Model-implied instrumental variable-generalized method of moments (MIIV-GMM) estimators for latent variable models

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Maximum Likelihood (ML) estimators for Structural Equation Models (SEMs) rely on strict assumptions rarely met in practice.
• Violations of model structure and distributional assumptions can compromise ML estimator performance.

Purpose of the Study:

• To propose novel Model-Implied Instrumental Variable - Generalized Method of Moments (MIIV-GMM) estimators for latent variable SEMs.
• To offer estimators that are more robust to assumption violations than traditional ML estimators.

Main Methods:

• The study introduces MIIV-GMM estimators for latent variable SEMs.
• These estimators are designed to be distribution-free and robust to heteroscedasticity.
• The paper includes an empirical example and simulation studies to evaluate performance.

Main Results:

• MIIV-GMM estimators are consistent, asymptotically unbiased, and asymptotically normal under less demanding assumptions.
• They possess overidentification goodness-of-fit J-tests with asymptotic chi-square distributions.
• MIIV-GMM estimators are scalable, allowing for targeted model testing and pinpointing of model fit issues.

Conclusions:

• MIIV-GMM estimators provide a robust and flexible alternative to ML estimators for SEMs.
• They perform well in finite samples and offer advantages in identifying model misspecification.
• The proposed methods enhance the reliability of SEM analyses in real-world applications.