A flexible model to fit over-dispersed longitudinal count data

A common way to deal with count data is to fit a generalized linear model. The most common approaches are the Poisson regression model and the negative binomial regression model. However, Conway-Maxwell Poisson (COM-Poisson) regression model is more flexible to fit count data. This model has been widely used to describe under- or over-dispersion problem for count data in cross-sectional setting. However, there is no application of the COM-Poisson model in longitudinal data. We propose and develop the COM-Poisson regression model to fit longitudinal count data. We compare this model with the Poisson regression model and the negative binomial model, under two different working correlation structures; exchangeable and autoregressive of order 1, AR(1). The results show that the COM-Poisson model is very suitable to longitudinal count data, even in presence of dispersion; it gives the smallest AIC values. Also, it is insensitive to the choice of the working structure. Extensive simulation is conducted for small, moderate and large sample sizes, to evaluate the proposed model. The proposed approach has good results compared with other models using different criteria.