Bayesian mixture of Extended Plackett-Luce models for the analysis of preference rankings

Choice behavior and preferences typically involve numerous and subjective aspects that are difficult to be identified and quantified. For this reason their exploration is frequently conducted through the collection of ordinal evidence in the form of ranking data. A ranking is an ordered sequence resulting from the comparative evaluation of a given set of items according to a specific criterion. 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 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 mixture. The Bayesian extension benefits from the data augmentation strategy and the conjugacy of the PL with the Gamma prior distribution, by making use of a Metropolis-Hastings step within the Gibbs Sampling scheme to simulate the discrete reference order parameter. The usefulness of the proposal is illustrated with applications to simulated and real datasets.