The consequences of misspecifying the random-effects distribution when fitting generalized linear mixed models

Generalized linear mixed models provide effective analyses of clustered and longitudinal data and typically require the specification of the distribution of the random effects. The consequences of misspecifying this distribution are subject to debate; some authors suggest that large biases can arise, while others show that there will typically be little bias for the parameters of interest. Using analytic results, simulation studies, and example data, I summarize the results of extensive assessments of the bias in parameter estimates due to random-effects distribution misspecification. I also present assessments of the accuracy of random-effects predictions under misspecification. These assessments indicate that random-effects distribution misspecification often produces little bias when estimating slope coefficients but may yield biased intercepts and variance-components estimators as well as mildly inaccurate predicted random effects.