One of the most frequently asked questions about
`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.
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2009q4/003115.html),
`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has been withdrawn (or more precisely,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 as LMMs.

likelihood ratio tests via

`anova`

or`drop1`

(MC,+)profile confidence intervals via

`profile.merMod`

and`confint.merMod`

(CI,+)parametric bootstrap confidence intervals and model comparisons via

`bootMer`

(or`PBmodcomp`

in the`pbkrtest`

package) (MC/CI,*,+)for random effects, simulation tests via the

`RLRsim`

package (MC,*)for fixed effects, F tests via Kenward-Roger approximation using

`KRmodcomp`

from the`pbkrtest`

package (MC,*)`car::Anova`

and`lmerTest::anova`

provide wrappers for Kenward-Roger-corrected tests using`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,*,+)

`arm::sim`

, or `bootMer`

, can be used
to compute confidence intervals on predictions.

For `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://www.phdcomics.com/comics/archive.php?comicid=905

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