Reparametrization of COM–Poisson regression models with applications in the analysis of experimental data. (October 2020)

• Record Type: Journal Article
• Authors: Ribeiro, Eduardo E; Zeviani, Walmes M; Bonat, Wagner H; Demetrio, Clarice GB; Hinde, John
• Is Part Of: Statistical modelling. Volume 20:Number 5(2020)
• Page Start: 443
• Page End: 466
• Publication Date: 2020-10
• Subjects: COM–Poisson -- Count data -- likelihood inference -- overdispersion -- underdispersion; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X19838651
• Languages: English
• ISSNs: 1471-082X

Abstract

The COM–Poisson distribution is a two-parameter generalization of the Poisson distribution that can deal with under-, equi- and overdispersed count data. Unfortunately, its location parameter does not correspond to the expectation, which complicates the parameter interpretation. In this article, we propose a straightforward reparametrization of the COM–Poisson distribution based on an approximation to the expectation. Estimation and inference are done using the likelihood paradigm. Simulation studies show that the maximum likelihood estimators are unbiased and consistent for both regression and dispersion parameters. In addition, the nature of the deviance surfaces suggests that these parameters are also orthogonal for most of the parameter space, which is advantageous for interpretation, inference and computational efficiency. Study of the distribution's properties, through a consideration of dispersion, zero-inflation and heavy tail indexes, together with the results of data analyses show the flexibility over standard approaches. The computational routines and datasets are available in the supplementary material.