pvalues {lme4} | R Documentation

## Getting p-values for fitted models

### Description

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were near zero (e.g. https://stat.ethz.ch/pipermail/r-sig-mixed-models/2009q4/003115.html), `mcmcsamp` has been withdrawn (or more precisely, not updated to work with `lme4` versions 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

[Package lme4 version 1.1-12 Index]