Joint latent space models for ranking data and social network

Human interaction and communication has become one of the essential features of social life. Individuals' preference may be influenced by those of their peers or friends in a social network. In the literature, individuals' rank-order preferences and their social network are often modeled separately. In this article, we propose a new joint probabilistic model for ranking data and social network. With a latent space for all the individuals and items, the proposed model assume that the social network and rankings of items are governed by the locations of individuals and items. Based on an efficient MCMC algorithm, we develop a set of Bayesian inference approaches for the proposed model, including procedures of model selection, criteria to evaluate model fitness and a test for conditional independence between individuals' rankings and their social network given their positions in the latent space. Simulation studies reveal the usefulness of our proposed methods for parameter estimation, model fitness evaluation, model selection and conditional independence testing. Finally, we apply our model to the CiaoDVD dataset which consists of users' trust relations and their implicit preferences on DVD categories.