALSE, sig2n_k=FALSE) summary(COL.lag.stslsWn, correlation=TRUE) #>  #> Call:stsls(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = lw,  #>     W2X = FALSE, sig2n_k = FALSE) #>  #> Residuals: #>        Min         1Q     Median         3Q        Max  #> -37.785778  -5.442414  -0.052649   6.170104  23.039123  #>  #> Coefficients:  #>              Estimate Std. Error t value  Pr(>|t|) #> Rho          0.444202   0.181257  2.4507  0.014259 #> (Intercept) 44.359512  10.691995  4.1489 3.341e-05 #> INC         -1.014319   0.371318 -2.7317  0.006301 #> HOVAL       -0.265681   0.088121 -3.0150  0.002570 #>  #> Residual variance (sigma squared): 95.203, (sigma: 9.7572) #> Anselin-Kelejian (1997) test for residual autocorrelation #> test value: 0.058156, p-value: 0.80943 #>  #> Correlation of Coefficients: #>             Rho   (Intercept) INC   #> (Intercept) -0.93                   #> INC          0.64 -0.77             #> HOVAL        0.04 -0.16       -0.36 #>  COL.lag.stslsR <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, lw, robust=TRUE, W2X=FALSE) summary(COL.lag.stslsR, correlation=TRUE) #>  #> Call:stsls(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = lw,  #>     robust = TRUE, W2X = FALSE) #>  #> Residuals: #>        Min         1Q     Median         3Q        Max  #> -37.785778  -5.442414  -0.052649   6.170104  23.039123  #>  #> Coefficients:  #>             Estimate HC0 std. Error z value  Pr(>|z|) #> Rho          0.44420        0.13748  3.2310  0.001234 #> (Intercept) 44.35951        7.67306  5.7812 7.417e-09 #> INC         -1.01432        0.44113 -2.2993  0.021486 #> HOVAL       -0.26568        0.17353 -1.5311  0.125752 #>  #> Residual variance (sigma squared): 103.67, (sigma: 10.182) #> Anselin-Kelejian (1997) test for residual autocorrelation #> test value: 0.056852, p-value: 0.81154 #>  #> Correlation of Coefficients: #>             Rho   (Intercept) INC   #> (Intercept) -0.90                   #> INC          0.15 -0.28             #> HOVAL        0.24 -0.24       -0.83 #>  COL.lag.stslsRl <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, lw, robust=TRUE, legacy=TRUE, W2X=FALSE) summary(COL.lag.stslsRl, correlation=TRUE) #>  #> Call:stsls(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = lw,  #>     robust = TRUE, legacy = TRUE, W2X = FALSE) #>  #> Residuals: #>        Min         1Q     Median         3Q        Max  #> -38.654607  -5.141303  -0.065221   5.864384  23.671589  #>  #> Coefficients:  #>             Estimate HC0 std. Error z value  Pr(>|z|) #> Rho          0.40138        0.13554  2.9613  0.003064 #> (Intercept) 47.37696        7.49975  6.3171 2.664e-10 #> INC         -1.15183        0.43490 -2.6485  0.008085 #> HOVAL       -0.25047        0.17333 -1.4450  0.148461 #>  #> Asymptotic robust residual variance: 96.446, (sigma: 9.8207) #> Anselin-Kelejian (1997) test for residual autocorrelation #> test value: 0.10254, p-value: 0.7488 #>  #> Correlation of Coefficients: #>             Rho   (Intercept) INC   #> (Intercept) -0.89                   #> INC          0.12 -0.26             #> HOVAL        0.25 -0.26       -0.83 #>  data(boston, package=\"spData\") gp2a <- stsls(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) + I(RM^2) +   AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),  data=boston.c, spdep::nb2listw(boston.soi)) summary(gp2a) #>  #> Call:stsls(formula = log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +  #>     I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B +  #>     log(LSTAT), data = boston.c, listw = spdep::nb2listw(boston.soi)) #>  #> Residuals: #>        Min         1Q     Median         3Q        Max  #> -0.5356002 -0.0758562 -0.0045074  0.0719613  0.7128012  #>  #> Coefficients:  #>                Estimate  Std. Error  t value  Pr(>|t|) #> Rho          4.5925e-01  3.8485e-02  11.9330 < 2.2e-16 #> (Intercept)  2.4025e+00  