Algorithms and diagnostics for the analysis of preference rankings with the Extended Plackett-Luce model

Abstract: 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 discrete 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 with order constraints on the reference order parameter. The restrictions for the discrete parameter reflect a meaningful rank assignment process and, in combination with the data augmentation strategy and the conjugacy of the Gamma prior distribution with the EPL, facilitate the construction of a tuned joint Metropolis-Hastings algorithm within Gibbs sampling to simulate from the posterior distribution. We additionally propose a novel model diagnostic to assess the adequacy of the EPL parametric specification. The usefulness of the proposal is illustrated with applications to simulated and real datasets.