docs

R/get_variances.R

@@ -68,16 +68,23 @@
 #' @section Distribution-specific (observation level) variance:
 #' The distribution-specific variance,
 #' \ifelse{html}{\out{&sigma;<sup>2</sup><sub>d</sub>}}{\eqn{\sigma^2_d}},
-#' is the conditional variance the response given the predictors , `Var[y|x]`,
-#' which depends on the model family. For Gaussian models, it is
-#' \ifelse{html}{\out{&sigma;<sup>2</sup>}}{\eqn{\sigma^2}} (i.e. `sigma(model)^2`).
-#' For models with binary outcome, it is \eqn{\pi^2 / 3} for logit-link, `1` for
-#' probit-link, and \eqn{\pi^2 / 6} for cloglog-links. Models from Gamma-families
-#' use \eqn{\mu^2} (as obtained from `family$variance()`). For all other models,
-#' the distribution-specific variance is by default based on lognormal approximation,
-#' \eqn{log(1 + var(x) / \mu^2)} (see _Nakagawa et al. 2017_). Other approximation
-#' methods can be specified with the `approximation` argument. The expected
-#' variance of a zero-inflated model is computed according to _Zuur et al. 2012, p277_.
+#' is the conditional variance of the response given the predictors , `Var[y|x]`,
+#' which depends on the model family.
+#' - **Gaussian:** For Gaussian models, it is
+#'   \ifelse{html}{\out{&sigma;<sup>2</sup>}}{\eqn{\sigma^2}} (i.e. `sigma(model)^2`).
+#' - **Bernoulli:** For models with binary outcome, it is \eqn{\pi^2 / 3} for
+#'   logit-link, `1` for probit-link, and \eqn{\pi^2 / 6} for cloglog-links.
+#' - **Binomial:** For other binomial models, the distribution-specific variance
+#'   for Bernoulli models is used, divided by a weighting factor based on the
+#'   number of trials and successes.
+#' - **Gamma:** Models from Gamma-families use \eqn{\mu^2} (as obtained from
+#'   `family$variance()`).
+#' - For all other models, the distribution-specific variance is by default
+#'   based on lognormal approximation, \eqn{log(1 + var(x) / \mu^2)} (see
+#'   _Nakagawa et al. 2017_). Other approximation methods can be specified with
+#'   the `approximation` argument.
+#' - **Zero-inflation models:** The expected variance of a zero-inflated model
+#'   is computed according to _Zuur et al. 2012, p277_.
 #'
 #' @section Variance for the additive overdispersion term:
 #' The variance for the additive overdispersion term,