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Given data on the choices made by consumers for different offer sets, a keychallenge is to develop parsimonious models that describe and predict consumerchoice behavior while being amenable to prescriptive tasks such as pricing andassortment optimization. The marginal distribution model (MDM) is one suchmodel, that requires only the specification of marginal distributions of therandom utilities. This paper aims to establish necessary and sufficientconditions for given choice data to be consistent with the MDM hypothesis,inspired by the utility of similar characterizations for the random utilitymodel (RUM). This endeavor leads to an exact characterization of the set ofchoice probabilities that the MDM can represent. Verifying the consistency ofchoice data with this characterization is equivalent to solving apolynomial-sized linear program. Since the analogous verification task for RUMis computationally intractable and neither of these models subsumes the other,MDM is helpful in striking a balance between tractability and representationalpower. The characterization is convenient to be used with robust optimizationfor making data-driven sales and revenue predictions for new unseenassortments. When the choice data lacks consistency with the MDM hypothesis,finding the best-fitting MDM choice probabilities reduces to solving a mixedinteger convex program. The results extend naturally to the case where thealternatives can be grouped based on the similarity of the marginaldistributions of the utilities. Numerical experiments show that MDM providesbetter representational power and prediction accuracy than multinominal logitand significantly better computational performance than RUM.

A Nonparametric Approach with Marginals for Modeling Consumer Choice