On Hinde-Demétrio regression models for overdispersed count data

We introduce the Hinde-Demétrio (HD) regression models in order to analyze overdispersed count data. We mainly investigate the effect of the dispersion parameter. The HD distributions are discrete additive exponential dispersion models (depending on canonical and dispersion parameters) with a third real index parameter p. They have been characterized by the unit variance function μ+μp. For p equal to 2, 3, …, the corresponding distributions are concentrated on non-negative integers, overdispersed and zero-inflated with respect to a Poisson distribution having the same mean. The negative binomial (p=2), strict arcsine (p=3) and Poisson (p→∞) distributions are particular count HD families. In a generalized linear modelling framework, the effect of the dispersion parameter in the HD regression models is, among other things, pointed out through the two parametrizations for the mean: unit and standard means. In this particular additive model, this effect must be negligible within an adequate HD model for fixed p. The estimation of the integer p is also examined separately. The results are illustrated and discussed on a horticultural data set.