Bivariate Negative Binomial and Multinomial Models

Abstract

In this chapter, the generalized linear models for bivariate negative binomial or more specifically negative multinomial and bivariate multinomial models are presented. It is often necessary to use multinomial and negative binomial distributions for representing a set of counts as possible outcomes. In other words, these models can be used as alternative to Poisson models in case of under- or overdispersion. An alternative procedure for addressing the overdispersion problem is illustrated in this chapter based on the connection between Poisson and multinomial for both marginal and conditional models which are used to develop the bivariate multinomial model. Tests for goodness of fit, overdispersion, and comparison of models are also shown for bivariate count data using both negative multinomial and bivariate multinomial models. The estimation and test procedures are illustrated with examples. For comparison of models, a generalized Voung test is also illustrated.