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Statistical models that include random effects are commonly used to analyzelongitudinal and correlated data, often with strong and parametric assumptionsabout the random effects distribution. There is marked disagreement in theliterature as to whether such parametric assumptions are important orinnocuous. In the context of generalized linear mixed models used to analyzeclustered or longitudinal data, we examine the impact of random effectsdistribution misspecification on a variety of inferences, including prediction,inference about covariate effects, prediction of random effects and estimationof random effects variances. We describe examples, theoretical calculations andsimulations to elucidate situations in which the specification is and is notimportant. A key conclusion is the large degree of robustness of maximumlikelihood for a wide variety of commonly encountered situations.

Misspecifying the Shape of a Random Effects Distribution: Why Getting It Wrong May Not Matter