A heterogeneous multivariate probit model with cross effects of marketing variables to analyse cross category dependences

第一项任务是选择那些产品类别，在这些类别中，应使用两种营销措施，但其最大数量受到限制。要最大化的目标函数是考虑所有25个类别的销售收入。对于有或没有营销变量交叉影响的多变量概率模型，应该确定产品类别的选择。应对两种模型的选择结果进行比较。为了解决这个优化问题，必须开发一个合适的模拟退火法。第二个任务是研究通过形成产品类别簇而得到的较简单的多变量概率模型是否仍然具有良好的统计性能。通过只允许属于同一集群的产品类别之间的营销变量的交叉影响，实现了较低的模型复杂性。星团的形成既是先验的，也是由必须开发的有限混合模型形成的。这个有限混合模型将被整合到多变量概率模型的整体估计过程中。应以与原始模型相同的方式(例如，通过模拟退火法)得出这些模型的管理影响。

The first task consist in selecting those product categories in which two marketing measures should be used subject to restrictions on their maximum numbers. The objective function to be maximized is sales revenue across all 25 categories considered.. Selection of product categories should be determined for multivariate probit models both with and without cross effects of marketing variables. Selection results on the basis of both models should be compared. To solve tthe optimization proble an appropriate simulated annealing algorithm should be developed.The second task consists in investigating if less complex multivariate probit models obtained by forming clusters of product categories still attain a good statistical performance. Lower model complexity is achieved by allowing cross effects of marketing variables only between product categories which belong to the same cluster. Clusters are formed both a priori and alternatively by a finite mixture model which has to be developed. This finite mixture model will be integrated into the overall estimation process of the multivariate probit model. Managerial implications for these models should be derived in the same way (e.g., by simulated annealing) as for the original models.