Prof. M. Ataharul Islam, PhD
Department of Applied Statistics
East West University
Plenary Talk Title: Generalized Linear Models for Bivariate Count Data
Abstract: Dependence in outcome variables poses formidable difficulty in various fields including health sciences, traffic accidents, economics, actuarial science, social sciences, environmental studies, genetic studies, etc. A widely studied topic in bivariate modeling of count data is traffic accidents and number of fatalities. Bivariate Poisson distribution is commonly employed for modelling bivariate count data. Some attempts have been made in the past to develop bivariate Poisson model using a trivariate reduction method. Bivariate data provide the repeated measures for two time points or two events on same experimental units and the modeling of repeated measures data is a formidable challenge to researchers and users due to the fact that we need to take into account both the relationships between outcome variables as well as between outcome variables and covariates. In other words, dependence in outcome variables needs to be considered. Another important aspect concerning the Poisson models is the under or over-dispersion due to violation of the equality of mean and variance. A third problem associated with analysis of count data is truncation in the data for univariate or bivariate cases. In this paper, several models are developed using the extended generalized linear models for bivariate count data to address the problems of bivariate count modelling of correlated outcomes, truncation and under or over-dispersion. In addition, test procedures are also shown for both goodness of fit and under or over-dispersion. The proposed models and test procedures are illustrated with examples.