Most researchers acknowledge that virtually all structural equation models (SEMs) are approximations due to violating distributional assumptions and structural misspecifications. There is a large literature on the unmet distributional assumptions, but much less on structural misspecifications. In this paper, we examine the robustness to structural misspecification of the model implied instrumental variable, two-stage least square (MIIV-2SLS) estimator of SEMs. We introduce two types of robustness: robust-unchanged and robust-consistent. We develop new robustness analytic conditions for MIIV-2SLS and illustrate these with hypothetical models, simulated data, and an empirical example. Our conditions enable a researcher to know whether, for example, a structural misspecification in the latent variable model influences the MIIV-2SLS estimator for measurement model equations and vice versa. Similarly, we establish robustness conditions for correlated errors. The new robustness conditions provide guidance on the types of structural misspecifications that affect parameter estimates and they assist in diagnosing the source of detected problems with MIIVs.

中文翻译：

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当潜在变量或测量模型在结构上错误指定时 MIIV-2SLS 的稳健性条件

大多数研究人员承认，由于违反分布假设和结构错误说明，几乎所有结构方程模型 (SEM) 都是近似值。有大量关于未满足分布假设的文献，但关于结构错误指定的文献则少得多。在本文中，我们检查了模型隐含工具变量、SEM 的两阶段最小二乘 (MIIV-2SLS) 估计量的结构错误指定的稳健性。我们引入了两种类型的健壮性：健壮不变和健壮一致。我们为 MIIV-2SLS 开发了新的稳健性分析条件，并用假设模型、模拟数据和经验示例来说明这些条件。我们的条件使研究人员能够知道，例如，潜在变量模型中的结构错误指定影响测量模型方程的 MIIV-2SLS 估计器，反之亦然。同样，我们为相关错误建立了稳健性条件。新的稳健性条件为影响参数估计的结构错误指定类型提供了指导，它们有助于诊断 MIIV 检测到的问题的来源。