Youngjin Han | Searcharxiv

arXiv2026

Multilevel Regression Discontinuity Models with Latent Variables

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.

stat.ME↗

arXiv2024

A New Fit Assessment Framework for Common Factor Models Using Generalized Residuals

Assessing fit in common factor models solely through the lens of mean and covariance structures, as is commonly done with conventional goodness-of-fit (GOF) assessments, may overlook critical aspects of misfit, potentially leading to misleading conclusions. To achieve more flexible fit assessment, we extend the theory of generalized residuals (Haberman & Sinharay, 2013), originally developed for models with categorical data, to encompass more general measurement models. Within this extended framework, we propose several fit test statistics designed to evaluate various parametric assumptions involved in common factor models. The examples include assessing the distributional assumptions of latent variables and functional form assumptions of individual manifest variables. The performance of the proposed statistics is examined through simulation studies and an empirical data analysis. Our findings suggest that generalized residuals are promising tools for detecting misfit in measurement models, often masked when assessed by conventional GOF testing methods.

stat.ME↗