2.1710e-01  11.0661 < 2.2e-16 #> CRIM        -7.3557e-03  1.0345e-03  -7.1100 1.160e-12 #> ZN           3.6435e-04  3.9311e-04   0.9268 0.3540112 #> INDUS        1.1992e-03  1.8365e-03   0.6530 0.5137794 #> CHAS1        1.1929e-02  2.6632e-02   0.4479 0.6542202 #> I(NOX^2)    -2.8874e-01  9.2546e-02  -3.1199 0.0018091 #> I(RM^2)      6.6991e-03  1.0192e-03   6.5728 4.938e-11 #> AGE         -2.5810e-04  4.0940e-04  -0.6304 0.5284073 #> log(DIS)    -1.6043e-01  2.6107e-02  -6.1451 7.993e-10 #> log(RAD)     7.1704e-02  1.4926e-02   4.8038 1.557e-06 #> TAX         -3.6857e-04  9.5315e-05  -3.8668 0.0001103 #> PTRATIO     -1.2957e-02  4.1334e-03  -3.1347 0.0017203 #> B            2.8845e-04  8.0266e-05   3.5937 0.0003261 #> log(LSTAT)  -2.3984e-01  2.2470e-02 -10.6740 < 2.2e-16 #>  #> Residual variance (sigma squared): 0.020054, (sigma: 0.14161) #> Anselin-Kelejian (1997) test for residual autocorrelation #> test value: 4.3942, p-value: 0.036062 #>"},{"path":"https://r-spatial.github.io/spatialreg/reference/trW.html","id":null,"dir":"Reference","previous_headings":"","what":"Spatial weights matrix powers traces — trW","title":"Spatial weights matrix powers traces — trW","text":"function used prepare vector traces powers spatial weights matrix","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/trW.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Spatial weights matrix powers traces — trW","text":"","code":"trW(W=NULL, m = 30, p = 16, type = \"mult\", listw=NULL, momentsSymmetry=TRUE) mom_calc(lw, m) mom_calc_int2(is, m, nb, weights, Card)"},{"path":"https://r-spatial.github.io/spatialreg/reference/trW.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Spatial weights matrix powers traces — trW","text":"W spatial weights matrix CsparseMatrix form m number powers; must even number ‘type’=“moments” (default changed 100 30 (2010-11-17)) p number samples used Monte Carlo simulation traces type MC (default changed 50 16 (2010-11-17)) type Either “mult” (default) powering sparse matrix (moderate larger N, matrix becomes dense, may lead swapping), “MC” Monte Carlo simulation traces (first two simulated traces replaced analytical equivalents), “moments” use looping space saving algorithm proposed Smirnov Anselin (2009) - “moments”, W must symmetric, row-standardised weights similarity transformation listw, lw listw object, either fully symmetric, constructed similar symmetric intrinsically symmetric neighbours using similar.listw, used ‘type’=“moments” momentsSymmetry default TRUE; assert Smirnov/Anselin symmetry assumption (used internally mom_calc_int2 ‘type’=“moments” cluster) nb (used internally mom_calc_int2 ‘type’=“moments” cluster) weights (used internally mom_calc_int2 ‘type’=“moments” cluster) Card (used internally mom_calc_int2 ‘type’=“moments” cluster)","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/trW.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Spatial weights matrix powers traces — trW","text":"numeric vector m traces, “timings” “type” attributes; ‘type’=“MC” also returns standard deviation p-vector V divided square root p measure spread trace estimates.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/trW.html","id":"note","dir":"Reference","previous_headings":"","what":"Note","title":"Spatial weights matrix powers traces — trW","text":"mom_calc mom_calc_int2 internal use ","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/trW.html","id":"references","dir":"Reference","previous_headings":"","what":"References","title":"Spatial weights matrix powers traces — trW","text":"LeSage J RK Pace (2009) Introduction Spatial Econometrics. CRC Press, Boca Raton, pp. 96–105; Smirnov O L Anselin (2009) O(N) parallel method computing Log-Jacobian variable transformation models spatial interaction lattice. Computational Statistics Data Analysis 53 (2009) 2983–2984.","code":""},{"path":"https://r-spatial.github.io/spatialreg/reference/trW.