A hyper-Poisson regression model for overdispersed and underdispersed count data

The Poisson regression model is the most common framework for modeling count data, but it is constrained by its equidispersion assumption. The hyper-Poisson regression model described in this paper generalizes it and allows for over- and under-dispersion, although, unlike other models with the same property, it introduces the regressors in the equation of the mean. Additionally, regressors may also be introduced in the equation of the dispersion parameter, in such a way that it is possible to fit data that present overdispersion and underdispersion in different levels of the observations. Two applications illustrate that the model can provide more accurate fits than those provided by alternative usual models.