A standard assumption in the fitting of unordered multinomial response models for J mutually exclusive nominal categories, on cross-sectional or longitudinal data, is that the responses arise from the same set of J categories between subjects. However, when responses measure a choice made by the subject, it is more appropriate to assume that the distribution of multinomial responses is conditioned on a subject-specific consideration set, where this consideration set is drawn from the power set of {1,2,...,J}. Because the cardinality of this power set is exponential in J, estimation is infeasible in general. In this paper, we provide an approach to overcoming this problem. A key step in the approach is a probability model over consideration sets, based on a general representation of probability distributions on contingency tables. Although the support of this distribution is exponentially large, the posterior distribution over consideration sets given parameters is typically sparse, and is easily sampled as part of an MCMC scheme that iterates sampling of subject-specific consideration sets given parameters, followed by parameters given consideration sets. The effectiveness of the procedure is documented in simulated longitudinal data sets with J=100 categories and real data from the cereal market with J=73 brands.

翻译：在无序多项响应模型拟合中，针对J个互斥名义类别，基于横截面或纵向数据，一个标准假设是响应均来自主体间相同的J个类别集。然而，当响应反映主体所作的选择时，更合理的假设是：多项响应的分布受限于主体特定的考虑集，该考虑集从{1,2,...,J}的幂集中抽取。由于该幂集的基数随J呈指数增长，估计在一般情况下不可行。本文提出了一种克服该问题的方法。该方法的关键步骤是基于列联表概率分布的一般表示，构建考虑集的概率模型。尽管该分布的支持集呈指数级规模，但给定参数后考虑集的后验分布通常稀疏，且易于通过MCMC方案采样——该方案交替采样给定参数下的主体特定考虑集，以及给定考虑集后的参数。通过包含J=100个类别的模拟纵向数据集和包含J=73个品牌的谷物市场真实数据，验证了该方法的有效性。