Modeling Overdispersion in R

Abstract

The book Overdispersion Models in SAS by Morel and Neerchal (2012) discusses statistical analysis of categorical and count data which exhibit overdispersion, with a focus on computational procedures using SAS. This document retraces some of the ground covered in the book, which we abbreviate throughout as OMSAS, with the objective of carrying out similar analyses in R (R Core Team, 2014). Rather than attempting to cover every example in OMSAS, we will focus on two specific goals: analysis based on binomial/multinomial likelihoods which support extra variation, and model selection with the binomial goodness-of-fit (GOF) test. We will not cover examples based on count data, but extension to those should not be difficult. We will generally not spend much time discussing the data, on justification for the selected models, or on interpretation of the results. The reader should refer to OMSAS for more complete discussions of the examples and statistical models. In several places we will present additional material not found in OMSAS, such as the binomial finite mixture and the recently proposed Mixture Link binomial model.