The Limit of the Marginal Distribution Model in 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 characterisation of the set of choice probabilities which are representable by the marginal distribution model consistently across any collection of assortments. Allowing for the possibility of alternatives to be grouped based on the marginal distribution of their utilities, we show (a) verifying consistency of choice probability data with this model is possible in polynomial time and (b) finding the closest fit reduces to solving a mixed integer convex program. Our results show that the marginal distribution model provides much better representational power as compared to multinomial logit and much better computational performance as compared to the random utility model.