The project focuses on parametric modelling of ranking data, aiming at introducing a series of methodological advances and efficient computational strategies to enhance the analysis of preferences from ranked data. Our research interests concern the class of Mallows models (MMs), relying on the distance notion among permutations and occupying a central role in the ranking literature. Despite the wide range of metrics, the choice is typically limited to the Kendall or Cayley metrics, due to the related analytical simplifications. Within our project, we intend to go beyond these conventional few options and explore the formal properties of the MM with the Spearman distance (theta-model). The attractive feature of this model is its correspondence with the restriction of the normal distribution over the permutation set, for which it is expected to enjoy convenient closed-form expressions that could solve the critical estimation of the modal ranking. This means that, differently from the MMs with the other metrics, efficient and accurate inferential procedures could be developed, where the computational burden of inferring the discrete parameter is significantly reduced. The possibility of relaxing the exploration of the permutation space would favor the analysis of rankings of many alternatives, as well as the handling of censored observations via data augmentation. Additionally, an efficient estimation within the finite mixture framework is still an open area of research, to be pursued for enlarging the applicability of theta-models to samples characterized by a group structure. We stress that these further novelties require a methodological effort to construct new approximations of the Spearman distance distribution and the study of their behaviour under various model parameters settings and number of items. Another contribution will concern the release of a new R package to fill the gap of publicly available softwares to implement theta-models and mixtures thereof.