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"Spatial weights matrix powers traces — trW","text":"Roger Bivand Roger.Bivand@nhh.","code":""},{"path":[]},{"path":"https://r-spatial.github.io/spatialreg/reference/trW.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Spatial weights matrix powers traces — trW","text":"","code":"require(\"sf\", quietly=TRUE)  columbus <- st_read(system.file(\"shapes/columbus.gpkg\", package=\"spData\")[1], quiet=TRUE) #require(spdep, quietly=TRUE) col.gal.nb <- spdep::read.gal(system.file(\"weights/columbus.gal\", package=\"spData\")[1]) listw <- spdep::nb2listw(col.gal.nb) W <- as(listw, \"CsparseMatrix\") system.time(trMat <- trW(W, type=\"mult\")) #>    user  system elapsed  #>   0.002   0.000   0.002  str(trMat) #>  num [1:30] 0 10.91 3.65 5.62 3.66 ... #>  - attr(*, \"timings\")= Named num [1:2] 0.002 0.002 #>   ..- attr(*, \"names\")= chr [1:2] \"user.self\" \"elapsed\" #>  - attr(*, \"type\")= chr \"mult\" #>  - attr(*, \"n\")= int 49 set.seed(1100) system.time(trMC <- trW(W, type=\"MC\")) #>    user  system elapsed  #>   0.005   0.000   0.005  str(trMC) #>  num [1:30] 0 10.91 3.69 5.36 3.64 ... #>  - attr(*, \"sd\")= num [1:30] NA NA 0.598 0.495 0.489 ... #>  - attr(*, \"timings\")= Named num [1:2] 0.005 0.005 #>   ..- attr(*, \"names\")= chr [1:2] \"user.self\" \"elapsed\" #>  - attr(*, \"type\")= chr \"MC\" #>  - attr(*, \"n\")= int 49 plot(trMat, trMC) abline(a=0, b=1) for(i in 3:length(trMC)) {  segments(trMat[i], trMC[i]-2*attr(trMC, \"sd\")[i], trMat[i],   trMC[i]+2*attr(trMC, \"sd\")[i]) }  listwS <- similar.listw(listw) W <- forceSymmetric(as(listwS, \"CsparseMatrix\")) system.time(trmom <- trW(listw=listwS, m=24, type=\"moments\")) #>    user  system elapsed  #>   0.002   0.000   0.002  str(trmom) #>  num [1:24] 0 10.91 3.65 5.62 3.66 ... #>  - attr(*, \"timings\")= Named num [1:2] 0.002 0.002 #>   ..- attr(*, \"names\")= chr [1:2] \"user.self\" \"elapsed\" #>  - attr(*, \"type\")= chr \"moments\" #>  - attr(*, \"n\")= int 49 all.equal(trMat[1:24], trmom, check.attributes=FALSE) #> [1] TRUE system.time(trMat <- trW(W, m=24, type=\"mult\")) #>    user  system elapsed  #>   0.003   0.000   0.003  str(trMat) #>  num [1:24] 0 10.91 3.65 5.62 3.66 ... #>  - attr(*, \"timings\")= Named num [1:2] 0.003 0.003 #>   ..- attr(*, \"names\")= chr [1:2] \"user.self\" \"elapsed\" #>  - attr(*, \"type\")= chr \"mult\" #>  - attr(*, \"n\")= int 49 all.equal(trMat, trmom, check.attributes=FALSE) #> [1] TRUE set.seed(1) system.time(trMC <- trW(W, m=24, type=\"MC\")) #>    user  system elapsed  #>   0.006   0.000   0.006  str(trMC) #>  num [1:24] 0 10.91 2.44 4.97 2.82 ... #>  - attr(*, \"sd\")= num [1:24] NA NA 0.618 0.501 0.451 ... #>  - attr(*, \"timings\")= Named num [1:2] 0.006 0.006 #>   ..- attr(*, \"names\")= chr [1:2] \"user.self\" \"elapsed\" #>  - attr(*, \"type\")= chr \"MC\" #>  - attr(*, \"n\")= int 49 # \\dontrun{ data(boston, package=\"spData\") listw <- spdep::nb2listw(boston.soi) listwS <- similar.listw(listw) system.time(trmom <- trW(listw=listwS, m=24, type=\"moments\")) #>    user  system elapsed  #>   0.116   0.000   0.117  str(trmom) #>  num [1:24] 0 124.2 32.7 63.7 33.2 ... #>  - attr(*, \"timings\")= Named num [1:2] 0.116 0.117 #>   ..