USING INSTRUMENTAL VARIABLE TESTS TO EVALUATE MODEL SPECIFICATION IN LATENT VARIABLE STRUCTURAL EQUATION MODELS

Authors


  • The views expressed in this paper are those of the authors, and no official endorsement by the Agency for Healthcare Research and Quality or the Department of Health and Human Services is intended or should be inferred. The authors would like to thank the editor and reviewers for their valuable comments. Bollen gratefully acknowledges support from NSF SES 0617276, NIDA 1-R01-DA13148-01, and DA013148-05A2. Direct correspondence to James B. Kirby, Agency for Healthcare Research and Quality, 540 Gaither Road, Rockville, MD 20850; e-mail: jkirby@ahrq.gov.

Abstract

Structural equation modeling (SEM) with latent variables 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 (ML) estimator, 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 with 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 not only to 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.

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