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#############################################################################
# Copyright (c) 2013-2018 Alexandra Kuznetsova, Per Bruun Brockhoff, and
# Rune Haubo Bojesen Christensen
#
# This file is part of the lmerTest package for R (*lmerTest*)
#
# *lmerTest* is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 2 of the License, or
# (at your option) any later version.
#
# *lmerTest* is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# A copy of the GNU General Public License is available at
# <https://www.r-project.org/Licenses/> and/or
# <http://www.gnu.org/licenses/>.
#############################################################################
#
# ranova.R - random effects ANOVA table
# ------- Contents: --------
#
# --- exported function: ---
#
# ranova
# rand
#
# --- utility functions: ---
#
# rm_complete_terms
# get_lm_call
# get_newforms
# get_logLik
# mk_LRtab
# has_ranef
# has_terms
# get_lhs
# get_rhs
#
##############################################
######## ranova(); rand()
##############################################
#' ANOVA-Like Table for Random-Effects
#'
#' Compute an ANOVA-like table with tests of random-effect terms in the model.
#' Each random-effect term is reduced or removed and likelihood ratio tests of
#' model reductions are presented in a form similar to that of
#' \code{\link[=drop1.lmerModLmerTest]{drop1}}.
#' \code{rand} is an alias for \code{ranova}.
#'
#' If the model is fitted with REML the tests are REML-likelihood ratio tests.
#'
#' A random-effect term of the form \code{(f1 + f2 | gr)} is reduced to
#' terms of the form \code{(f2 | gr)} and \code{(f1 | gr)} and these reduced
#' models are compared to the original model.
#' If \code{reduce.terms} is \code{FALSE} \code{(f1 + f2 | gr)} is removed
#' instead.
#'
#' A random-effect term of the form \code{(f1 | gr)} is reduced to \code{(1 | gr)}
#' (unless \code{reduce.terms} is \code{FALSE}).
#'
#' A random-effect term of the form \code{(1 | gr)} is not reduced but
#' simply removed.
#'
#' A random-effect term of the form \code{(0 + f1 | gr)} or \code{(-1 + f1 | gr)}
#' is reduced (if \code{reduce.terms = TRUE}) to \code{(1 | gr)}.
#'
#' A random-effect term of the form \code{(1 | gr1/gr2)} is automatically
#' expanded to two terms: \code{(1 | gr2:gr1)} and \code{(1 | gr1)} using
#' \code{\link[lme4]{findbars}}.
#'
#' In this exposition it is immaterial whether \code{f1} and \code{f2} are
#' factors or continuous variables.
#'
#' @note Note that \code{anova} can be used to compare two models and will often
#' be able to produce the same tests as \code{ranova}. This is, however, not always the
#' case as illustrated in the examples.
#'
#' @section Warning:
#' In certain cases tests of non-nested models may be generated. An example
#' is when \code{(0 + poly(x, 2) | gr)} is reduced (the default) to \code{(1 | gr)}.
#' To our best knowledge non-nested model comparisons are only generated in
#' cases which are statistical nonsense anyway (such as in this example where
#' the random intercept is suppressed).
#'
#'
#' @param model a linear mixed effect model fitted with \code{lmer()}
#' (inheriting from class \code{lmerMod}).
#' @param reduce.terms if \code{TRUE} (default) random-effect terms are
#' reduced (if possible). If \code{FALSE} random-effect terms are simply
#' removed.
#' @param ... currently ignored
#'
#' @return an ANOVA-like table with single term deletions of random-effects
#' inheriting from class \code{anova} and \code{data.frame} with the columns:
#' \item{npar}{number of model parameters.}
#' \item{logLik}{the log-likelihood for the model. Note that this is the
#' REML-logLik if the model is fitted with REML.}
#' \item{AIC}{the AIC for the model evaluated as \code{-2*(logLik - npar)}.
#' Smaller is better.}
#' \item{LRT}{the likelihood ratio test statistic; twice the difference in
#' log-likelihood, which is asymptotically chi-square distributed.}
#' \item{Df}{degrees of freedom for the likelihood ratio test: the difference in
#' number of model parameters.}
#' \item{Pr(>Chisq)}{the p-value.}
#' @export
#' @author Rune Haubo B. Christensen and Alexandra Kuznetsova
#'
#' @seealso \code{\link[=drop1.lmerModLmerTest]{drop1}} for tests of marginal
#' fixed-effect terms and
#' \code{\link{anova}} for usual anova tables for fixed-effect terms.
