Marginalized zero-inflated generalized Poisson regression

The generalized Poisson (GP) regression model has been used to model count data that exhibit over-dispersion or under-dispersion. The zero-inflated GP (ZIGP) regression model can additionally handle count data characterized by many zeros. However, the parameters of ZIGP model cannot easily be used for inference on overall exposure effects. In order to address this problem, a marginalized ZIGP is proposed to directly model the population marginal mean count. The parameters of the marginalized zero-inflated GP model are estimated by the method of maximum likelihood. The regression model is illustrated by three real-life data sets.