  In the analysis of count data often the equidispersion assumption is not
suitable, hence the Poisson regression model is inappropriate. As a
generalization of the Poisson distribution, the COM-Poisson distribution can
deal with under-, equi- and overdispersed count data. It is a member of the
exponential family of distributions and has well known special cases. In spite
of the nice properties of the COM-Poisson distribution, its location parameter
does not correspond to the expectation, which complicates the interpretation of
regression models. In this paper, we propose a straightforward
reparametrization of the COM-Poisson distribution based on an approximation to
the expectation of this distribution. The main advantage of our new
parametrization is the straightforward interpretation of the regression
coefficients in terms of the expectation, as usual in the context of
generalized linear models. Furthermore, the estimation and inference for the
new COM-Poisson regression model can be done based on the likelihood paradigm.
We carried out simulation studies to verify the finite sample properties of the
maximum likelihood estimators. The results from our simulation study show that
the maximum likelihood estimators are unbiased and consistent for both
regression and dispersion parameters. We observed that the empirical
correlation between the regression and dispersion parameter estimators is close
to zero, which suggests that these parameters are orthogonal. We illustrate the
application of the proposed model through the analysis of three data sets with
over-, under- and equidispersed count data. The study of distribution
properties through a consideration of dispersion, zero-inflated and heavy tail
indexes, together with the results of data analysis show the flexibility over
standard approaches.