- attr(*, \"names\")= chr [1:2] \"user.self\" \"elapsed\" #>  - attr(*, \"type\")= chr \"moments\" #>  - attr(*, \"n\")= int 506 library(parallel) nc <- max(2L, detectCores(logical=FALSE), na.rm = TRUE)-1L # set nc to 1L here if (nc > 1L) nc <- 1L coresOpt <- get.coresOption() invisible(set.coresOption(nc)) if(!get.mcOption()) {   cl <- makeCluster(get.coresOption())   set.ClusterOption(cl) } system.time(trmomp <- trW(listw=listwS, m=24, type=\"moments\")) #>    user  system elapsed  #>   0.119   0.000   0.119  if(!get.mcOption()) {   set.ClusterOption(NULL)   stopCluster(cl) } all.equal(trmom, trmomp, check.attributes=FALSE) #> [1] TRUE invisible(set.coresOption(coresOpt)) # }"},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-13-6-development","dir":"Changelog","previous_headings":"","what":"Version 1.3-6 (development)","title":"Version 1.3-6 (development)","text":"#56 add Anselin-Kelejian (1997) test stsls, reported summary method, analogous reporting summary method lagsarlm Lagrange multiplier test, residual spatial autocorrelation adding missing man page anchors","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-13-5-2024-08-19","dir":"Changelog","previous_headings":"","what":"Version 1.3-5 (2024-08-19)","title":"Version 1.3-5 (2024-08-19)","text":"CRAN release: 2024-08-19 conforming STRICT_R_HEADERS=1 Condition forthcoming tmap 4 #52 subgraph updates","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-13-4-2024-06-10","dir":"Changelog","previous_headings":"","what":"Version 1.3-4 (2024-06-10)","title":"Version 1.3-4 (2024-06-10)","text":"CRAN release: 2024-06-10 migrate ESRI Shapefile GeoPackage #50","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-13-3-2024-05-31","dir":"Changelog","previous_headings":"","what":"Version 1.3-3 (2024-05-31)","title":"Version 1.3-3 (2024-05-31)","text":"CRAN release: 2024-05-31 protect errorsarlm missing Durbin= intercept fix longstanding bugs getVmate non-default side logic branch add return_impacts= lmSLX work around issues aliased variables; impacts improved handle case time permits add sqrt=TRUE calls Matrix determinant methods matrix_ldet add igraph (>= 2.0.0) DESCRIPTION re-named igraph functions","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-13-2-2024-02-06","dir":"Changelog","previous_headings":"","what":"Version 1.3-2 (2024-02-06)","title":"Version 1.3-2 (2024-02-06)","text":"CRAN release: 2024-02-06 pass SlX formula call re-corrected #19 fitted model weights component may NULL suppress warning multcomp::glht test throws warning discarded","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-13-1-2023-11-23","dir":"Changelog","previous_headings":"","what":"Version 1.3-1 (2023-11-23)","title":"Version 1.3-1 (2023-11-23)","text":"CRAN release: 2023-11-23 move expm Imports Suggests #42 added zero.policy pass-spdep::mat2listw calls predict.Sarlm spdep::sn2listw sids_models.Rmd; set spdep requirement 1.3-1 corrected #19 fitted model weights component never NULL, may single unique value","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-12-9-2023-05-25","dir":"Changelog","previous_headings":"","what":"Version 1.2-9 (2023-05-25)","title":"Version 1.2-9 (2023-05-25)","text":"CRAN release: 2023-05-25 raised #39, support weights SEM/SDEM/SLX #39 address #37; #38 remains (formula Durbin support prediction using Sarlm object) address #19 reporting AIC case weights used spautolm errorsarlm address bug predict() new data, SDEM. Others #37, #38 need work. added checking SLX/SDEM impacts edge/corner cases; starting transition use multcomp place og gmodels","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-12-8-2023-03-01","dir":"Changelog","previous_headings":"","what":"Version 1.2-8 (2023-03-01)","title":"Version 1.2-8 (2023-03-01)","text":"CRAN release: 2023-03-01 Attending SLX/Durbin/non-W-style weights: #7, #36, #26, #35, #30 #24, #23, partly based #13","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-12-6-2022-10-07","dir":"Changelog","previous_headings":"","what":"Version 1.2-6 (2022-10-07)","title":"Version 1.2-6 (2022-10-07)","text":"CRAN release: 2022-10-07 make local copy gmodels::estimable() lm objects , add authors package contributors -Wstrict-prototypes fixes","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-12-5-2022-08-16","dir":"Changelog","previous_headings":"","what":"Version 1.2-5 (2022-08-16)","title":"Version 1.2-5 (2022-08-16)","text":"CRAN release: 2022-08-16 updating coercion