lme4 is "how do I calculate p-values for estimated
parameters?" Previous versions of lme4 provided
the 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
version of 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mcmcsamp has been withdrawn (or more precisely,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
the 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 MC
provide explicit model comparisons; CI denotes confidence
intervals; and 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="" lmms.<="" p="">
anova(MC,+)profile.merModandconfint.merMod(CI,+)bootMer (or PBmodcomp in the
pbkrtest package) (MC/CI,*,+)RLRsim package
(MC,*)KRmodcomp from the
pbkrtest package (MC)car::Anova and
lmerTest::anova provide wrappers for
pbkrtest: lmerTest::anova also provides t tests via the
Satterthwaite approximation (P,*)afex::mixed is another wrapper for
pbkrtest and anova providing
"Type 3" tests of all effects (P,*,+)bootMer