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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
profile confidence intervals via
parametric bootstrap confidence intervals and model comparisons via
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)
lmerTest::anova provide wrappers for
lmerTest::anova also provides t tests via the Satterthwaite approximation (P,*)
afex::mixed is another wrapper for
anova providing "Type 3" tests of all effects (P,*,+)
bootMer, can be used to compute confidence intervals on predictions.
When all else fails, don't forget to keep p-values in perspective.