The situation is aggravated if more than one random effect is included in the model. The type I error rate and the power of the commonly used inferential procedures are also severely affected. Given that the variance components are the only tool to study the variability of the true distribution, it is difficult to assess whether problems in the estimation of the mean structure occur. However, the estimates of this variability are always severely biased. The bias induced in the mean-structure parameters is generally small, as far as the variability of the underlying random-effects distribution is small as well. It is shown that the maximum likelihood estimators are inconsistent in the presence of misspecification. In this paper we study, through simulations, the impact of misspecifying the random-effects distribution on the estimation and hypothesis testing in GLMMs. However, the validity of this assumption is sometimes difficult to verify. Estimation in generalized linear mixed models (GLMMs) is often based on maximum likelihood theory, assuming that the underlying probability model is correctly specified.
