A new multivariate count data model to study multi-category physician prescription behavior

Multivariate count models represent a natural way of accommodating data from multiple product categories when the dependent variable in each category is represented by a positive integer. In this paper, we propose a new simultaneous equation multi-category count data model–the Poisson-lognormal simultaneous equation model–that allows for the Poisson parameter in one equation to be a function of the Poisson parameters in other equations. While generally applicable to any situation where simultaneity is an issue and the dependent variables are measured as counts, such a specification is particularly useful for our empirical application where physicians prescribe drugs in multiple categories. Accounting for the endogeneity of detailing in such situations requires us to explicitly allow for pharmaceutical firms’ detailing activities in one category to be influenced by their activities in other categories. Estimation of such a system of equations using traditional maximum likelihood method is cumbersome, so we propose a simple solution based on using Markov Chain Monte Carlo methods. Our simulation study demonstrates the validity of the solution algorithm and the biases that would result if such simultaneity is ignored in the estimation process.We apply our methodology to study multi-category physician prescription behavior, while accounting for the endogeneity and simultaneity of firms’ detailing efforts within and across categories, at individual physician level. Substantively, we show that detailing responsiveness estimates, as well as their implications for physician segmentation and firms’ profits are significantly affected when we leverage data from multiple categories to account for endogeneity in detailing decisions.