Latent moderated structural equation (LMS) is one of the most common techniques for estimating interaction effects involving latent variables (i.e., XWITH command in Mplus). However, empirical applications of LMS often overlook that this estimation technique assumes normally distributed variables and that violations of this assumption may lead to seriously biased parameter estimates. Against this backdrop, we study the robustness of LMS to different shapes and sources of nonnormality and examine whether various statistical tests can help researchers detect such distributional misspecifications. In four simulations, we show that LMS can be severely biased when the latent predictors or the structural disturbances are nonnormal. On the contrary, LMS is unaffected by nonnormality originating from measurement errors. As a result, testing for the multivariate normality of observed indicators of the latent predictors can lead to erroneous conclusions, flagging distributional misspecifications in perfectly unbiased LMS results and failing to reject seriously biased results. To solve this issue, we introduce a novel Hausman-type specification test to assess the distributional assumptions of LMS and demonstrate its performance. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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潜在交互模型中的正态性假设。


潜在调节结构方程 (LMS) 是估计涉及潜在变量的交互效应的最常用技术之一（即 Mplus 中的 XWITH 命令）。然而，LMS 的实证应用经常忽视这种估计技术假设变量呈正态分布，并且违反此假设可能会导致参数估计出现严重偏差。在此背景下，我们研究了 LMS 对不同形状和非正态性来源的鲁棒性，并检验各种统计检验是否可以帮助研究人员检测这种分布错误。在四次模拟中，我们表明，当潜在预测变量或结构扰动非正态时，LMS 可能会出现严重偏差。相反，LMS 不受测量误差引起的非正态性的影响。因此，对潜在预测变量的观察指标的多元正态性进行测试可能会导致错误的结论，在完全无偏的 LMS 结果中标记分布错误，并且无法拒绝严重偏倚的结果。为了解决这个问题，我们引入了一种新颖的 Hausman 型规范测试来评估 LMS 的分布假设并证明其性能。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。