Models for Bivariate Count Data: Bivariate Poisson Distribution

Abstract

The dependence in the count outcome variables is observed in many instances in the fields of health sciences, traffic accidents, economics, actuarial science, social sciences, environmental studies, etc. A typical example of such dependence arises in the traffic accidents where the extent of physical injuries may lead to fatalities. The bivariate Poisson distribution has been developed following various assumptions. In this chapter, several bivariate Poisson models including bivariate GLM for Poisson–Poisson, generalized zero-truncated bivariate Poisson, right-truncated bivariate Poisson, and bivariate double Poisson are discussed. The generalized linear models are shown for analyzing bivariate count data and the over- or underdispersion problems are also discussed. The problem of truncation for bivariate count data is also highlighted in this chapter. Tests for over- or underdispersion as well as tests for goodness of fit are illustrated with examples.