A Bayesian Approach to Estimate Causal Peer Influence Accounting for Latent Network Homophily

Abstract: Researchers have focused on understanding how individual's behavior is influenced by the behaviors of their peers in observational studies of social networks. Identifying and estimating causal peer influence, however, is challenging due to confounding by homophily, where people tend to connect with those who share similar characteristics with them. Moreover, since all the attributes driving homophily are generally not always observed and act as unobserved confounders, identifying and estimating causal peer influence becomes infeasible using standard causal identification assumptions. In this paper, we address this challenge by leveraging latent locations inferred from the network itself to disentangle homophily from causal peer influence, and we extend this approach to multiple networks by adopting a Bayesian hierarchical modeling framework. To accommodate the nonlinear dependency of peer influence on individual behavior, we employ a Bayesian nonparametric method, specifically Bayesian Additive Regression Trees (BART), and we propose a Bayesian framework that accounts for the uncertainty in inferring latent locations. We assess the operating characteristics of the estimator via extensive simulation study. Finally, we apply our method to estimate causal peer influence in advice-seeking networks of teachers in secondary schools, in order to assess whether the teachers' belief about mathematics education is influenced by the beliefs of their peers from whom they receive advice. Our results suggest that, overlooking latent homophily can lead to either underestimation or overestimation of causal peer influence, accompanied by considerable estimation uncertainty.