A Bayesian approach to estimate causal peer influence accounting for latent network homophily

Abstract Researchers have focused on understanding how an individual’s behaviour is influenced by their peers behaviours 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. Moreover, since all the attributes driving homophily are generally not always observed, 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 to disentangle homophily from causal peer influence, and extend this approach to multiple networks by adopting a Bayesian hierarchical modelling framework. To accommodate nonlinear peer influence on individual behaviour, we employ a Bayesian nonparametric method, Bayesian Additive Regression Trees, and propose a Bayesian framework that accounts for uncertainty in inferring latent locations. We assess the estimators' performance via simulations, and apply our method to advice-seeking networks of teachers in secondary schools, assessing whether teachers’ beliefs about mathematics education are 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.