Mean and variance modeling of under-dispersed and over-dispersed grouped binary data

Abstract

This article describes the R package BinaryEPPM and its use in determining maximum likelihood estimates of the parameters of extended Poisson process models for grouped binary data. These provide a Poisson process family of flexible models that can handle unlimited under-dispersion but limited over-dispersion in such data, with the binomial distribution being a special case. Within BinaryEPPM, models with the mean and variance related to covariates are constructed to match a generalized linear model formulation. Combining such under-dispersed models with standard over-dispersed models such as the beta binomial distribution provides a very general form of residual distribution for modeling grouped binary data. Use of the package is illustrated by application to several data-sets.