The analysis of rank ordered data has a long history in the statistical literature across a diverse range of applications. In this paper we consider the Extended Plackett-Luce model that induces a flexible (discrete) distribution over permutations. The parameter space of this distribution is a combination of potentially high-dimensional discrete and continuous components and this presents challenges for parameter interpretability and also posterior computation. Particular emphasis is placed on the interpretation of the parameters in terms of observable quantities and we propose a general framework for preserving the mode of the prior predictive distribution. Posterior sampling is achieved using an effective simulation based approach that does not require imposing restrictions on the parameter space. Working in the Bayesian framework permits a natural representation of the posterior predictive distribution and we draw on this distribution to make probabilistic inferences and also to identify potential lack of model fit. The flexibility of the Extended Plackett-Luce model along with the effectiveness of the proposed sampling scheme are demonstrated using several simulation studies and real data examples.
The authors are grateful to an Associate Editor and two anonymous reviewers for their comments and suggestions on an earlier version of this paper. This work forms part of the Ph.D. dissertation of the first author, funded by Newcastle University, UK.
"On Bayesian inference for the Extended Plackett-Luce model." Bayesian Anal. Advance Publication 1 - 26, 2021. https://doi.org/10.1214/21-BA1258