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

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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.