Functional Forms for Negative Binomial, Generalized Poisson, Zero-Inflated Negative Binomial, and Zero-Inflated Generalized Poisson Regression Models

This study relates negative binomial and generalized Poisson regression models through the mean-variance relationship, and suggests the application of these models for overdispersed or underdispersed count data. In addition, this study relates zero- inflated negative binomial and zero-inflated generalized Poisson regression models through the mean-variance relationship, and suggests the application of these zero-inflated models for zero- inflated and overdispersed count data. The negative binomial and gene ralized Poisson regression models were fitted to the Malaysian OD claim count data, whereas the zero-inflated negative binomial and zero-inflated generalized Poisson regression models were fitted to the German healthcare count data.

Keywords: negative binomial regression, generalized Poisson regression, zero-inflated negative binomial regression, zero-inflated generalized Poisson regression.