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has been withdrawn (or more precisely,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.merMod
andconfint.merMod
(CI,+)bootMer
(orPBmodcomp
in thepbkrtest
package) (MC/CI,*,+)RLRsim
package
(MC,*)KRmodcomp
from thepbkrtest
package (MC)car::Anova
andlmerTest::anova
provide 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: