Bayesian mixture of Plackett-Luce models for partially ranked data

The Plackett-Luce model is one of the most popular and frequently applied parametric distributions to analyze partial top-rankings of a finite set of items. A Bayesian finite mixture of Plackett-Luce models is illustrated, that extends a Bayesian device recently introduced in the literature in order to account for unobserved sample heterogeneity. We describe an efficient way to incorporate the latent group structure in the data augmentation approach and how to interpret existing maximum likelihood procedures as special instances of the proposed Bayesian analysis. Bayesian inference is conducted with the combination of the Expectation-Maximization algorithm for maximum a posteriori estimation and the Gibbs sampling iterative procedure, with a focus on the identifiability problems that can affect the results of the MCMC technique. The novel Bayesian Plackett- Luce mixture is illustrated with an analysis of real preference partially ranked data, which discusses the application of several relabeling algorithms to solve the label-switching issue and the resulting posterior estimates.