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mcmcsamp has been withdrawn (or more precisely,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:
anova(MC,+)profile.merModandconfint.merMod(CI,+)bootMer(orPBmodcompin thepbkrtestpackage) (MC/CI,*,+)RLRsimpackage
(MC,*)KRmodcompfrom thepbkrtestpackage (MC)car::AnovaandlmerTest::anovaprovide wrappers forpbkrtest: the latter also provides t tests via the
Satterthwaite approximation (P,*)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=""> When all else fails, don't forget to keep p-values in
perspective: