Estimation methods for structural equation models with interactions of latent variables were compared in several studies. Yet none of these studies examined models that were structurally misspecified. Here, the model-implied instrumental variable 2-stage least square estimator (MIIV-2SLS; Bollen, 1995; Bollen & Paxton, 1998), the 2-stage method of moments estimator (2SMM; Wall & Amemiya, 2003), the nonlinear structural equation mixture model approach (NSEMM; Kelava, Nagengast, & Brandt, 2014), and the unconstrained product indicator approach (UPI; Marsh, Wen, & Hau, 2004) were compared in a Monte Carlo simulation. The design included structural misspecifications in the measurement model involving the scaling indicator or not, the size of the misspecification, normal and nonnormal data, the indicators' reliability, and sample size. For the structural misspecifications that did not involve the scaling indicator, we found that MIIV-2SLS' parameter estimates were less biased compared with 2SMM, NSEMM, and UPI. If the reliability was high, the RMSE for all approaches was very similar; for low reliability, MIIV-2SLS' RMSE became larger compared with the other approaches. If the structural misspecification involved the scaling indicator, all estimators were seriously biased, with the largest bias for MIIV-2SLS. In most scenarios, this bias was more severe for the linear effects than for the interaction effect. The RMSE for conditions with misspecified scaling indicators was smallest for 2SMM, especially for low reliability scenarios, but the overall magnitude of bias was such that we cannot recommend any of the estimators in this situation. Our article showed the damage done when researchers omit cross-loadings of the scaling indicator and the importance of giving more attention to these indicators particularly if the indicators' reliability is low. It also showed that no one estimator is superior to the others across all conditions. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

中文翻译：

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比较结构和分布不正确情况下潜在交互模型的估计量。

在一些研究中比较了具有潜在变量相互作用的结构方程模型的估计方法。然而，这些研究都没有检查结构错误指定的模型。这里，模型暗示的工具变量2级最小二乘估计器（MIIV-2SLS; Bollen，1995; Bollen＆Paxton，1998），2阶矩估计器（2SMM; Wall＆Amemiya，2003）在蒙特卡洛模拟中比较了结构方程混合模型方法（NSEMM; Kelava，Nagengast，＆Brandt，2014）和无约束产品指标方法（UPI; Marsh，Wen，＆Hau，2004）。设计包括测量模型中的结构错位（涉及或不涉及缩放指标），错位的大小，正常和非正常数据，指标的可靠性，和样本量。对于不涉及缩放指标的结构错误规格，我们发现与2SMM，NSEMM和UPI相比，MIIV-2SLS的参数估计偏差较小。如果可靠性很高，则所有方法的RMSE都非常相似；由于可靠性低，MIIV-2SLS的RMSE与其他方法相比更大。如果结构错误指定涉及缩放指标，则所有估计量均存在严重偏差，其中MIIV-2SLS的偏差最大。在大多数情况下，线性效应的偏倚比相互作用效应更严重。对于2SMM，具有错误指定缩放指标的条件的RMSE最小，尤其是对于低可靠性场景，但总体偏倚幅度使得在这种情况下我们不推荐任何估计器。我们的文章显示了当研究人员忽略缩放指标的交叉加载时所造成的损害，以及在这些指标的可靠性较低的情况下应特别注意这些指标的重要性。它还表明，在所有条件下，没有一个估计者优于其他估计。（PsycINFO数据库记录（c）2019 APA，保留所有权利）。