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#' Delete random effect terms with zero variance
#'
#' Is used in the \code{\link{cAIC}} function if \code{method = "steinian"} and
#' \code{family = "gaussian"}. The function deletes all random effects terms
#' from the call if corresponding variance parameter is estimated to zero and
#' updates the model in \code{\link[lme4]{merMod}}.
#'
#' For \code{\link{merMod}} class models:
#' Uses the \code{cnms} slot of \code{m} and the relative covariance factors to
#' rewrite the random effects part of the formula, reduced by those parameters
#' that have an optimum on the boundary. This is necessary to obtain the true
#' conditional corrected Akaike information. For the theoretical justification
#' see Greven and Kneib (2010). The reduced model formula is then updated. The
#' function deleteZeroComponents is then called iteratively to check if in the
#' updated model there are relative covariance factors parameters on the
#' boundary.
#'
#' For \code{\link[nlme]{lme}} class models:
#' ...
#'
#' @param m An object of class \code{\link[lme4]{merMod}} fitted by
#' \code{\link[lme4]{lmer}} of the lme4-package or of class
#' \code{\link[nlme]{lme}}.
#' @return An updated object of class \code{\link[lme4]{merMod}}
#' or of class \code{\link[nlme]{lme}}.
#' @section WARNINGS : For models called via \code{gamm4} or \code{gamm}
#' no automated update is available.
#' Instead a warning with terms to omit from the model is returned.
#' @author Benjamin Saefken \& David Ruegamer \& Philipp Baumann
#' @seealso \code{\link[lme4]{lme4-package}}, \code{\link[lme4]{lmer}},
#' \code{\link[lme4]{getME}}
#' @references Greven, S. and Kneib T. (2010) On the behaviour of marginal and
#' conditional AIC in linear mixed models. Biometrika 97(4), 773-789.
#' @keywords regression
#' @rdname deleteZeroComponents
#' @examples
#'
#' ## Currently no data with variance equal to zero...
#' b <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
#'
#' deleteZeroComponents(b)
#' @importFrom mgcv gamm
#' @importFrom nlme pdDiag
#' @export
deleteZeroComponents <- function(m) UseMethod("deleteZeroComponents")
#' @return \code{NULL}
#'
#' @rdname deleteZeroComponents
#' @export
deleteZeroComponents.lme <-
function(m) {
theta <- get_theta(m)
thetazero <- which(theta == 0)
if (is.null(names(theta))) {
true_re <- rep(T, length(theta))
} else {
true_re <- names(theta) == ""
}
if (length(thetazero) == 0) {
return(m)
}
varBlockMatrices <- get_ST(m)
re_name <- m$modelStruct$reStruct[1]
cnms <- attr(m$modelStruct$reStruct[[1]], "Dimnames")[1]
cnms <- cor_re(m, cnms)
smooth_names <- attr(m, "smooth_names")
cnms <- c(cnms, smooth_names)
for (i in 1:length(varBlockMatrices)) {
cnms[[i]] <- cnms[[i]][which(diag(varBlockMatrices[[i]]) != 0)]
}
# modify random argument for refit
no_re <- sum(true_re)
left_bar <- deparse(attr(re_name[[1]], "formula")[[2]])
right_bar <- names(re_name)
is_indpt <- "pdDiag" %in% class(re_name[[1]])
r_effect <- formula(re_name)
if (no_re == 3) {
if (theta[2] == 0) {
r_effect <- list()
r_effect[[right_bar]] <- pdDiag(as.formula(paste("~", left_bar)))
}
if (theta[1] == 0 & theta[2] == 0) {
r_effect <- list()
r_effect[[right_bar]] <- as.formula(paste("~ -1 + ", left_bar, "|",
right_bar))
}
if (theta[2] == 0 & theta[3] == 0) {
r_effect <- list()
r_effect[[right_bar]] <- as.formula(paste("~ 1", "|", right_bar))
}
}
if (is_indpt) {
if (theta[1] == 0) {
r_effect <- list()
r_effect[[right_bar]] <- as.formula(paste("~ -1 + ", left_bar, "|",
right_bar))
}
if (theta[2] == 0) {
r_effect <- list()
r_effect[[right_bar]] <- as.formula(paste("~ 1", "|", right_bar))
}
}
if (no_re == 1 & theta[1] == 0) cat("No random effect variance.")
if (!attr(m, "is_gamm")) {
new_lme <- update(m, formula(m), random = r_effect, evaluate = TRUE)
attr(new_lme, "is_gamm") <- FALSE
return(deleteZeroComponents(new_lme))
}
g_m <- gamm(attr(m, "gam_form"), random = r_effect, data = m$data)
attr(g_m$lme, "smooth_names") <- get_names(g_m) # old names
attr(g_m$lme, "is_gamm") <- TRUE # add indicator for mgcv::gamm
attr(g_m$lme, "gam_form") <- formula(g_m$gam) # for refit
g_m <- g_m$lme
attr(g_m, "ordered_smooth") <- sort_sterms(g_m) # names as in gamm4
return(deleteZeroComponents(g_m))
}
#' @return \code{NULL}
#'
#' @rdname deleteZeroComponents
#' @export
deleteZeroComponents.merMod <-
function(m) {
# A function that deletes all random effects terms if corresponding variance
# parameter is estimated to zero.
#
# Args:
# m = Object of class lmerMod. Obtained by lmer()
#
# Returns:
# m/newMod = A model without zero estimated variance component
#
theta <- getME(m, "theta")
thetazero <- which(theta == 0)
if (length(thetazero) == 0) { # every thing's fine
return(m)
}
if (length(theta) == length(thetazero)) { # only lm left
warning("Model has no random effects variance components larger than zero.")
return(lm(nobars(formula(m)), model.frame(m)))
}
varBlockMatrices <- getME(m, "ST")
cnms <- m@cnms
if(exists("gamm4", m@optinfo)) { # for gamm4 what to exclude from the model
for(i in 1:length(varBlockMatrices)){
if(any(diag(varBlockMatrices[[i]]) == 0)) {
termWithZero <- cnms[[i]][which(diag(varBlockMatrices[[i]]) == 0)]
cat("The term", ifelse(termWithZero=="(Intercept)",
names(cnms)[[i]],
termWithZero[[1]]),
"has zero variance components. \n")
}
}
stop("After removing the terms with zero variance components and refitting
the model cAIC can be called again.", call. = FALSE)
}
# if(is.null(m@optinfo$conv$lme4$code) ||
# m@optinfo$conv$lme4$code == -1) {
for(i in 1:length(varBlockMatrices)){
cnms[[i]] <- cnms[[i]][which(diag(varBlockMatrices[[i]]) != 0)]
}
# } else { # in case of convergence failures
# nc <- vapply(cnms, length, 1L)
# thl <- split(theta, rep.int(seq_along(nc), (nc * (nc + 1))/2))
# for (i in 1:length(nc)) {
# ranVars <- thl[[i]][1:nc[i]]
# cnms[[i]] <- cnms[[i]][which(ranVars != 0)]
# }
# }
reFormula <- cnms2formula(cnms)
if(suppressWarnings(nobars(formula(m)) == formula(m)[[2]])) {
# if there are no fixed effects
rhs <- reFormula
} else {
rhs <- c(attr(terms(nobars(formula(m))), "term.labels"), reFormula)
}
lhs <- formula(m)[[2]] # left hand side of the formula
newFormula <- reformulate(rhs, lhs) # merge both sides
newMod <- update(m, formula. = newFormula, evaluate = TRUE)
return(deleteZeroComponents(newMod))
}
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