  Statistical models that include random effects are commonly used to analyze
longitudinal and correlated data, often with strong and parametric assumptions
about the random effects distribution. There is marked disagreement in the
literature as to whether such parametric assumptions are important or
innocuous. In the context of generalized linear mixed models used to analyze
clustered or longitudinal data, we examine the impact of random effects
distribution misspecification on a variety of inferences, including prediction,
inference about covariate effects, prediction of random effects and estimation
of random effects variances. We describe examples, theoretical calculations and
simulations to elucidate situations in which the specification is and is not
important. A key conclusion is the large degree of robustness of maximum
likelihood for a wide variety of commonly encountered situations.
