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

Abstract

Structural Equation Modeling with latent variables (SEM) is a powerful tool for social and behavioral scientists, combining many of the strengths of psychometrics and econometrics into a single framework. The most common estimator for SEM is the full-information maximum likelihood estimator (ML), but there is continuing interest in limited information estimators because of their distributional robustness and their greater resistance to structural specification errors. However, the literature discussing model fit for limited information estimators for latent variable models is sparse compared to that for full information estimators. We address this shortcoming by providing several specification tests based on the 2SLS estimator for latent variable structural equation models developed by Bollen (1996). We explain how these tests can be used to not only identify a misspecified model, but to help diagnose the source of misspecification within a model. We present and discuss results from a Monte Carlo experiment designed to evaluate the finite sample properties of these tests. Our findings suggest that the 2SLS tests successfully identify most misspecified models, even those with modest misspecification, and that they provide researchers with information that can help diagnose the source of misspecification.

Figure 1

Path diagram representation of Model 1 Note: numbers shown are unstandardized parameter values with standardized values in parenthesis; solid and dashed lines represent the population model structure, and dashed lines represent omitted parameters under model misspecification.

Figure 2

Path diagram representation of Model 2 Note: numbers shown are unstandardized parameter values with standardized values in parenthesis; solid and dashed lines represent the population model structure, and dashed lines represent omitted parameters under model misspecification.

Figure 3

Path diagram representation of Model 3. Note: numbers shown are unstandardized parameter values with standardized values in parenthesis; solid and dashed lines represent the population model structure, and dashed lines represent omitted parameters under model misspecification.