Using Instrumental Variable (IV) Tests to Evaluate Model Specification in Latent Variable Structural Equation Models.

Area of Science:

• Social and Behavioral Sciences
• Econometrics
• Psychometrics

Background:

• Structural Equation Modeling (SEM) integrates psychometrics and econometrics.
• Full-information maximum likelihood (ML) is common, but limited information estimators offer robustness.
• Limited literature exists on model fit for limited information estimators in latent variable models.

Purpose of the Study:

• To address the scarcity of model fit literature for limited information estimators in latent variable SEM.
• To provide specification tests based on the 2SLS estimator for latent variable SEM.
• To enable identification and diagnosis of model misspecification.

Main Methods:

• Developed specification tests based on Bollen's (1996) 2SLS estimator for latent variable SEM.
• Utilized a Monte Carlo experiment to evaluate the finite sample properties of these tests.
• Assessed the tests' ability to identify and diagnose model misspecification.

Main Results:

• The 2SLS specification tests successfully identified most misspecified models, including those with modest misspecification.
• The tests provided valuable information for diagnosing the source of misspecification.
• Findings support the utility of these tests in SEM research.

Conclusions:

• The developed 2SLS specification tests are effective tools for latent variable SEM.
• These tests enhance model diagnostics, aiding researchers in identifying and understanding misspecification.
• The study contributes to the literature on limited information estimators in SEM.