Statistical Modelling 20 (5) (2020), 443–466
Reparametrization of COM–Poisson regression models with applications in the analysis of experimental data
Eduardo E Ribeiro, Jr,
Department of Exact Sciences,
University of São Paulo ’ ESALQ,
Piracicaba, SP,
Brazil,
e-mail: jreduardo@usp.br
Walmes M Zeviani,
Department of Statistics,
Paraná Federal University,
Curitiba, PR,
Brazil.
Wagner H Bonat,
Department of Statistics,
Paraná Federal University,
Curitiba, PR,
Brazil.
Clarice GB Demetrio,
Department of Exact Sciences,
University of São Paulo ’ ESALQ,
Piracicaba, SP,
Brazil.
John Hinde,
School of Mathematics, Statistics and Applied Mathematics,
National University of Ireland Galway,
Galway,
Ireland.
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.
Keywords:
COM–Poisson, Count data, likelihood inference, overdispersion, underdispersion.
Downloads:
Example data, code and supplementary material can be found here.
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