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.

翻译：针对消费者在不同商品组合中做出选择的数据，核心挑战在于构建能够描述和预测消费者选择行为的简约模型。边际分布模型是其中一种选择模型，它仅需指定各选项随机效用的边际分布即可解释选择数据。本文给出了可通过边际分布模型一致表示的（任意商品组合集合上的）选择概率集的精确刻画。考虑基于效用边际分布对选项进行分组的可能性，我们证明了：（a）在多项式时间内可验证选择概率数据与该模型的一致性；（b）寻找最优拟合解可归结为求解混合整数凸规划问题。研究结果表明，与多项Logit模型相比，边际分布模型具有更强的表征能力；与随机效用模型相比，其计算性能显著更优。