One of the most frequently asked questions about
lme4 is "how do I calculate p-values for estimated
parameters?" Previous versions of
mcmcsamp function, which efficiently generated
a Markov chain Monte Carlo sample from the posterior
distribution of the parameters, assuming flat (scaled
likelihood) priors. Due to difficulty in constructing a
mcmcsamp that was reliable even in
cases where the estimated random effect variances were
near zero (e.g.
mcmcsamp has been withdrawn (or more precisely,
not updated to work with
lme4 versions >=1.0.0).
Many users, including users of the
aovlmer.fnc function from
languageR package which relies on
mcmcsamp, will be
deeply disappointed by this lacuna. Users who need p-values have a
variety of options. In the list below, the methods marked
provide explicit model comparisons;
CI denotes confidence
P denotes parameter-level or sequential tests of
all effects in a model. The starred (*) suggestions provide
finite-size corrections (important when the number of groups is <50);
those marked (+) support GLMMs as well as LMMs.
likelihood ratio tests via
profile confidence intervals via
parametric bootstrap confidence intervals and model comparisons via
PBmodcomp in the
pbkrtest package) (MC/CI,*,+)
for random effects, simulation tests via the
for fixed effects, F tests via Kenward-Roger
KRmodcomp from the
pbkrtest package (MC,*)
lmerTest::anova provide wrappers for
Kenward-Roger-corrected tests using
lmerTest::anova also provides t tests via the
Satterthwaite approximation (P,*)
afex::mixed is another wrapper for
"Type 3" tests of all effects (P,*,+)
bootMer, can be used
to compute confidence intervals on predictions.
glmer models, the
summary output provides p-values
based on asymptotic Wald tests (P); while this is standard practice
for generalized linear models, these tests make assumptions both about
the shape of the log-likelihood surface and about the accuracy of
a chi-squared approximation to differences in log-likelihoods.
When all else fails, don't forget to keep p-values in perspective: http://phdcomics.com/comics/archive.php?comicid=905
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