Misspecification in Generalized Linear Mixed Models and Its Impact on the Statistical Wald Test

Abstract

Generalized linear mixed models are commonly used in repeated measurement studies and account for the dependence between observations obtained from the same experimental unit. The designs of repeated measurements in which each experimental unit (e.g., subject) is proven in more than one experimental condition are widespread in psychology, neuroscience, medicine, social sciences and agricultural research. Estimation in generalized linear mixed models is often based on the maximum likelihood theory, which assumes that the assumptions about the underlying probability model are correct. These assumptions include the specification of the distribution of random effects. This research study aimed to identify the impact of the incorrect specification of this distribution on the probability of a type I error and the statistical power of the Wald test. This was achieved through a simulation study where different distributions were considered for random effects in generalized linear mixed models with Poisson and negative binomial responses. Evidence of the impact of the incorrect specification was presented in distributions for random effects different from the normal ones. Lognormal was used for random intercepts and bivariate exponential and Tukey for random intercepts and slopes. Lognormal has positive asymmetry and high kurtosis. Exponential has moderate asymmetry and kurtosis, and Tukey has moderate asymmetry and high kurtosis.