Modelling and Analysis of Rank Ordered Data with Ties via a Generalized Plackett-Luce Model

Abstract

Bayesian inference for a simple generative model for rank ordered data with ties is considered. 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.