We propose a two-step procedure to estimate structural equation models (SEMs). In a first step, the latent variable is replaced by its conditional expectation given the observed data. This conditional expectation is estimated using a James–Stein type shrinkage estimator. The second step consists of regressing the dependent variables on this shrinkage estimator. In addition to linear SEMs, we also derive shrinkage estimators to estimate polynomials. We empirically demonstrate the feasibility of the proposed method via simulation and contrast the proposed estimator with ML and MIIV estimators under a limited number of simulation scenarios. We illustrate the method on a case study.

我们提出了一个两步程序来估计结构方程模型 (SEM)。在第一步中，给定观察到的数据，潜在变量被其条件期望替换。这个条件期望是使用 James-Stein 型收缩估计器估计的。第二步包括对这个收缩估计量的因变量进行回归。除了线性 SEM 之外，我们还推导出收缩估计量来估计多项式。我们通过模拟实验证明了所提出方法的可行性，并在有限数量的模拟场景下将所提出的估计器与 ML 和 MIIV 估计器进行了对比。我们通过案例研究来说明该方法。