Bayesian mixture of Plackett-Luce models for partially ranked data

TL;DR

This paper introduces a Bayesian mixture of Plackett-Luce models to better analyze partially ranked data, capturing unobserved heterogeneity and improving inference through efficient algorithms and diagnostic tools.

Contribution

It develops a Bayesian finite mixture model for partially ranked data, integrating latent group structure and providing novel inference and model selection methods.

Findings

Effective Bayesian inference for heterogenous ranking data

Comparison shows improved performance over frequentist and nonparametric methods

Diagnostic tools enhance understanding of ranking data heterogeneity

Abstract

The elicitation of an ordinal judgment on multiple alternatives is often required in many psychological and behavioral experiments to investigate preference/choice orientation of a specific population. The Plackett-Luce model is one of the most popular and frequently applied parametric distributions to analyze rankings of a finite set of items. The present work introduces a Bayesian finite mixture of Plackett-Luce models to account for unobserved sample heterogeneity of partially ranked data. We describe an efficient way to incorporate the latent group structure in the data augmentation approach and the derivation of existing maximum likelihood procedures as special instances of the proposed Bayesian method. Inference can be conducted with the combination of the Expectation-Maximization algorithm for maximum \textit{a posteriori} estimation and the Gibbs sampling iterative procedure. We additionally investigate several Bayesian criteria for selecting the optimal mixture configuration and describe diagnostic tools for assessing the fitness of ranking distributions conditionally and unconditionally on the number of ranked items. The utility of the novel Bayesian parametric Plackett-Luce mixture for characterizing sample heterogeneity is illustrated with several applications to simulated and real preference ranked data. We compare our method with the frequentist approach and a Bayesian nonparametric mixture model both assuming the Plackett-Luce model as a mixture component. Our analysis on real datasets reveals the importance of an accurate diagnostic check for an appropriate in-depth understanding of the heterogenous nature of the partial ranking data.