Robustness against Misspecified Random Effects in Poisson Generalized Linear Mixed Models

Abstract

Generalized linear mixed models (GLMM's) are usually formulated by making parametric assumptions about the distribution of the random effects in the model. In practical applications, little information is available to the statistician to justify such assumptions. In this talk, we first present an overview of GLMM's, robustness and the concept of influence functions. Next we examine the effect of misspecification of random effects in certain mixed Poisson regression models by formulating an influence function for misspecification. For certain commonly used models we can analyze this influence function and prove that it is bounded. This means that small misspecification of the random effect leads to small biases in estimates of regression coefficients and variance components. However, simulation studies show that while estimates of regression coefficients are only slightly affected by misspecification of random effects, estimates of variance components are seriously affected, even by minor misspecification.