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.
Highlights
Most often, discussions are based on fitting distributions for over-dispersed data
We present regression models (GLM) for the class of Conway-Maxwell-Poisson (Com-Poisson) distributions
We present brief discussions of this class of Com-Poisson distributions
Summary
Discussions are based on fitting distributions for over-dispersed data. Not much is focussed on under-dispersed count data. Our goal here is to fit the generalized linear model versions to the class of Com-Poisson to these data sets. The second data set is the 2003 U.S Medical Expenditure Panel Survey (MEPS) data set relating to the number of doctor visits (Y=docvis) in 2003 for a number of elderly patients as well as several other covariates relating to patients’ characteristics. We present here a brief introductory discussions on the Com-Poisson distributions and its extensions These are models that are subsequently applied to the three data sets described above
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