Model-based clustering for multivariate partial ranking data

Abstract

This paper proposes the first model-based clustering algorithm dedicated to multivariate partial ranking data. This is an extension of the Insertion Sorting Rank (isr) model for ranking data, which has the dual property to be a meaningful model through its location and scale parameters description and to be a kind of “physical” model through its derivation from the ranking generating process assumed to be an insertion sorting algorithm. The heterogeneity of the rank population is modeled by a mixture of isr, whereas a conditional independence assumption allows the extension to multivariate ranking. Maximum likelihood estimation is performed through a SEM-Gibbs algorithm, and partial rankings are considered as missing data, that allows us to simulate them during the estimation process. After having validated the estimation algorithm as well as the robustness of the model on simulated datasets, three real datasets were studied: the 1980 American Psychological Association (APA) presidential election votes, the results of French students to a general knowledge test and the votes of the European countries to the Eurovision song contest. The proposed model appears to be relevant in comparison with the most standard competitor ranking models (when available) and leads to significant interpretation for each application. In particular, regional alliances between European countries are exhibited in the Eurovision contest, which are often suspected but never proved.