Extending parametric models for ranked data

The thesis deals with the problem of analyzing ranking data and focuses, in particular, on the probabilistic modeling of complete/partial rankings drawn from populations with an underlying group composition. After a structured review of the literature on statistical ranking models, the dissertation concentrates on the stagewise parametric modeling and, in this context, develops some original extensions of the popular Plackett-Luce model, aimed at accounting for the order in the ranking elicitation process. The thesis further generalizes such contributions to the finite mixture framework to address heterogeneous configurations of the target population. Corresponding inferential procedures are detailed and rely on a hybrid iterative technique that, in order to efficiently solve the likelihood optimization over a mixed-type parameter space, combines the ordinary EM scheme with Minorization-Maximization algorithm. As additional contribution the dissertation illustrates a Bayesian finite mixture of Plackett-Luce models, that extends a Bayesian device recently introduced in the literature. It describes 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 EM algorithm for maximum a posteriori estimation and the Gibbs sampling procedure, paying special attention on the identifiability problems that can affect the results of the MCMC technique. The practical relevance of the methodological proposals are illustrated with applications to both simulated and real data sets.