Abstract
This article describes the R package CountsEPPM and its use in determining maximum likelihood estimates of the parameters of extended Poisson process models. These provide a Poisson process based family of flexible models that can handle both underdispersion and overdispersion in observed count data, with the negative binomial and Poisson distributions being special cases. Within CountsEPPM models with mean and variance related to covariates are constructed to match a generalized linear model formulation. Use of the package is illustrated by application to several published datasets.
Highlights
Modeling using extended Poisson process models (EPPMs) was originally developed in Faddy (1997), where the construction of discrete probability distributions having very general dispersion properties was described
Faddy and Smith (2008) incorporated covariate dependence in the mean via a reparameterization using an approximate form of the mean; and Faddy and Smith (2011) extended this to incorporate covariate dependence in the dispersion, this being achieved by a reparameterization using an approximate form of the variance
The supplementary material for Faddy and Smith (2011) contained R code illustrating fitting these models. This R code has been extended and generalized to have inputs and outputs more akin to those of a generalized linear model (GLM) as in the R function glm and the R function betareg (Cribari-Neto and Zeileis 2010, Grün, Kosmidis, and Zeileis 2012). Both Hilbe (2011) and Hilbe (2014) have comments about a software package for EPPMs being developed in the R system (R Core Team 2016); the package CountsEPPM (Smith and Faddy 2016) whose use is described in this article is that software
Summary
Modeling using extended Poisson process models (EPPMs) was originally developed in Faddy (1997), where the construction of discrete probability distributions having very general dispersion properties was described. The supplementary material for Faddy and Smith (2011) contained R code illustrating fitting these models This R code has been extended and generalized to have inputs and outputs more akin to those of a generalized linear model (GLM) as in the R function glm and the R function betareg (Cribari-Neto and Zeileis 2010, Grün, Kosmidis, and Zeileis 2012). Both Hilbe (2011) and Hilbe (2014) have. The important differences between versions 1.0 and 2.0, 2.1 involve the use of arguments formula and data when running the function CountsEPPM
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