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Comparing estimators for latent interaction models under structural and distributional misspecifications
Holger Brandt1, Nora Umbach2, Augustin Kelava3
1Department of Psychology.
Psychological Methods
|November 1, 2019
Summary
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.
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.
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