On Hinde-Demetrio Regression Models for Overdispersed Count Data

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 + p. For p equals to 2; 3; , the corresponding distributions are concentrated on nonnegative integers, overdispersed and zero-in‡ated with respect to a Poisson distribution having the same mean. The negative binomial (p = 2), strict arcsine (p = 3) and Poisson (p ! 1) distributions are particular count HD families. From generalized linear modelling framework, the e¤ect 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 e¤ect must be negligible within an adequate HD model for …xed integer p. The estimation of the integer p is also examined separately. The results are illustrated and discussed on a horticultural data set. Key words: Additive exponential dispersion model, compound Poisson, generalized linear model, model selection, unit variance function, zero-in‡ation. AMS classi…cation: Primary 62J02; Secondary 62J12, 62F07. Abbreviated title: Hinde-Demétrio regression models. Address for correspondence: C.C. Kokonendji. Université de Pau et des Pays de l’Adour. Laboratoire de Mathématiques Appliquées UMR 5142 CNRS. Département STID. Avenue de l’Université. 64000 Pau, France. Tel +33(0)559 407 145; Fax +33(0)559 407 140. Email addresses: [email protected] (Célestin C. Kokonendji), [email protected] (Clarice G.B. Demétrio), [email protected] (Silvio S. Zocchi). Preprint submitted to LMA, Technical Report No. 0609 15 March 2006 ha l-0 02 22 74 8, v er si on 1 29 J an 2 00 8