Menu-choice modeling with interactions and heterogeneous correlated preferences

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This study focuses on the menus typically found in the marketplace (e.g., restaurants and Internet vendors), where the consumer may choose one or more from dozens of options or menu items, each at a posted price or fee. We show that modeling choices out of the typical menu leads to the “curse of dimensionality,” which transpires in two ways. First, the choice set (all possible menu selections) grows geometrically with the number of items in the menu. Second, the number of interactions among menu items also grows disproportionately to the number of items in the menu. We propose a menu choice model that circumvents these two problems in a feasible and flexible, but parsimonious way.We test the proposed model on synthetic data from Monte-Carlo simulations and find that the proposed estimation approach produces consistent parameter estimates while significantly reducing the dimensionality of the problem. We then apply the proposed approach to an actual choice experiment where a sample of consumers made multiple choices from eight different menus, each combining a base system with selections from 25 optional features. Our empirical results show that menu items do interact (positively or negatively) and the proposed approach produces a graphical representation of these interactions. We also perform an optimal pricing policy experiment to further illustrate the practical features of the proposed menu-choice modeling approach.