Matrix 1.4-2 updating dontrun/donttest package split (previously unchecked, mostly aple)","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-12-3-2022-04-18","dir":"Changelog","previous_headings":"","what":"Version 1.2-3 (2022-04-18)","title":"Version 1.2-3 (2022-04-18)","text":"CRAN release: 2022-04-18 protect definition USE_FC_LEN_T unescape underscores help pages","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-12-1-2021-11-11","dir":"Changelog","previous_headings":"","what":"Version 1.2-1 (2021-11-11)","title":"Version 1.2-1 (2021-11-11)","text":"CRAN release: 2021-11-11 Add Fortran character handling USE_FC_LEN_T WRE §6.6.1 Add spdep split-functionality","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-11-8-2021-05-03","dir":"Changelog","previous_headings":"","what":"Version 1.1-8 (2021-05-03)","title":"Version 1.1-8 (2021-05-03)","text":"CRAN release: 2021-05-03 #18 standardize use coef() methods () fitted model summary objects https://github.com/tidymodels/broom/issues/1003#issuecomment-798694400 changing spatialreg model output class names: spdep sarlm -> spatialreg Sarlm, spautolm -> Spautolm, stsls -> Stsls, gmsar -> Gmsar, lagmess -> Lagmess, SLX -> , SlX, MCMC_s*_g -> MCMC_s*_G, SFResult -> SfResult, ME_res -> Me_res, lagImpact -> LagImpact, WXImpact -> WXimpact #16 merged coordination impacts methods (Gianfranco Piras) #14 merged correction SDEM SLX impacts lagged intercept present (Tobias Rüttenauer).","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-11-5-2019-12-01","dir":"Changelog","previous_headings":"","what":"Version 1.1-5 (2019-12-01)","title":"Version 1.1-5 (2019-12-01)","text":"CRAN release: 2019-12-01 #6, #11 na.action precomputed eigenvalue bug #9 Griddy Gibbs issue #8 Predict method SLX #7, #13-14 Offset impacts SDEM/SLX #5, #10 Panel Durbin= argument","code":""},{"path":"https://r-spatial.github.io/spatialreg/news/index.html","id":"version-11-3-2019-04-01","dir":"Changelog","previous_headings":"","what":"Version 1.1-3 (2019-04-01)","title":"Version 1.1-3 (2019-04-01)","text":"CRAN release: 2019-04-01 #2 Split spatialreg spdep; spdep functions still present deprecated","code":""}]
diff --git a/docs/sitemap.xml b/docs/sitemap.xml
index 4333ad9..19ad5f4 100644
--- a/docs/sitemap.xml
+++ b/docs/sitemap.xml
@@ -1,108 +1,38 @@
-
-
-  
-    /404.html
-  
-  
-    /articles/SpatialFiltering.html
-  
-  
-    /articles/index.html
-  
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-    /articles/nb_igraph.html
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-    /articles/sids_models.html
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-    /authors.html
-  
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-    /index.html
-  
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-    /news/index.html
-  
-  
-    /reference/GMerrorsar.html
-  
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-    /reference/MCMCsamp.html
-  
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-    /reference/ME.html
-  
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-    /reference/ML_models.html
-  
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-    /reference/SET_MCMC.html
-  
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-    /reference/SLX.html
-  
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-    /reference/SpatialFiltering.html
-  
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-    /reference/aple.html
-  
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-    /reference/aple.mc.html
-  
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-    /reference/aple.plot.html
-  
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-    /reference/do_ldet.html
-  
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-    /reference/eigenw.html
-  
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-    /reference/gstsls.html
-  