#' @importFrom stats formula nobs update
#' @importFrom lme4 getME findbars nobars
#'
#' @examples
#'
#' # Test reduction of (Days | Subject) to (1 | Subject):
#' fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
#' ranova(fm1) # 2 df test
#'
#' # This test can also be achieved with anova():
#' fm2 <- lmer(Reaction ~ Days + (1|Subject), sleepstudy)
#' anova(fm1, fm2, refit=FALSE)
#'
#' # Illustrate reduce.test argument:
#' # Test removal of (Days | Subject):
#' ranova(fm1, reduce.terms = FALSE) # 3 df test
#'
#' # The likelihood ratio test statistic is in this case:
#' fm3 <- lm(Reaction ~ Days, sleepstudy)
#' 2*c(logLik(fm1, REML=TRUE) - logLik(fm3, REML=TRUE)) # LRT
#'
#' # anova() is not always able to perform the same tests as ranova(),
#' # for example:
#' anova(fm1, fm3, refit=FALSE) # compares REML with ML and should not be used
#' anova(fm1, fm3, refit=TRUE) # is a test of ML fits and not what we seek
#'
#' # Also note that the lmer-fit needs to come first - not an lm-fit:
#' # anova(fm3, fm1) # does not work and gives an error
#'
#' # ranova() may not generate all relevant test:
#' # For the following model ranova() indicates that we should not reduce
#' # (TVset | Assessor):
#' fm <- lmer(Coloursaturation ~ TVset * Picture + (TVset | Assessor), data=TVbo)
#' ranova(fm)
#' # However, a more appropriate model is:
#' fm2 <- lmer(Coloursaturation ~ TVset * Picture + (1 | TVset:Assessor), data=TVbo)
#' anova(fm, fm2, refit=FALSE)
#' # fm and fm2 has essentially the same fit to data but fm uses 5 parameters
#' # more than fm.
#'
ranova <- function(model, reduce.terms=TRUE, ...) {
if(!inherits(model, "lmerMod"))
stop("'model' should be an lmer-fit: \"inherits(model, 'lmerMod')\" is not TRUE")
isREML <- getME(model, "is_REML")
nobs_model <- nobs(model)
orig_form <- formula(model)
orig_rhs <- orig_form[[length(orig_form)]]
if(!has_ranef(orig_rhs))
stop("Model should have at least one random-effects term")
# Reconstruct formula - needed for terms like (1 | g1 / g2):
fe_rhs <- safeDeparse(nobars(orig_rhs))
reforms <- lapply(findbars(orig_rhs), safeDeparse) # random-effect forms
re_rhs <- lapply(reforms, function(rf) paste0("(", rf, ")"))
full_rhs <- paste(c(list(fe_rhs), re_rhs), collapse=" + ")
full_form <- update(orig_form, paste0(". ~", full_rhs))
# Compute new model formulae with reduced ranef formulae:
new_forms <- if(!reduce.terms)
rm_complete_terms(reforms, full_form) else
unlist(lapply(reforms, get_newforms, full_formula=full_form))
ll <- get_logLik(model) # store df and logLik
for(nform in new_forms) { # For each new formula. nform <- new_forms[[1]]
newfit <- if(!has_ranef(nform)) { # If no random effects: fit with lm
lm_call <- get_lm_call(model, nform)
eval.parent(as.call(lm_call))
} else eval.parent(update(model, formula=nform))
# } else eval.parent(update(model, formula=nform, ...))
# Check that models were fit to the same number of observations:
nobs_newfit <- nobs(newfit)
if(all(is.finite(c(nobs_model, nobs_newfit))) && nobs_newfit != nobs_model)
stop("number of rows in use has changed: remove missing values?")
ll <- rbind(ll, get_logLik(newfit, REML=isREML)) # store df and logLik
}
# Collect information in ANOVA table and return:
aov <- mk_LRtab(ll)
rownames(aov) <- c("<none>", names(new_forms))
head <- c("ANOVA-like table for random-effects: Single term deletions",
"\nModel:", deparse(full_form))
attr(aov, "formulae") <- new_forms
structure(aov, heading = head, class = c("anova", "data.frame"))
}
#' @rdname ranova
#' @export
rand <- ranova
##############################################
######## ranova utility functions below
##############################################
#' Remove Terms from Formula
#'
#' Remove fixef or ranef terms from formula, return a list of modified formulae
#' with environment restored to that of the original formula.
#'
#' @param terms character vector (or list) of terms to remove from
#' \code{full_formula}
#' @param full_formula formula
#' @param random if \code{TRUE} names of the return list have parentheses around
#' them.
