GLM for Some Class of Com-Poisson Distributions with Applications

Abstract

In this paper, we present regression models (GLM) for the class of Conway-Maxwell-Poisson (Com-Poisson) distributions. This class of models include the Com-Poisson, the Com-Poisson negative binomial, the Generalized Com-Poisson and the Extended Com-Poisson distributions, all of which have been presented in various literatures within the last five years. While these distributions have been applied most especially to frequency count data exhibiting over or under dispersion, not much has been presented in the application of this class of models to data having several covariates (the exception being the Com-Poisson itself). Thus in this paper, we present the generalized linear model formulation for these distributions and compare our results with the baseline Com-Poisson and Poisson models. Two data sets are employed in this application. We further extended our discussion to the zero-inflated versions of these distributions and applying same to a well established data with having 64\% zero observations. All the models are fitted using SAS PROC NLMIXED. In all cases, empirical means and variances are generated which leads to our ability to compute the Wald's goodness-of-fit test statistic for all the models employed in this paper.