Characterizing the Performance of the Conway‐Maxwell Poisson Generalized Linear Model

Abstract

Count data are pervasive in many areas of risk analysis; deaths, adverse health outcomes, infrastructure system failures, and traffic accidents are all recorded as count events, for example. Risk analysts often wish to estimate the probability distribution for the number of discrete events as part of doing a risk assessment. Traditional count data regression models of the type often used in risk assessment for this problem suffer from limitations due to the assumed variance structure. A more flexible model based on the Conway-Maxwell Poisson (COM-Poisson) distribution was recently proposed, a model that has the potential to overcome the limitations of the traditional model. However, the statistical performance of this new model has not yet been fully characterized. This article assesses the performance of a maximum likelihood estimation method for fitting the COM-Poisson generalized linear model (GLM). The objectives of this article are to (1) characterize the parameter estimation accuracy of the MLE implementation of the COM-Poisson GLM, and (2) estimate the prediction accuracy of the COM-Poisson GLM using simulated data sets. The results of the study indicate that the COM-Poisson GLM is flexible enough to model under-, equi-, and overdispersed data sets with different sample mean values. The results also show that the COM-Poisson GLM yields accurate parameter estimates. The COM-Poisson GLM provides a promising and flexible approach for performing count data regression.

Information initiatives of mobile retailers: a regression analysis of zero‐truncated count data with underdispersion

“…§ Third, despite its popularity in the literature [20,22,23], on the basis of the AIC the ZT CMP model is somewhat outperformed by the ZT Consul's generalized Poisson model in our case. Although the Consul's generalized Poisson distribution is not in the exponential family (and has no natural sufficient statistic), it is still a reasonable and competitive alternative to the CMP distribution according to our analysis.…”

Modeling over-dispersed crash data with a long tail: Examining the accuracy of the dispersion parameter in Negative Binomial models

“…The following paragraph summarizes the simulation procedure for experiment one. The simulation setting considered in this study was first proposed by Francis et al (2012). The values of dispersion parameter are selected according to the finding in Table 1.…”

“…The bias of an estimator is defined as the difference between an estimator's expected value and the true value of the parameter being estimated (Francis et al, 2012). The estimation bias of the dispersion parameter α is calculated as follows:…”

“…In contrast, in a simulation, it is possible to generate crash data with known regression parameters and dispersion levels. The simulation analysis was used in previous transportation safety studies (Lord, 2006;Francis et al, 2012) to characterize the performance of different estimators. To complement the output of the simulation study, crash data collected in Texas are also used to compare the dispersion parameter and dispersion term.…”

Evaluating the double Poisson generalized linear model

“…However, Francis et al (2012) Based on the new parameterization, Guikema and Coffelt (2008) developed a COMPoisson GLM framework to model discrete count data using Bayesian framework in WinBUGS (Spiegelhalter et al, 2003). Their modeling framework is a dual-link GLM in which both the mean and variance depend on the covariates.…”