diff --git a/04-roadmap.Rmd b/04-roadmap.Rmd
index c9fd629..c2e7741 100644
--- a/04-roadmap.Rmd
+++ b/04-roadmap.Rmd
@@ -417,16 +417,15 @@ library(dagitty)
 library(ggdag)
 
 # make DAG by specifying dependence structure
-dag <- dagitty(
-  "dag {
-    W -> A
-    W -> Y
-    A -> Y
-    W -> A -> Y
-  }"
-)
-exposures(dag) <- c("A")
-outcomes(dag) <- c("Y")
+dag <- dagitty("dag{
+    W -> A ;
+    W -> Y ;
+    A -> Y ;
+    W -> A -> Y ;
+    W [confounders]
+    A [exposure]
+    Y [outcome]
+  }")
 tidy_dag <- tidy_dagitty(dag)
 
 # visualize DAG
diff --git a/renv.lock b/renv.lock
index ae58be7..df6f921 100644
--- a/renv.lock
+++ b/renv.lock
@@ -58,9 +58,15 @@
     },
     "MASS": {
       "Package": "MASS",
-      "Version": "7.3-60",
+      "Version": "7.3-61",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "MASS",
+      "RemoteRef": "MASS",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "7.3-61",
       "Requirements": [
         "R",
         "grDevices",
@@ -69,7 +75,7 @@
         "stats",
         "utils"
       ],
-      "Hash": "a56a6365b3fa73293ea8d084be0d9bb0"
+      "Hash": "0cafd6f0500e5deba33be22c46bf6055"
     },
     "Matrix": {
       "Package": "Matrix",
@@ -155,14 +161,20 @@
     },
     "Rcpp": {
       "Package": "Rcpp",
-      "Version": "1.0.8.3",
+      "Version": "1.0.13",
       "Source": "Repository",
-      "Repository": "CRAN",
+      "Repository": "RSPM",
+      "RemoteType": "standard",
+      "RemotePkgRef": "Rcpp",
+      "RemoteRef": "Rcpp",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.0.13",
       "Requirements": [
         "methods",
         "utils"
       ],
-      "Hash": "32e79b908fda56ee57fe518a8d37b864"
+      "Hash": "f27411eb6d9c3dada5edd444b8416675"
     },
     "RcppArmadillo": {
       "Package": "RcppArmadillo",
@@ -271,16 +283,22 @@
     },
     "V8": {
       "Package": "V8",
-      "Version": "5.0.0",
+      "Version": "5.0.1",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "V8",
+      "RemoteRef": "V8",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "5.0.1",
       "Requirements": [
         "Rcpp",
         "curl",
         "jsonlite",
         "utils"
       ],
-      "Hash": "9eb7b2df315593e726b029200fc0276c"
+      "Hash": "7f3867df00a91c63089beb85b9ef0208"
     },
     "abind": {
       "Package": "abind",
@@ -471,15 +489,21 @@
     },
     "boot": {
       "Package": "boot",
-      "Version": "1.3-28",
+      "Version": "1.3-31",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "boot",
+      "RemoteRef": "boot",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.3-31",
       "Requirements": [
         "R",
         "graphics",
         "stats"
       ],
-      "Hash": "0baa960e3b49c6176a4f42addcbacc59"
+      "Hash": "de2a4646c18661d6a0a08ec67f40b7ed"
     },
     "brew": {
       "Package": "brew",
@@ -717,9 +741,15 @@
     },
     "colorspace": {
       "Package": "colorspace",
-      "Version": "2.0-3",
+      "Version": "2.1-1",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "colorspace",
+      "RemoteRef": "colorspace",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "2.1-1",
       "Requirements": [
         "R",
         "grDevices",
@@ -727,7 +757,7 @@
         "methods",
         "stats"
       ],
-      "Hash": "bb4341986bc8b914f0f0acf2e4a3f2f7"
+      "Hash": "d954cb1c57e8d8b756165d7ba18aa55a"
     },
     "commonmark": {
       "Package": "commonmark",
@@ -813,9 +843,15 @@
     },
     "dagitty": {
       "Package": "dagitty",
-      "Version": "0.3-1",
+      "Version": "0.3-4",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "dagitty",
+      "RemoteRef": "dagitty",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "0.3-4",
       "Requirements": [
         "MASS",
         "R",
@@ -828,7 +864,7 @@
         "stats",
         "utils"
       ],
-      "Hash": "22d2afac8432f195aabdf417ce42fdf4"
