  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.
