Bayesian analysis of ranking data with the constrained Extended Plackett-Luce model

TL;DR

This paper introduces a Bayesian estimation method for the Extended Plackett-Luce model with order constraints, improving inference on ranking data by leveraging data augmentation and MCMC techniques.

Contribution

It develops a Bayesian framework with order constraints for the EPL, enhancing inference accuracy and uncertainty assessment over previous frequentist methods.

Findings

Effective Bayesian estimation demonstrated on simulated data

Application to real datasets shows practical utility

Improved inference on reference order parameter

Abstract

Multistage ranking models, including the popular Plackett-Luce distribution (PL), rely on the assumption that the ranking process is performed sequentially, by assigning the positions from the top to the bottom one (forward order). A recent contribution to the ranking literature relaxed this assumption with the addition of the discrete-valued reference order parameter, yielding the novel Extended Plackett-Luce model (EPL). Inference on the EPL and its generalization into a finite mixture framework was originally addressed from the frequentist perspective. In this work, we propose the Bayesian estimation of the EPL with order constraints on the reference order parameter. The proposed restrictions reflect a meaningful rank assignment process. By combining the restrictions with the data augmentation strategy and the conjugacy of the Gamma prior distribution with the EPL, we facilitate the construction of a tuned joint Metropolis-Hastings algorithm within Gibbs sampling to simulate from the posterior distribution. The Bayesian approach allows to address more efficiently the inference on the additional discrete-valued parameter and the assessment of its estimation uncertainty. The usefulness of the proposal is illustrated with applications to simulated and real datasets.