#'
#' @importFrom stats update.formula
#' @keywords internal
rm_complete_terms <- function(terms, full_formula, random=TRUE) {
# Remove random-effect formula terms from original model formula (full_formula)
forms <- lapply(terms, function(reform) {
form <- update.formula(full_formula, paste0("~.- (", reform, ")"))
environment(form) <- environment(full_formula)
form
})
names(forms) <- if(!random) terms else
sapply(terms, function(form) paste0("(", form, ")"))
forms
}
#' @importFrom stats getCall
get_lm_call <- function(object, formula) {
# object: lmerMod object
# formula: model formula without random effects
Call <- as.list(getCall(object))
notkeep <- c("control", "start", "verbose", "devFunOnly", "REML")
Call <- Call[!names(Call) %in% notkeep]
Call$formula <- formula
Call[[1]] <- as.name("lm")
Call
}
#' @importFrom stats update.formula drop.scope
get_newforms <- function(form, full_formula) {
# Update full_formula by reducing the random-effect structure of 'form'
#
# form: a deparse'd random-effect formula term
# full_formula: the original model formula with lhs, fixed and random terms
#
rhs <- get_rhs(form) # rhs of random term: (lhs | rhs)
lhs <- get_lhs(form) # lhs of random term: (lhs | rhs)
scope <- drop.scope(lhs) # Detemine terms to drop from lhs
# Determine list of updates to 'form'
update_forms <- if(!has_terms(lhs) || length(scope) == 0L) {# length(scope) >= 1
# Remove entire re-term if lhs is '1':
setNames(list(paste0("~.- (", form, ")")), paste0("(", form, ")"))
} else {
# Drop terms from lhs of random term:
ll <- lapply(scope, function(scp) { # scp <- scope
# If there are no other terms in lhs than scp set new_lhs to just ~1:
new_lhs <- if(setequal(attr(terms(lhs), "term.labels"), scp)) "1" else {
tmp <- safeDeparse(update.formula(lhs, paste("~.-", scp)))
gsub("~", "", tmp, fixed=TRUE)
}
new_form <- paste0("(", new_lhs, " | ", rhs, ")")
paste0("~.- (", form, ")", " + ", new_form)
})
names(ll) <- paste(scope, paste0("in (", form, ")"))
ll
}
# Update original formula 'full_formula' with update_forms and return:
lapply(update_forms, function(upd) {
form <- update.formula(full_formula, upd)
environment(form) <- environment(full_formula)
form
})
}
#' @importFrom stats logLik
get_logLik <- function(object, ...) {
# Extract data.frame with "df" and "logLik" values from object.
ll <- logLik(object, ...)
data.frame("Df"=attr(ll, "df"), "logLik"=c(ll))
}
#' @importFrom stats pchisq
mk_LRtab <- function(x) {
# Compute drop1-table with LR-tests
# x: a 2-col data.frame with "Df" and "logLik"; 1st row is the full model
chisq_pval <- function(q, df, ...) pchisq(q=q, ifelse(df > 0, df, NA_real_), ...)
stopifnot(is.data.frame(x), colnames(x) == c("Df", "logLik"))
res <- data.frame("npar" = x[, "Df"],
"logLik" = x[, "logLik"],
"AIC" = -2*x[, "logLik"] + 2*x[, "Df"],
"LRT" = NA_real_,
"Df" = NA_real_,
"Pr(>Chisq)" = NA_real_, check.names = FALSE)
if(nrow(x) >= 2) {
res[-1, "LRT"] <- 2*(x[1, "logLik"] - x[-1, "logLik"])
res[-1, "Df"] <- x[1, "Df"] - x[-1, "Df"]
res[-1, "Pr(>Chisq)"] <-
chisq_pval(res[-1, "LRT"], res[-1, "Df"], lower.tail=FALSE)
}
rownames(res) <- rownames(x)
res
}
has_ranef <- function(form) {
# Determine if formula 'form' contain random effect terms.
if(is.character(form)) form <- safeDeparse(form)
length(grep("|", form, fixed=TRUE)) > 0
}
has_terms <- function(form) {
# Determine if formula 'form' contain any terms beyond intercept.
length(attr(terms(form), "term.labels")) > 0
}
get_lhs <- function(ranef_term) {
# Extract lhs in (lhs | rhs)
if(!is.character(ranef_term)) ranef_term <- safeDeparse(ranef_term)
lhs <- trimws(gsub("\\|.*$", "", ranef_term))
form <- as.formula(paste0("~", lhs))
form
## Add "1" for intercept if is suppressed:
# FIXME: Only if there no other terms in lhs?
# if(attr(terms(form), "intercept") == 1) form else
# as.formula(paste0("~1 + ", lhs))
}
get_rhs <- function(ranef_term) {
# Extract rhs in (lhs | rhs)
if(!is.character(ranef_term)) ranef_term <- safeDeparse(ranef_term)
trimws(gsub("^.*\\|", "", ranef_term))
}
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