Regression discontinuity design (RDD) is widely adopted for causal inference under intervention determined by a continuous variable. While one is interested in treatment effect heterogeneity by subgroups in many applications, RDD typically suffers from small subgroup-wise sample sizes, which makes the estimation results highly instable. To solve this issue, we introduce hierarchical RDD (HRDD), a hierarchical Bayes approach for pursuing treatment effect heterogeneity in RDD. A key feature of HRDD is to employ a pseudo-model based on a loss function to estimate subgroup-level parameters of treatment effects under RDD, and assign a hierarchical prior distribution to ``borrow strength" from other subgroups. The posterior computation can be easily done by a simple Gibbs sampling. We demonstrate the proposed HRDD through simulation and real data analysis, and show that HRDD provides much more stable point and interval estimation than separately applying the standard RDD method to each subgroup.

翻译：断点回归设计（RDD）广泛用于基于连续变量确定干预的因果推断。尽管在许多应用中研究者关注子群体间的处理效应异质性，但RDD通常面临子群体样本量过小的问题，导致估计结果高度不稳定。为解决这一问题，我们提出层次化断点回归（HRDD），这是一种采用层次贝叶斯方法探索RDD中处理效应异质性的框架。HRDD的核心特征在于，基于损失函数构建伪模型来估计RDD下子群体层面的处理效应参数，并通过赋予层次化先验分布从其他子群体中“借力”。后验计算可通过简单的吉布斯采样轻松完成。我们通过模拟实验和真实数据分析验证了所提出的HRDD，结果表明：相较于对各子群体单独应用标准RDD方法，HRDD能提供更稳定的点估计和区间估计。