A New Multivariate Count Data Model to Study Multi-Category Physician Prescription Behavior

51 Pages Posted: 7 Feb 2009 Last revised: 22 Mar 2018

See all articles by Xiaojing Dong

Xiaojing Dong

Santa Clara University - Marketing

Pradeep K. Chintagunta

University of Chicago

Puneet Manchanda

University of Michigan, Stephen M. Ross School of Business

Date Written: January 31, 2011

Abstract

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 and account for endogeneity in detailing decisions.

Suggested Citation

Dong, Xiaojing and Chintagunta, Pradeep K. and Manchanda, Puneet, A New Multivariate Count Data Model to Study Multi-Category Physician Prescription Behavior (January 31, 2011). Chicago Booth School of Business Research Paper No. 09-10. Available at SSRN: https://ssrn.com/abstract=1339142 or http://dx.doi.org/10.2139/ssrn.1339142

Xiaojing Dong (Contact Author)

Santa Clara University - Marketing ( email )

Santa Clara, CA 95053
United States

Pradeep K. Chintagunta

University of Chicago ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-702-8015 (Phone)
773-702-0458 (Fax)

Puneet Manchanda

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States
734-936-2445 (Phone)
734-936-8716 (Fax)

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