Characterizing the Performance of the Bayesian Conway-maxwell Poisson Generalized Linear Model

This paper documents the performance of a Bayesian Conway-Maxwell-Poisson (COM-Poisson) generalized linear model (GLM). This distribution was originally developed as an extension of the Poisson distribution in 1962 and has a unique characteristic, in that it can handle both under-dispersed and over-dispersed count data. Previous work by the authors lead to the development of a dual-link GLM based on the COM-Poisson distribution and applied this model to analyzing power system reliability and motor vehicle crash data. Parameter estimation for this model is done within the Bayesian framework using Markov Chain Monte Carlo methods. The objectives of this paper are to (1) characterize the parameter estimation accuracy of the Markov Chain Monte Carlo (MCMC) implementation of the COM GLM and (2) estimate the computational burden of this MCMC implementation. We use simulated datasets to assess the performance of the COM GLM. The results of the study indicate that the COM GLM is flexible enough to model under-, equi-and over-dispersed datasets with different sample mean values. The results also show that the MCMC implementation of the COM GLM yields accurate parameter estimates. Furthermore, we show that a previously suggested asymptotic approximation of the mean of the COM-Poisson distribution holds true even when the sample mean of the data is substantially below the lower bound previously suggested. However, the approximation is less accurate for very lower sample mean values, and we characterize the degree of this inaccuracy. Our results also show that the computational burden of the COM GLM is not prohibitive. The COM GLM provides a promising and flexible approach for performing count data regression.