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.

翻译：在社交网络的观察性研究中，研究者一直致力于理解个体行为如何受同伴行为的影响。然而，由于同质性（即人们倾向于与具有相似特征的人建立连接）造成的混杂效应，识别和估计因果同伴影响具有挑战性。此外，由于驱动同质性的所有属性通常并非总能被观测到，它们作为未观测的混杂因子，使得基于标准因果识别假设来识别和估计因果同伴影响变得不可行。本文通过利用从网络本身推断出的潜在位置来区分同质性与因果同伴影响，从而应对这一挑战，并采用贝叶斯分层建模框架将此方法扩展到多个网络。为适应同伴影响对个体行为的非线性依赖关系，我们采用了贝叶斯非参数方法，特别是贝叶斯加性回归树（BART），并提出了一个考虑潜在位置推断不确定性的贝叶斯框架。我们通过广泛的模拟研究评估了估计量的操作特性。最后，我们将该方法应用于中学教师寻求建议的网络中，以估计因果同伴影响，从而评估教师关于数学教育的信念是否受到他们寻求建议的同伴信念的影响。我们的结果表明，忽视潜在同质性可能导致对因果同伴影响的低估或高估，并伴随相当大的估计不确定性。