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has been withdrawn (or more precisely,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.merMod
andconfint.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