arXiv subjects

Youjin Sung

Publications and source records attributed to Youjin Sung.

4 recordsLinked to original sources

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↗

arXiv2026

Asymptotic Standard Errors for Reliability Coefficients in Item Response Theory

In a recent review, Liu, Pek, & Maydeu-Olivares (2025b) classified reliability coefficients into two types: classical test theory (CTT) reliability and proportional reduction in mean squared error (PRMSE). This article focuses on quantifying the sampling variability of these coefficients under item response theory (IRT) models. While some existing standard error (SE) formulas are accurate when variability arises only from item parameter estimation, the reliability estimators considered in our work involve additional variability from substituting population moments with sample moments. We propose a general strategy to derive SEs that incorporates both sources of sampling error simultaneously, enabling the estimation of model-based reliability coefficients and their SEs in such settings. We then apply our general theory to derive SEs for two specific estimators under the graded response model: (1) CTT reliability for the expected a posteriori score of the latent variable and (2) PRMSE for the latent variable. Simulation results show that the derived SEs accurately capture the sampling variability across various test lengths in moderate to large samples. We conclude with an empirical illustration and directions for future research.

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arXiv2026

Two-stage Estimation of Latent Variable Regression Models: A General, Root-N Consistent Solution

Latent variable (LV) models are widely used in psychological research to investigate relationships among unobservable constructs. When one-stage estimation of the overall LV model is challenging, two-stage factor score regression (FSR) serves as a convenient alternative: the measurement model is fitted to obtain factor scores in the first stage, which are then used to fit the structural model in the subsequent stage. However, naive application of FSR is known to yield biased estimates of structural parameters. In this paper, we develop a generic bias-correction framework for two-stage estimation of parametric statistical models and tailor it specifically to FSR. Unlike existing bias-corrected FSR solutions, the proposed method applies to a broader class of LV models and does not require computing specific types of factor scores. We establish the root-n consistency of the proposed bias-corrected two-stage estimator under mild regularity conditions. To ensure broad applicability and minimize reliance on complex analytical derivations, we introduce a stochastic approximation algorithm for point estimation and a Monte Carlo-based procedure for variance estimation. In a sequence of Monte Carlo experiments, we demonstrate that the bias-corrected FSR estimator performs comparably to the ``gold standard'' one-stage maximum likelihood estimator. These results suggest that our approach offers a straightforward yet effective alternative for estimating LV models.

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arXiv2025

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.

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