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

TL;DR

This paper introduces a broad, bias-corrected two-stage estimation method for latent variable regression models that is root-n consistent and performs comparably to maximum likelihood estimation in simulations.

Contribution

The paper develops a general bias-correction framework for two-stage latent variable model estimation, applicable to a wide class of models without complex factor score computations.

Findings

Bias-corrected estimator achieves root-n consistency.

Performs comparably to one-stage maximum likelihood in simulations.

Applicable to various latent variable models without complex calculations.

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.