+      "Hash": "dfbd13468fb3d6747b4d9541a648df9d"
     },
     "data.table": {
       "Package": "data.table",
@@ -997,12 +1033,19 @@
     },
     "dplyr": {
       "Package": "dplyr",
-      "Version": "1.0.9",
+      "Version": "1.1.4",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "dplyr",
+      "RemoteRef": "dplyr",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.1.4",
       "Requirements": [
         "R",
         "R6",
+        "cli",
         "generics",
         "glue",
         "lifecycle",
@@ -1015,7 +1058,7 @@
         "utils",
         "vctrs"
       ],
-      "Hash": "f0bda1627a7f5d3f9a0b5add931596ac"
+      "Hash": "fedd9d00c2944ff00a0e2696ccf048ec"
     },
     "dtplyr": {
       "Package": "dtplyr",
@@ -1100,22 +1143,34 @@
     },
     "fansi": {
       "Package": "fansi",
-      "Version": "1.0.3",
+      "Version": "1.0.6",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "fansi",
+      "RemoteRef": "fansi",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.0.6",
       "Requirements": [
         "R",
         "grDevices",
         "utils"
       ],
-      "Hash": "83a8afdbe71839506baa9f90eebad7ec"
+      "Hash": "962174cf2aeb5b9eea581522286a911f"
     },
     "farver": {
       "Package": "farver",
-      "Version": "2.1.0",
+      "Version": "2.1.2",
       "Source": "Repository",
       "Repository": "CRAN",
-      "Hash": "c98eb5133d9cb9e1622b8691487f11bb"
+      "RemoteType": "standard",
+      "RemotePkgRef": "farver",
+      "RemoteRef": "farver",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "2.1.2",
+      "Hash": "680887028577f3fa2a81e410ed0d6e42"
     },
     "fastmap": {
       "Package": "fastmap",
@@ -1150,17 +1205,25 @@
     },
     "forcats": {
       "Package": "forcats",
-      "Version": "0.5.1",
+      "Version": "1.0.0",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "forcats",
+      "RemoteRef": "forcats",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.0.0",
       "Requirements": [
         "R",
-        "ellipsis",
+        "cli",
+        "glue",
+        "lifecycle",
         "magrittr",
         "rlang",
         "tibble"
       ],
-      "Hash": "81c3244cab67468aac4c60550832655d"
+      "Hash": "1a0a9a3d5083d0d573c4214576f1e690"
     },
     "foreach": {
       "Package": "foreach",
@@ -1296,14 +1359,20 @@
     },
     "generics": {
       "Package": "generics",
-      "Version": "0.1.2",
+      "Version": "0.1.3",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "generics",
+      "RemoteRef": "generics",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "0.1.3",
       "Requirements": [
         "R",
         "methods"
       ],
-      "Hash": "177475892cf4a55865868527654a7741"
+      "Hash": "15e9634c0fcd294799e9b2e929ed1b86"
     },
     "gert": {
       "Package": "gert",
@@ -1639,14 +1708,24 @@
     },
     "gtable": {
       "Package": "gtable",
-      "Version": "0.3.0",
+      "Version": "0.3.5",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "gtable",
+      "RemoteRef": "gtable",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "0.3.5",
       "Requirements": [
         "R",
-        "grid"
+        "cli",
+        "glue",
+        "grid",
+        "lifecycle",
+        "rlang"
       ],
-      "Hash": "ac5c6baf7822ce8732b343f14c072c4d"
+      "Hash": "e18861963cbc65a27736e02b3cd3c4a0"
     },
     "gtools": {
       "Package": "gtools",
@@ -2083,14 +2162,20 @@
     },
     "labeling": {
       "Package": "labeling",
-      "Version": "0.4.2",
+      "Version": "0.4.3",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "labeling",
+      "RemoteRef": "labeling",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "0.4.3",
       "Requirements": [
         "graphics",
         "stats"
       ],
-      "Hash": "3d5108641f47470611a32d0bdf357a72"
+      "Hash": "b64ec208ac5bc1852b285f665d6368b3"
     },
     "later": {
       "Package": "later",
