Multilevel Regression Discontinuity Models with Latent Variables
含潜变量的多层断点回归模型AI 解读 ↓
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含潜变量的多层断点回归模型
- 研究问题
- 当断点回归的运行变量由含噪指标测量，且学生嵌套于班级或学校时，如何估计异质性效应并进行阈值外外推？
- 方法与思路
- 作者将潜变量断点回归扩展至多层结构，分别讨论群组层面和群组内个体层面的分配，并嵌入多层测量模型。
- 材料陈述的贡献
- 摘要称在群组层面样本量充足时，模拟能够恢复平均处理效应及阈值外外推效应，拓展该框架在教育研究中的使用。
- 阅读关注点
- 应核对潜在运行变量与实际分配规则的关系、测量模型识别和群组数量要求，尤其检查阈值外效应依赖的外推假设。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要未量化充足样本规模，模拟恢复不保证阈值外效应具有普遍识别。
原文摘要
Regression discontinuity (RD) analysis with latent variables as introduced by Morell et al. (2025), offers a useful augmentation of the conventional RD by incorporating measurement model. This approach is particularly relevant in education research, where noisy proxy (e.g., observed test score) of underlying latent construct is adopted for the running variable. This extension enables extrapolation of average treatment effect (ATE) away from the cutoff score and assessment of heterogeneous treatment effects. However, a key limitation of the original framework is its single-level structure, which does not account for the multilevel structure commonly found in education data, such as students nested within classrooms or schools. In this study, we extend the framework to multilevel contexts. We discuss models for both hierarchical RD design, where treatment is assigned at the cluster level, and multisite RD design, where treatment is assigned at the individual level within clusters. In both cases, multilevel measurement model is incorporated to describe the relationship between the latent running variable and observed indicators. Monte Carlo simulations demonstrate recovery of ATEs including extrapolated estimates beyond the cutoff given adequate cluster-level sample sizes. The study highlights the applicability of RD analysis with latent variables for broader use in educational research, without being restricted by the limitations of multilevel data.