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.

翻译：潜变量模型在心理学研究中被广泛用于探究不可观测构念之间的关系。当整体潜变量模型的一阶段估计面临挑战时，两阶段因子得分回归作为一种便捷的替代方案：第一阶段拟合测量模型以获得因子得分，随后在第二阶段使用这些得分来拟合结构模型。然而，已知因子得分回归的简单应用会导致结构参数估计产生偏差。本文针对参数统计模型的两阶段估计，开发了一个通用的偏差校正框架，并将其专门应用于因子得分回归。与现有的偏差校正因子得分回归解决方案不同，所提出的方法适用于更广泛的潜变量模型类别，且无需计算特定类型的因子得分。我们在温和的正则性条件下，证明了所提出的偏差校正两阶段估计量具有根号n一致性。为确保广泛的适用性并最小化对复杂解析推导的依赖，我们引入了一种用于点估计的随机逼近算法，以及一种基于蒙特卡罗方法的方差估计程序。在一系列蒙特卡罗实验中，我们证明偏差校正后的因子得分回归估计量与"黄金标准"的一阶段最大似然估计量性能相当。这些结果表明，我们的方法为估计潜变量模型提供了一种直接而有效的替代方案。