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

机译：用于研究多类别医师处方行为的新的多元计数数据模型

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摘要

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.
机译：当每个类别中的因变量用正整数表示时，多元计数模型代表一种自然的方式来容纳来自多个产品类别的数据。在本文中，我们提出了一种新的联立方程多类别计数数据模型-Poisson-对数正态联立方程模型-该模型允许一个方程中的Poisson参数成为其他方程中的Poisson参数的函数。虽然通常适用于同时发生问题并且因变量以计数为单位的任何情况，但这种规范对于我们的经验应用特别有用，在该应用中，医生开出了多种类别的药物。考虑到这种情况下细节的内生性，我们需要明确允许制药公司在一类中的细节活动受到其另一类活动的影响。使用传统的最大似然法估算这样的方程组很麻烦，因此我们提出了一种基于马尔可夫链蒙特卡罗方法的简单解决方案。我们的仿真研究证明了求解算法的有效性，以及在估计过程中忽略这种同时性会导致的偏差。我们运用我们的方法来研究多类别医生的处方行为，同时考虑了公司在单个医生级别内和跨类别的详细说明工作的内生性和同时性。实质上，我们表明，当我们利用多个类别的数据来解释决策的内生性时，详细的响应度估计及其对医师细分和公司利润的影响会受到显着影响。

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