A general EM approach for maximum likelihood estimation in mixed Poisson regression models

An EM type algorithm for maximum likelihood estimation is proposed for the case of mixed Poisson regression models. The algorithm makes use of the mixture representation of such models. Two members of this family are examined in depth, the negative binomial regression model and the Poisson-inverse Gaussian regression model. Closed form expressions are derived for both models leading to easily programmable algorithms. Especially for the case of the Poisson-inverse Gaussian model no special numerical techniques are needed. The algorithms are applied to a real data set concerning crime data from Greece.