The COM–Poisson distribution is a two-parameter generalization of the Poisson distribution that can deal with under-, equi- and overdispersed count data. Unfortunately, its location parameter does not correspond to the expectation, which complicates the parameter interpretation. In this article, we propose a straightforward reparametrization of the COM–Poisson distribution based on an approximation to the expectation. Estimation and inference are done using the likelihood paradigm. Simulation studies show that the maximum likelihood estimators are unbiased and consistent for both regression and dispersion parameters. In addition, the nature of the deviance surfaces suggests that these parameters are also orthogonal for most of the parameter space, which is advantageous for interpretation, inference and computational efficiency. Study of the distribution’s properties, through a consideration of dispersion, zero-inflation and heavy tail indexes, together with the results of data analyses show the flexibility over standard approaches. The computational routines and datasets are available in the supplementary material.
Marginal regression models for clustered count data based on zero-inflated Conway-Maxwell-Poisson distribution with applications
