The impact of model misspecification on random effects models for count data

Abstract

It is typical to assume a normal distribution for the random effects in generalized linear mixed model (GLMM). Also it is not easy to check that assumption whether right to assume normal distribution for the random effects. The objective of this project is to study via simulations how estimation and statistical test in the random effects models for count data are affected by misspecification of the random effects distribution. The result of this thesis reveals that for count longitudinal data misspecifying the distribution of a random effect induce substantial bias on maximum likelihood estimates. Also, the type I error and the power of the Wald test associated with the intercept parameter and associated to the parameter of the treatment effect are considerably influenced. In addition the result of the sensitive analysis carried out by specifying non-normal random effects distribution in GLMM using the probability integral transformation shows that assuming a normal random effect is mo