R Statistics Cookbook

How it works...

The lmer function can estimate a model using Maximum Likelihood (ML) or Restricted Maximum Likelihood (REML). ML yields biased estimates for the variance components (the variances for our random effects) but can be used for comparing results between different models that contain different fixed effects formulations (the usual case). REML provides unbiased estimates for the variance components, but can't be used for comparing between different models. By default, lmer uses REML, which can be changed via REML = FALSE.

ML estimates have a lower variance than REML but are, of course, biased. Nevertheless, the bias disappears as the sample size rises to infinity. That is why ML is preferred when n is large, and REML is preferred ...