@@ -2343,22 +2428,20 @@
     },
     "munsell": {
       "Package": "munsell",
-      "Version": "0.5.0",
+      "Version": "0.5.1",
       "Source": "Repository",
       "Repository": "CRAN",
-      "RemotePkgRef": "munsell@0.5.0",
       "RemoteType": "standard",
-      "RemoteEtag": "\"2c97d-56e6a4ec0bce6\"",
-      "RemotePackaged": "TRUE",
+      "RemotePkgRef": "munsell",
       "RemoteRef": "munsell",
-      "RemoteRepos": "https://cloud.r-project.org",
-      "RemotePkgPlatform": "source",
-      "RemoteSha": "0.5.0",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "0.5.1",
       "Requirements": [
         "colorspace",
         "methods"
       ],
-      "Hash": "6dfe8bf774944bd5595785e3229d8771"
+      "Hash": "4fd8900853b746af55b81fda99da7695"
     },
     "mvtnorm": {
       "Package": "mvtnorm",
@@ -2502,13 +2585,17 @@
     },
     "pillar": {
       "Package": "pillar",
-      "Version": "1.7.0",
+      "Version": "1.9.0",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "pillar",
+      "RemoteRef": "pillar",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.9.0",
       "Requirements": [
         "cli",
-        "crayon",
-        "ellipsis",
         "fansi",
         "glue",
         "lifecycle",
@@ -2517,7 +2604,7 @@
         "utils",
         "vctrs"
       ],
-      "Hash": "51dfc97e1b7069e9f7e6f83f3589c22e"
+      "Hash": "15da5a8412f317beeee6175fbc76f4bb"
     },
     "pkgbuild": {
       "Package": "pkgbuild",
@@ -2656,13 +2743,19 @@
     },
     "polyclip": {
       "Package": "polyclip",
-      "Version": "1.10-0",
+      "Version": "1.10-7",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "polyclip",
+      "RemoteRef": "polyclip",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.10-7",
       "Requirements": [
         "R"
       ],
-      "Hash": "cb167f328b3ada4ec5cf67a7df4c900a"
+      "Hash": "5879bf5aae702ffef0a315c44328f984"
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     "praise": {
       "Package": "praise",
@@ -3474,16 +3567,26 @@
     },
     "stringr": {
       "Package": "stringr",
-      "Version": "1.4.0",
+      "Version": "1.5.1",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "stringr",
+      "RemoteRef": "stringr",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.5.1",
       "Requirements": [
         "R",
+        "cli",
         "glue",
+        "lifecycle",
         "magrittr",
-        "stringi"
+        "rlang",
+        "stringi",
+        "vctrs"
       ],
-      "Hash": "0759e6b6c0957edb1311028a49a35e76"
+      "Hash": "960e2ae9e09656611e0b8214ad543207"
     },
     "survival": {
       "Package": "survival",
@@ -3589,12 +3692,17 @@
     },
     "tibble": {
       "Package": "tibble",
-      "Version": "3.1.7",
+      "Version": "3.2.1",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "tibble",
+      "RemoteRef": "tibble",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "3.2.1",
       "Requirements": [
         "R",
-        "ellipsis",
         "fansi",
         "lifecycle",
         "magrittr",
@@ -3605,19 +3713,26 @@
         "utils",
         "vctrs"
       ],
-      "Hash": "08415af406e3dd75049afef9552e7355"
+      "Hash": "a84e2cc86d07289b3b6f5069df7a004c"
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     "tidygraph": {
       "Package": "tidygraph",
-      "Version": "1.2.1",
+      "Version": "1.3.1",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "tidygraph",
+      "RemoteRef": "tidygraph",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.3.1",
       "Requirements": [
         "R6",
         "cli",
         "cpp11",
         "dplyr",
         "igraph",
+        "lifecycle",
         "magrittr",
         "pillar",
         "rlang",
@@ -3627,44 +3742,58 @@
         "tools",
         "utils"
       ],
-      "Hash": "19f5f240d255ff0bf91e76d062fdc176"
+      "Hash": "2149824d406f233b57b087be72c5f163"
     },
