Ricerc@Sapienza

The project focuses on the extension of parametric modeling for ranked data within the Bayesian framework, with a special attention on methodological and computational innovations for an efficient implementation of ranking data analysis. The ranking literature offers numerous parametric distributions but, despite the large availability of options, models in their basic form are often unable to embody the appropriate flexibility to represent sample heterogeneity. Consequently, it is natural to extend them to the mixture context for capturing possible patterns of rankers with similar preferences. Our interest concerns the finite mixture approach from the Bayesian inferential perspective, by developing a generalization of the popular Plackett-Luce model (PL) as mixture component. The PL assumes that the ranking process is performed sequentially by assigning the ranks from the top to the bottom one (forward order). A recent extension relaxed this assumption with the addition of the reference order parameter, yielding the novel Extended PL (EPL). A first contribution could be the investigation of a restricted version of the EPL with order constraints on the reference order that reflect a sensible and interpretable rank assignment process. The parameter restrictions could be fruitfully combined with the data augmentation strategy for the mixture setting and the existence of a conjugate prior to ease the construction of an MCMC algorithm and hence the Bayesian estimation of the new mixture model. From a computational perspective, ranking data analysis can be challenging due to the special structure of observations taking values in the set of permutations. This typically requires the development of specialised software which is not available for a wider use. The project additionally aims at building an R package to promote the use of sophisticated ranking models in practice. The usefulness of the proposals will be widely investigated with applications to real experiments.