Multilevel Regression Discontinuity Models with Latent Variables

TL;DR

This paper extends multilevel regression discontinuity models with latent variables to better analyze hierarchical educational data, enabling treatment effect estimation beyond the cutoff and accounting for nested data structures.

Contribution

It introduces a multilevel framework for RD models with latent variables, applicable to hierarchical and multisite designs in education research.

Findings

Monte Carlo simulations show accurate recovery of ATEs

Extension allows extrapolation of treatment effects beyond cutoff

Models handle nested data structures effectively

Abstract

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.