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#' @title Standard error of sample mean for mixed models
#' @name se_ybar
#'
#' @description Compute the standard error for the sample mean for mixed models,
#' regarding the extent to which clustering affects the standard errors.
#' May be used as part of the multilevel power calculation for cluster sampling
#' (see \cite{Gelman and Hill 2007, 447ff}).
#'
#' @param fit Fitted mixed effects model (\code{\link[lme4]{merMod}}-class).
#'
#' @return The standard error of the sample mean of \code{fit}.
#'
#' @references Gelman A, Hill J. 2007. Data analysis using regression and multilevel/hierarchical models. Cambridge, New York: Cambridge University Press
#'
#' @examplesIf require("lme4")
#' fit <- lmer(Reaction ~ 1 + (1 | Subject), sleepstudy)
#' se_ybar(fit)
#' @export
se_ybar <- function(fit) {
# get model icc
vars <- insight::get_variance(fit, verbose = FALSE)
# get group variances
tau.00 <- unname(vars$var.intercept)
# total variance
tot_var <- sum(tau.00, vars$var.residual)
# get number of groups
m.cnt <- vapply(fit@flist, nlevels, 1)
# compute number of observations per group (level-2-unit)
obs <- round(stats::nobs(fit) / m.cnt)
# compute simple icc
icc <- tau.00 / tot_var
# compute standard error of sample mean
se <- unlist(lapply(seq_len(length(m.cnt)), function(.x) {
sqrt((tot_var / stats::nobs(fit)) * design_effect(n = obs[.x], icc = icc[.x]))
}))
# give names for se, so user sees, which random effect has what impact
names(se) <- names(m.cnt)
se
}
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