Scalable Estimation of Multinomial Response Models with Random Consideration Sets

研究问题: 当不同消费者只考虑部分备选项时，如何估计具有随机考虑集的多项选择模型，并应对备选项数量增长带来的计算困难？
方法与思路: 作者将考虑集分布表示为纳入与排除概率乘积的混合，并利用时间不变考虑集下的后验稀疏性构建可扩展 MCMC。
材料陈述的贡献: 摘要称，在正则条件下响应概率与参数后验一致，并以包含一百零一个品牌的每周谷物购买纵向数据展示方法。
阅读关注点: 应核对混合表示与参数识别的关系、一致性所需条件、考虑集时间不变假设，以及算法复杂度、收敛和应用拟合。
阅读边界: 依据 arXiv 2308.12470v5 预印本摘要；不能据此声称该版本已同行评审或被期刊接收，也不能推断 DOI 对应刊本的条件与变化。

GPT-6.1 Sol · 高 · 2026-10-10

原文摘要

A common assumption in the fitting of unordered multinomial response models for $J$ mutually exclusive categories is that the responses arise from the same set of $J$ categories across subjects. However, when responses measure a choice made by the subject, it is more appropriate to condition the distribution of multinomial responses on a subject-specific consideration set, drawn from the power set of $\{1,2,\ldots,J\}$ . This leads to a mixture of multinomial response models governed by a probability distribution over the $J^{\ast} = 2^J -1$ consideration sets. We introduce a novel method for estimating such generalized multinomial response models based on the fundamental result that any mass distribution over $J^{\ast}$ consideration sets can be represented as a mixture of products of $J$ component-specific inclusion-exclusion probabilities. Moreover, under time-invariant consideration sets, the conditional posterior distribution of consideration sets is sparse. These features enable a scalable MCMC algorithm for sampling the posterior distribution of parameters, random effects, and consideration sets. Under regularity conditions, the posterior distributions of the marginal response probabilities and the model parameters satisfy consistency. The methodology is demonstrated in a longitudinal data set on weekly cereal purchases that cover $J = 101$ brands, a dimension substantially beyond the reach of existing methods.A common assumption in the fitting of unordered multinomial response models for $J$ mutually exclusive categories is that the responses arise from the same set of $J$ categories across subjects. However, when responses measure a choice made by the subject, it is more appropriate to condition the distribution of multinomial responses on a subject-specific consideration set, drawn from the power set of $\{1,2,\ldots,J\}$. This leads to a mixture of multinomial response models governed by a probability distribution over the $J^{\ast} = 2^J -1$ consideration sets. We introduce a novel method for estimating such generalized multinomial response models based on the fundamental result that any mass distribution over $J^{\ast}$ consideration sets can be represented as a mixture of products of $J$ component-specific inclusion-exclusion probabilities. Moreover, under time-invariant consideration sets, the conditional posterior distribution of consideration sets is sparse. These features enable a scalable MCMC algorithm for sampling the posterior distribution of parameters, random effects, and consideration sets. Under regularity conditions, the posterior distributions of the marginal response probabilities and the model parameters satisfy consistency. The methodology is demonstrated in a longitudinal data set on weekly cereal purchases that cover $J = 101$ brands, a dimension substantially beyond the reach of existing methods.

摘要来源：arXiv 2308.12470v5 · 预印本版本摘要

笔记与分组

分类依据与纠错

Scalable Estimation of Multinomial Response Models with Random Consideration Sets

代码、数据与补充材料

随机考虑集多项响应模型的可扩展估计

原文摘要

同方向的基础文献

相关领域论文