On Hinde-Demetrio Regression Models for Overdispersed Count Data
Résumé
In this paper we introduce the Hinde-Demétrio (HD) regression models for analyzing overdispersed count data and, mainly, investigate the e¤ect of dispersion parameter. The HD distributions are discrete additive exponential dispersion models (depending on canonical and dispersion parameters) with a third real index parameter p and have been characterized by its unit variance function $\mu+\mu^p$. For p equals to 2; 3, ..., the corresponding distributions are concentrated on nonnegative 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 ($p \rightarrow \infty$) distributions are particular count HD families. From generalized linear modelling framework, the effect of dispersion parameter in the HD regression models, among other things, is pointed out through the double mean parametrization: unit and standard means. In the particular additive model, this effect must be negligible within an adequate HD model for fixed integer $p$. The estimation of the integer $p$ is also examined separately. The results are illustrated and discussed on a horticultural data set.
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