Social order statistics models for ranking data with analysis of preferences in social networks

Abstract

In the National Longitudinal Study of Adolescent to Adult Health (Add Health) in the United States during the 1994–95 school year, sampled high school students were asked to rank 17 romantic relationship activities in ideal chronological order and to nominate up to five male and five female best friends within the school. It is natural to see that the students’ rank-order progression of social, romantic and sexual relationships may be influenced strongly by their peers or friends. So far, traditional ranking models do not account for such social network dependency. In this article we introduce a new class of models, called social order statistics (SOS) models, to learn ranking data in social networks. The new models combine the order statistics models and spatial autoregressive models to account for social dependencies among the individuals. A flexible formulation of weight matrices in the spatial model is adopted to provide diverse network effects among the individuals for different items. Efficient and scalable MCMC algorithms are developed to perform Bayesian inference in a parallel manner for large networks with even a few thousand nodes. Analysis of the Add Health dataset reveals that social network effects are different for students’ preferences toward different activities in a relationship. In particular, students’ preferences on romantic and sexual events generally have stronger peer effects than those on social events, and opinions of close friends of the same gender tend to have a larger impact on the preferences on sexual events.