Zero-inflated generalized Poisson regression mod- els: Asymptotic theory and applications

Abstract: Poisson regression models for count variables have been utilized in many applications. However, in many problems overdispersion and zero-inflation occur. In this paper we study regression models associated with the generalized Poisson distribution (Consul (1989)). These regression models which have been used for about 15 years do not belong to the class of generalized linear models considered by McCullagh and Nelder (1989) for which an established asymptotic theory is available. We prove consistency and asymptotic normality of the maximum likelihood estimators in zero-inflated generalized Poisson regression models. Further the accuracy of the asymptotic normality approximation is investigated through a simulation study. It is also shown that a Wald test for detecting zero-inflation or zero-deflation based on our results is considerable more powerful than the score test in zero-modified Poisson regression models. The usefulness of the considered models is demonstrated in two applications.