     "tidyr": {
       "Package": "tidyr",
-      "Version": "1.2.0",
+      "Version": "1.3.1",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "tidyr",
+      "RemoteRef": "tidyr",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.3.1",
       "Requirements": [
         "R",
+        "cli",
         "cpp11",
         "dplyr",
-        "ellipsis",
         "glue",
         "lifecycle",
         "magrittr",
         "purrr",
         "rlang",
+        "stringr",
         "tibble",
         "tidyselect",
         "utils",
         "vctrs"
       ],
-      "Hash": "d8b95b7fee945d7da6888cf7eb71a49c"
+      "Hash": "915fb7ce036c22a6a33b5a8adb712eb1"
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     "tidyselect": {
       "Package": "tidyselect",
-      "Version": "1.1.2",
+      "Version": "1.2.1",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "tidyselect",
+      "RemoteRef": "tidyselect",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.2.1",
       "Requirements": [
         "R",
-        "ellipsis",
+        "cli",
         "glue",
-        "purrr",
+        "lifecycle",
         "rlang",
-        "vctrs"
+        "vctrs",
+        "withr"
       ],
-      "Hash": "17f6da8cfd7002760a859915ce7eef8f"
+      "Hash": "829f27b9c4919c16b593794a6344d6c0"
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@@ -3872,18 +4001,24 @@
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     "tweenr": {
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-      "Version": "1.0.2",
+      "Version": "2.0.3",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "tweenr",
+      "RemoteRef": "tweenr",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "2.0.3",
       "Requirements": [
         "R",
-        "Rcpp",
+        "cpp11",
         "farver",
-        "grDevices",
         "magrittr",
-        "rlang"
+        "rlang",
+        "vctrs"
       ],
-      "Hash": "6cc663f970a529dbf776f11d5bcd1a2e"
+      "Hash": "82fac2b73e6a1f3874fc000aaf96d8bc"
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@@ -3957,13 +4092,19 @@
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     "utf8": {
       "Package": "utf8",
-      "Version": "1.2.2",
+      "Version": "1.2.4",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "utf8",
+      "RemoteRef": "utf8",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "1.2.4",
       "Requirements": [
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-      "Hash": "c9c462b759a5cc844ae25b5942654d13"
+      "Hash": "62b65c52671e6665f803ff02954446e9"
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       "Package": "uuid",
@@ -4004,13 +4145,19 @@
     },
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-      "Version": "0.4.0",
+      "Version": "0.4.2",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "viridisLite",
+      "RemoteRef": "viridisLite",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "0.4.2",
       "Requirements": [
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-      "Hash": "55e157e2aa88161bdb0754218470d204"
+      "Hash": "c826c7c4241b6fc89ff55aaea3fa7491"
     },
     "visNetwork": {
       "Package": "visNetwork",
@@ -4105,16 +4252,21 @@
     },
     "withr": {
       "Package": "withr",
-      "Version": "2.5.0",
+      "Version": "3.0.1",
       "Source": "Repository",
       "Repository": "CRAN",
+      "RemoteType": "standard",
+      "RemotePkgRef": "withr",
+      "RemoteRef": "withr",
+      "RemoteRepos": "https://cran.rstudio.com",
+      "RemotePkgPlatform": "aarch64-apple-darwin20",
+      "RemoteSha": "3.0.1",
       "Requirements": [
         "R",
         "grDevices",
-        "graphics",
-        "stats"
+        "graphics"
       ],
-      "Hash": "c0e49a9760983e81e55cdd9be92e7182"
+      "Hash": "07909200e8bbe90426fbfeb73e1e27aa"
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     "xfun": {
       "Package": "xfun",