Bayesian Plackett-Luce Mixture Models for Partially Ranked Data

Area of Science:

• Psychology
• Behavioral Science
• Statistics

Background:

• Ordinal judgments on multiple alternatives are crucial in psychological and behavioral experiments.
• The Plackett-Luce model is a standard for analyzing item rankings.
• Unobserved sample heterogeneity often complicates the analysis of preference data.

Purpose of the Study:

• To introduce a Bayesian finite mixture of Plackett-Luce models.
• To address unobserved sample heterogeneity in partially ranked data.
• To provide a flexible framework for analyzing preference and choice orientation.

Main Methods:

• Developed a Bayesian finite mixture of Plackett-Luce models.
• Incorporated latent group structure using a data augmentation approach.
• Utilized Expectation-Maximization (EM) and Gibbs sampling for inference.
• Investigated Bayesian criteria for mixture configuration selection and diagnostic tools.

Main Results:

• The proposed Bayesian method efficiently accounts for sample heterogeneity.
• Existing maximum likelihood procedures are shown as special cases.
• Demonstrated utility with simulated and real preference ranked data.
• Bayesian criteria and diagnostic tools aid in model selection and assessment.

Conclusions:

• The novel Bayesian Plackett-Luce mixture effectively characterizes sample heterogeneity in preference data.
• Accurate diagnostic checks are vital for understanding heterogeneous partial ranking data.
• The method offers a robust alternative to frequentist and nonparametric approaches.