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

Holger Brandt1, Nora Umbach2, Augustin Kelava3

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Structural equation models with latent variable interactions face bias when misspecified. The model-implied instrumental variable 2-stage least square estimator (MIIV-2SLS) showed less bias for non-scaling indicator misspecifications, but all methods failed when scaling indicators were misspecified.

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Area of Science:

  • Quantitative Psychology
  • Structural Equation Modeling
  • Statistical Methods

Background:

  • Structural equation models (SEMs) with latent variable interactions are widely used.
  • Existing research on estimation methods has not sufficiently addressed structural misspecification.
  • Misspecification, particularly involving scaling indicators, can significantly impact model estimation.

Purpose of the Study:

  • To compare the performance of four estimation methods under structural misspecification in SEMs with latent variable interactions.
  • To evaluate the impact of measurement model misspecifications, including those involving scaling indicators, on parameter bias and RMSE.
  • To identify which estimation method is most robust to different types of structural misspecification.

Main Methods:

  • A Monte Carlo simulation study was conducted.
  • Four estimators were compared: model-implied instrumental variable 2-stage least square (MIIV-2SLS), 2-stage method of moments (2SMM), nonlinear structural equation mixture model (NSEMM), and unconstrained product indicator (UPI).
  • The simulation varied factors such as structural misspecification (involving scaling indicator or not), misspecification size, data normality, indicator reliability, and sample size.

Main Results:

  • For misspecifications not involving the scaling indicator, MIIV-2SLS exhibited less bias than 2SMM, NSEMM, and UPI.
  • Indicator reliability influenced RMSE; MIIV-2SLS showed higher RMSE with low reliability.
  • When scaling indicators were misspecified, all estimators were severely biased, with MIIV-2SLS showing the largest bias, particularly for linear effects.

Conclusions:

  • Structural misspecification, especially omitting cross-loadings of scaling indicators, can severely damage SEM estimation.
  • No single estimator is universally superior across all conditions.
  • Researchers must pay close attention to scaling indicators, particularly when indicator reliability is low.