Title: A Bayesian mixture of finite mixtures for jointly modeling ratings and rankings
Abstract: Rankings and ratings are commonly used to express preferences over a given collection of objects or individuals such as movies, grant proposals, or political candidates. Rankings give ordinal and scale-free comparisons but lack granularity; ratings provide cardinal and granular assessments but may be highly subjective or inconsistent. Because of this distinct and complementary information, collecting and analyzing rankings and ratings jointly may therefore be advantageous for understanding preferences. However, individual preferences may differ according to a latent construct such as a scientific or voter ideology. This talk presents a flexible, joint statistical model for rankings and ratings that allows us to capture heterogeneous preferences: the Bradley-Terry-Luce-Binomial (BTL-Binomial). We employ a Bayesian mixture of finite mixtures (MFM) approach to estimate heterogeneous preferences, understand their inherent uncertainty, and make accurate decisions based on ranking and ratings jointly. We demonstrate the efficiency and practicality of the BTL-Binomial MFM approach on real and simulated datasets of ranking and rating preferences in peer review and survey data contexts.