Monte Carlo Studies on Conway-Maxwell Poisson Generalized Linear Mixed Effects Model for Under-Dispersed Count Data

Abstract

 Poisson regression is the traditional technique for handling count data. The assumption of equality of mean and variance which is an important property of the Poisson distribution makes the application of the distribution on count data highly restrictive since in reality count data do not always satisfy this assumption. The Generalized Poisson distribution and the ConwayMaxwell Poisson regression are some of the proposed remedies for handling under dispersed data. Our recent work on theoretical exposition of the re-parameterization and extension of the Conway-Maxwell-Poisson regression models to accommodate random effects appeared in the literature. This paper presents a simulation study to evaluate the performance of the reparameterized Conway-Maxwell-Poisson Generalized Linear Mixed Effects Model (CMPGLMM) for handling the problem of under-dispersion in clustered data. The reparameterization allows the response to be directly related to the regression coefficients via an approximation of the mean, thereby, leading to straightforward interpretation of the coefficients. The simulation result showed that the implementation is reliable and the CMPGLMM produced results that are better than the traditional Poisson and NegativeBinomial models which imply that the CMPGLMM is a better alternative for under-dispersed clustered count data.