Comparing estimators for latent interaction models under structural and distributional misspecifications.

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).

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