Principal stratification provides a robust framework for causal inference, enabling the investigation of the causal link between air pollution exposure and social mobility, mediated by the education level. Studying the causal mechanisms through which air pollution affects social mobility is crucial to highlight the role of education as a mediator, and offering evidence that can inform policies aimed at reducing both environmental and educational inequalities for more equitable social outcomes. In this paper, we introduce a novel Bayesian nonparametric model for principal stratification, leveraging the dependent Dirichlet process to flexibly model the distribution of potential outcomes. By incorporating confounders and potential outcomes for the post-treatment variable in the Bayesian mixture model for the final outcome, our approach improves the accuracy of missing data imputation and allows for the characterization of treatment effects. We assess the performance of our method through a simulation study and demonstrate its application in evaluating the principal causal effects of air pollution on social mobility in the United States.

翻译：主分层分析为因果推断提供了一个稳健的框架，能够通过教育水平这一中介变量，研究空气污染暴露与社会流动性之间的因果联系。探究空气污染影响社会流动性的因果机制至关重要，这有助于阐明教育作为中介变量的作用，并为旨在减少环境与教育不平等、以实现更公平社会结果的政策提供证据。本文提出了一种新颖的贝叶斯非参数主分层模型，利用相依狄利克雷过程灵活地对潜在结果的分布进行建模。通过在最终结果的贝叶斯混合模型中纳入混杂因素及后处理变量的潜在结果，我们的方法提高了缺失数据插补的准确性，并允许对处理效应进行特征刻画。我们通过模拟研究评估了该方法的性能，并展示了其在美国空气污染对社会流动性主因果效应评估中的应用。