The lmerTest package provides p-values in type I, II or III
tables for linear mixed models (
lmer model fits cf. lme4)
via Satterthwaite's degrees of freedom method; a Kenward-Roger method is also
available via the pbkrtest package.
Model selection and assessment methods include
drop1, anova-like tables for random effects (
least-square means (LS-means;
and tests of linear contrasts of fixed effects (
lme4::lmer and produced an object of class
lmerModLmerTest which inherits from
lmerMod. In addition to
computing the model (using
computes a couple of components needed for the evaluation of Satterthwaite's
denominator degrees of freedom.
anova method for
lmer model fits produces
type I, II, and III anova tables for fixed-effect terms with
Satterthwaite and Kenward-Roger methods for denominator degrees of freedom
summary method for
lmer model fits adds
denominator degrees of freedom and p-values to the coefficient table.
anova-like table of random effects via likelihood ratio tests
with methods for both
ranova can either test reduction of random-effect terms to simpler
structures or it can test removal of entire random-effect terms.
F-tests of fixed-effect terms using Satterthwaite or
Kenward-Roger methods for denominator degrees of freedom. These 'single term
deletion' tables are useful for model selection and tests of marginal terms.
Compared to the likelihood ratio tests of
lme4::drop1 the F-tests and
lmerTest::drop1 are more accurate and considerably faster
since no additional model fitting is required.
tests of contrasts, i.e. tests of linear functions of the
fixed-effect coefficients. A user-friendly interface for tests of contrasts
with outputs either as a summary-like table of t-tests or an anova-like table
of F-tests (or a list of either). Contrasts can optionally be tested for
estimability. Contrasts are allowed to be rank-deficient as the rank is
automatically detected and appropriate adjustments made. Methods for
lmerModLmerTest as well as
lmerMod objects – the latter avoids
the Satterthwaite specific computations when the Kenward-Roger method is used.
a function which operates on anova tables and LS-means tables makes it possible to see exactly which functions of the coefficients are being tested. This is helpful when differences between type I, II and III anova tables are being considered and discussed.
computes the so-called least-squares means (classical Yates contrasts) as well as pairwise differences of these.
performs automatic backward model selection of fixed and random parts of the linear mixed model.
an explicit coerce function from class
The computational approach is to let
lmerTest::lmer compute the
Hessian and derivatives needed for evaluation of degrees of freedom and
t- and F-tests and to store these in the model object. The
Hessian and derivatives are therefore computed only once per model fit
and reused with each call to
summary, etc. Evaluation of
t and F-tests does not involve model re-fitting.
lmerTest::lmer roughly amounts to calling
lme4::lmer followed by
lmerTest::as_lmerModLmerTest, so for computationally intensive model
fits it can make sense to use
lme4::lmer rather than
if computational time is an issue and summary tables and anova tables will
not be needed.
Alexandra Kuznetsova, Per Bruun Brockhoff, Rune Haubo Bojesen Christensen
Alexandra Kuznetsova, Per B. Brockhoff and Rune H. B. Christensen (2017) lmerTest Package: Tests in Linear Mixed Effects Models. Journal of Statistical Software, 82(13), 1–26. doi:10.18637/jss.v082.i13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
## load lmerTest package library(lmerTest) ## Fit linear mixed model to the ham data: fm <- lmer(Informed.liking ~ Gender + Information * Product + (1 | Consumer) + (1 | Consumer:Product), data=ham) ## Summary including coefficient table with p-values for t-statistics using ## Satterthwaite's method for denominator degrees of freedom: summary(fm) ## Type III anova table with p-values for F-tests based on Satterthwaite's ## method: (aov <- anova(fm)) ## Inspect the contrast matrix for the Type III test of Product: show_tests(aov, fractions = TRUE)$Product ## Choose type II anova table with Kenward-Roger method for the F-test: ## Not run: if(requireNamespace("pbkrtest", quietly = TRUE)) anova(fm, type=2, ddf="Kenward-Roger") ## End(Not run) ## Anova-like table of random-effect terms using likelihood ratio tests: ranova(fm) ## F-tests of 'single term deletions' for all marginal terms: drop1(fm) ## Least-Square means and pairwise differences: (lsm <- ls_means(fm)) ls_means(fm, which = "Product", pairwise = TRUE) ## ls_means also have plot and as.data.frame methods: ## Not run: plot(lsm, which=c("Product", "Information")) as.data.frame(lsm) ## Inspect the LS-means contrasts: show_tests(lsm, fractions=TRUE)$Product ## End(Not run) ## Contrast test (contest) using a custom contrast: ## Here we make the 2-df joint test of the main effects of Gender and Information (L <- diag(length(fixef(fm)))[2:3, ]) contest(fm, L = L) ## backward elimination of non-significant effects: step_result <- step(fm) ## Elimination tables for random- and fixed-effect terms: step_result # Extract the model that step found: final_model <- get_model(step_result)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.