Modeling Preferences: A Bayesian Mixture of Finite Mixtures for Rankings and Ratings

• 成果类型: Article; Early Access
• 署名作者: Pearce, Michael; Erosheva, Elena A.
• 署名单位: Reed College - Portland; University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2444700
• 发表日期: 2025
• 关键词: NUMBER; score

摘要

Rankings and ratings are commonly used to express preferences but provide distinct and complementary information. Rankings give ordinal and scale-free comparisons but lack granularity; ratings provide cardinal and granular assessments but may be highly subjective or inconsistent. Collecting and analyzing rankings and ratings jointly has not been performed until recently due to a lack of principled methods. In this work, we propose a flexible, joint statistical model for rankings and ratings-the Bradley-Terry-Luce-Binomial (BTL-Binomial). The model captures rater effects and preference heterogeneity, respectively, with judge-specific random effects and a latent class mixture framework where the number of classes is unknown a priori. We propose computationally-efficient estimation via a Bayesian mixture of finite mixtures (MFM) approach. Finally, we demonstrate statistical inference and decision-making based on rankings and ratings jointly through applications to real and simulated datasets in academic peer review. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.