ROBUSTNESS OF MAXIMUM LIKELlliOOD ESTIMATES FOR MIXED POISSON REGRESSION MODELS by

Mixed Poisson regression models, a class of generalized linear mixed models, are commonly used to analyze count data that exhibit overdispersion. Because inference for these models can be computationally difficult, simplifying distributional assumptions are often made. We consider an influence function representing effects of infinitesimal perturbations of the mixing distribution. This function enables us to compute Gateaux derivatives of maximum likelihood estimates (MLEs) under perturbations of the mixing distribution for Poisson-gamma and Poisson-lognormal models. Provided the first two moments exist, these MLEs are robust in the sense that their Gateaux derivatives are bounded.