Applied Mathematical Sciences, Vol. 6, 2012, no. 137, 6843 - 6856 An EM Algorithm for Multivariate Mixed Poisson Regression Models and its Application M. E. Ghitany 1 , D. Karlis 2 , D.K. Al-Mutairi 1 and F. A. Al-Awadhi 1 1 Department of Statistics and Operations Research Faculty of Science, Kuwait University, Kuwait 2 Department of Statistics Athens University of Economics, Greece Abstract Although the literature on univariate count regression models allow- ing for overdispersion is huge, there are few multivariate count regression models allowing for correlation and overdiseprsion. The latter models can find applications in several disciplines such as epidemiology, mar- keting, sports statistics, criminology, just to name a few. In this paper, we propose a general EM algorithm to facilitate maximum likelihood estimation for a class of multivariate mixed Poisson regression models. We give specialemphasis to the multivariate negative binomial, Poisson inverse Gaussian and Poisson lognormal regression models. An applica- tion to a real dataset is also given to illustrate the use of the proposed EM algorithm to the considered multivariate regression models. Mathematics Subject Classification: 62J05, 65D15 Keywords: Mixed Poisson distributions, overdispersion, covariates, EM algorithm 1 Introduction Count data occur in several different disciplines. When only one count vari- able is considered the literature is vast. There are various models to fit such data and to make inferences on them. For example, traditionally one may use the simple Poisson distribution or extensions like mixed Poisson models which allow for overdispersion in the data (sample variance exceeds the sample mean). When considering jointly two or more count variables, things are more complicated and the literature is much smaller. Modeling correlated count