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.

翻译：针对消费者在不同商品组合中的选择数据，一个关键挑战是构建能够描述和预测消费者选择行为的简约模型。边际分布模型便是其中一种选择模型，该模型仅需指定备选方案随机效用的边际分布即可解释选择数据。本文精确刻画了该模型能表征的选择概率集合，并证明验证选择概率数据与该模型的一致性等价于求解一个多项式规模的线性规划。我们将结果扩展至基于效用边际分布对备选方案进行分组的情形。基于可表征性条件，我们通过求解混合整数凸规划获得选择数据的最佳拟合，并提出了针对未观测商品组合选择概率的新型预测区间。数值实验表明：边际分布模型在表征能力、估计性能与预测精度上显著优于多项式Logit模型，且计算性能远优于随机效用模型。