A Nonparametric Approach with Marginals for Modeling Consumer Choice

Given data on choices made by consumers for different assortments, a key challenge is to develop parsimonious models that describe and predict consumer choice behavior. One such choice model is the marginal distribution model, which requires only the specification of the marginal distributions of the random utilities of the alternatives to explain choice data. In this paper, we develop an exact characterization of the set of choice probabilities that can be represented by this model and show that verifying the consistency of choice probability data with this model is equivalent to solving a polynomial-size linear program. We extend these results to the case where alternatives are grouped based on the marginal distribution of their utilities. Based on the representable conditions, we find the best-fit to the choice data that reduces to solving a mixed integer convex program and develop novel prediction intervals for the choice probabilities of unseen assortments. Our numerical results show that the marginal distribution model provides much better representational power, estimation performance, and prediction accuracy than multinomial logit and much better computational performance than the random utility model.