Copula-Based Simultaneous Approach to Multivariate Alternative Choice and Quantity Choice

This paper aims to examine correlations in shopping situations. First, there is a certain amount of correlation between alternative choices. Specifically, the alternatives from different categories but from a same brand might be purchased together. Second, alternative choice and quantity choice could be correlated each other. A consumer tends to purchase tooth paste with large amount, but hand cream with small amount. Third, quantity choices could be correlated each other. The purchased quantity of fabric softener should depend on the purchased quantity of laundry detergent. To explain these correlations, the model must deal with multivariate incidence and quantity outcomes. Therefore, we developed a new copula-based approach to simultaneously deal with them, so that it could directly control and capture the correlations. Also, we found that if the copula function is a multivariate-FGM copula, then the likelihood is closed form that is easy to estimate. We apply this model to IRI scanner panel data and estimate the model by using Bayesian method. In this data set, we could find strong dependencies between alternative choices, between alternative choice and quantity choice, and between quantity choices. In addition, more efficient promotion strategy of two products from a same brand but different categories is drawn from our model