Finite Mixtures of Mean-Parameterized Conway–Maxwell–Poisson Regressions

As a generalization of the Poisson distribution and a common alternative to other discrete distributions, the Conway–Maxwell–Poisson (CMP) distribution has the flexibility to explicitly characterize data over- or under-dispersion. The mean-parameterized version of the CMP has received increasing attention in the literature due to its ability to directly model the data mean. When the mean further depends on covariates, then the mean-parameterized CMP regression model can be treated in a generalized linear models framework. In this work, we propose a mixture of mean-parameterized CMP regressions model to apply on data which are potentially comprised of subpopulations with different conditional means and varying degrees of dispersions. An EM algorithm is constructed to find maximum likelihood estimates of the model. A simulation study is performed to test the proposed mixture of mean-parameterized CMP regressions model, and to compare it to model fits using mixtures of Poisson regressions and mixtures of negative binomial regressions. We show the mixture of mean-parameterized CMP regressions to be a competitive model in analyzing two real datasets.