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Choice behavior and preferences typically involve numerous and subjectiveaspects that are difficult to be identified and quantified. For this reason,their exploration is frequently conducted through the collection of ordinalevidence in the form of ranking data. A ranking is an ordered sequenceresulting from the comparative evaluation of a given set of items according toa specific criterion. Multistage ranking models, including the popularPlackett-Luce distribution (PL), rely on the assumption that the rankingprocess is performed sequentially, by assigning the positions from the top tothe bottom one (forward order). A recent contribution to the ranking literaturerelaxed this assumption with the addition of the discrete reference orderparameter, yielding the novel Extended Plackett-Luce model (EPL). Inference onthe EPL and its generalization into a finite mixture framework was originallyaddressed from the frequentist perspective. In this work, we propose theBayesian estimation of the EPL with order constraints on the reference orderparameter. The restrictions for the discrete parameter reflect a meaningfulrank assignment process and, in combination with the data augmentation strategyand the conjugacy of the Gamma prior distribution with the EPL, facilitate theconstruction of a tuned joint Metropolis-Hastings algorithm within Gibbssampling to simulate from the posterior distribution. We additionally propose anovel model diagnostic to assess the adequacy of the EPL parametricspecification. The usefulness of the proposal is illustrated with applicationsto simulated and real datasets.

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