Correlation in Bivariate Poisson Regression Model

We consider a bivariate Poisson model that is based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed method using the data employed in one of the two aforementioned bivariate Poisson studies.