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-    /reference/impacts.html
-  
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-    /reference/index.html
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-    /reference/invIrM.html
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-    /reference/lagmess.html
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-    /reference/lextrB.html
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-    /reference/predict.sarlm.html
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-    /reference/sarlm_tests.html
-  
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-    /reference/set.mcOption.html
-  
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-    /reference/set.spChkOption.html
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-    /reference/similar.listw.html
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-    /reference/spautolm.html
-  
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-    /reference/stsls.html
-  
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-    /reference/trW.html
-  
+
+https://r-spatial.github.io/spatialreg/404.html
+https://r-spatial.github.io/spatialreg/articles/SpatialFiltering.html
+https://r-spatial.github.io/spatialreg/articles/index.html
+https://r-spatial.github.io/spatialreg/articles/nb_igraph.html
+https://r-spatial.github.io/spatialreg/articles/sids_models.html
+https://r-spatial.github.io/spatialreg/authors.html
+https://r-spatial.github.io/spatialreg/index.html
+https://r-spatial.github.io/spatialreg/news/index.html
+https://r-spatial.github.io/spatialreg/reference/GMerrorsar.html
+https://r-spatial.github.io/spatialreg/reference/MCMCsamp.html
+https://r-spatial.github.io/spatialreg/reference/ME.html
+https://r-spatial.github.io/spatialreg/reference/ML_models.html
+https://r-spatial.github.io/spatialreg/reference/SET_MCMC.html
+https://r-spatial.github.io/spatialreg/reference/SLX.html
+https://r-spatial.github.io/spatialreg/reference/SpatialFiltering.html
+https://r-spatial.github.io/spatialreg/reference/aple.html
+https://r-spatial.github.io/spatialreg/reference/aple.mc.html
+https://r-spatial.github.io/spatialreg/reference/aple.plot.html
+https://r-spatial.github.io/spatialreg/reference/do_ldet.html
+https://r-spatial.github.io/spatialreg/reference/eigenw.html
+https://r-spatial.github.io/spatialreg/reference/gstsls.html
+https://r-spatial.github.io/spatialreg/reference/impacts.html
+https://r-spatial.github.io/spatialreg/reference/index.html
+https://r-spatial.github.io/spatialreg/reference/invIrM.html
+https://r-spatial.github.io/spatialreg/reference/lagmess.html
+https://r-spatial.github.io/spatialreg/reference/lextrB.html
+https://r-spatial.github.io/spatialreg/reference/predict.sarlm.html
+https://r-spatial.github.io/spatialreg/reference/sarlm_tests.html
+https://r-spatial.github.io/spatialreg/reference/set.mcOption.html
+https://r-spatial.github.io/spatialreg/reference/set.spChkOption.html
+https://r-spatial.github.io/spatialreg/reference/similar.listw.html
+https://r-spatial.github.io/spatialreg/reference/sparse_mat.html
+https://r-spatial.github.io/spatialreg/reference/spautolm.html
+https://r-spatial.github.io/spatialreg/reference/stsls.html
+https://r-spatial.github.io/spatialreg/reference/trW.html
 
+
diff --git a/man/stsls.Rd b/man/stsls.Rd
index 29bf7d7..744c555 100644
--- a/man/stsls.Rd
+++ b/man/stsls.Rd
@@ -94,6 +94,8 @@ require(coda)
 HPDinterval(loobj1)
 COL.lag.stslsW <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, lw, W2X=FALSE)
 summary(COL.lag.stslsW, correlation=TRUE)
+COL.lag.stslsWn <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, lw, W2X=FALSE, sig2n_k=FALSE)
+summary(COL.lag.stslsWn, correlation=TRUE)
 COL.lag.stslsR <- stsls(CRIME ~ INC + HOVAL, data=COL.OLD, lw,
 robust=TRUE, W2X=FALSE)
 summary(COL.lag.stslsR, correlation=TRUE)