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

2026-01-24

AI Summary

Two-stage factor score regression (FSR) often yields biased structural parameter estimates due to the use of estimated factor scores. This work proposes a general bias-correction framework applicable to a broad class of parametric latent variable models, obviating the need to explicitly compute model-specific factor scores. The approach overcomes limitations of existing correction techniques and achieves √n-consistency under mild regularity conditions. Point estimates are obtained via a stochastic approximation algorithm, while variance estimation leverages Monte Carlo simulation, substantially reducing reliance on intricate analytical derivations. Simulation studies demonstrate that the proposed method attains estimation accuracy comparable to one-stage maximum likelihood estimation—the “gold standard”—offering a simple yet efficient alternative for two-stage modeling.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

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.

Problem

• latent variable models
• factor score regression
• bias correction
• two-stage estimation
• structural parameter estimation

Innovation

• bias correction
• factor score regression
• latent variable models
• root-n consistency
• two-stage estimation