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A bivariate Sarmanov regression model for count data with generalised Poisson marginals
Authors:Vera Hofer  Johannes Leitner
Institution:Department of Statistics and Operations Research , University of Graz , Universit?tsstra?e 15/E3, 8010 , Graz , Austria
Abstract:We present a bivariate regression model for count data that allows for positive as well as negative correlation of the response variables. The covariance structure is based on the Sarmanov distribution and consists of a product of generalised Poisson marginals and a factor that depends on particular functions of the response variables. The closed form of the probability function is derived by means of the moment-generating function. The model is applied to a large real dataset on health care demand. Its performance is compared with alternative models presented in the literature. We find that our model is significantly better than or at least equivalent to the benchmark models. It gives insights into influences on the variance of the response variables.
Keywords:bivariate count data  overdispersion  Sarmanov distribution  generalised Poisson distribution  health care demand
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