Modelling and analysis of rank ordered data with ties via a generalized Plackett-Luce model

TL;DR

This paper introduces a generalized Plackett-Luce (GPL) model for rank ordered data with ties, providing a flexible, tractable, and generative approach with efficient Bayesian inference methods, applicable to various real-world datasets.

Contribution

The paper proposes the GPL model as a novel, discrete counterpart to the PL model that handles ties and multiple comparisons, with closed-form likelihood and inference algorithms.

Findings

GPL model effectively handles data with ties and multiple comparisons

Inference algorithms are simple, efficient, and suitable for real data

Model demonstrates flexibility and predictive capability in applications

Abstract

A simple generative model for rank ordered data with ties is presented. The model is based on ordering geometric latent variables and can be seen as the discrete counterpart of the Plackett-Luce (PL) model, a popular, relatively tractable model for permutations. The model, which will be referred to as the GPL model, for generalized (or geometric) Plackett-Luce model, contains the PL model as a limiting special case. A closed form expression for the likelihood is derived. With a focus on Bayesian inference via data augmentation, simple Gibbs sampling and EM algorithms are derived for both the general case of multiple comparisons and the special case of paired comparisons. The methodology is applied to several real data examples. The examples highlight the flexibility of the GPL model to cope with a range of data types, the simplicity and efficiency of the inferential algorithms, and the ability of the GPL model to naturally facilitate predictive inference due to its simple generative construction.