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Model-Implied Instrumental Variable—Generalized Method of Moments (MIIV-GMM) Estimators for Latent Variable Models

Published online by Cambridge University Press:  01 January 2025

Kenneth A. Bollen ,
Stanislav Kolenikov  and
Shawn Bauldry
Kenneth A. Bollen*
Affiliation:
Department of Sociology, University of North Carolina at Chapel Hill
Stanislav Kolenikov
Affiliation:
Abt SRBI
Shawn Bauldry
Affiliation:
Department of Sociology, University of Alabama at Birmingham
*
Requests for reprints should be sent to Kenneth A. Bollen, Department of Sociology, University of North Carolina at Chapel Hill, CB 3210 Hamilton, Chapel Hill, NC 27599-3210, USA. E-mail: bollen@unc.edu
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Abstract

The common maximum likelihood (ML) estimator for structural equation models (SEMs) has optimal asymptotic properties under ideal conditions (e.g., correct structure, no excess kurtosis, etc.) that are rarely met in practice. This paper proposes model-implied instrumental variable – generalized method of moments (MIIV-GMM) estimators for latent variable SEMs that are more robust than ML to violations of both the model structure and distributional assumptions. Under less demanding assumptions, the MIIV-GMM estimators are consistent, asymptotically unbiased, asymptotically normal, and have an asymptotic covariance matrix. They are “distribution-free,” robust to heteroscedasticity, and have overidentification goodness-of-fit J-tests with asymptotic chi-square distributions. In addition, MIIV-GMM estimators are “scalable” in that they can estimate and test the full model or any subset of equations, and hence allow better pinpointing of those parts of the model that fit and do not fit the data. An empirical example illustrates MIIV-GMM estimators. Two simulation studies explore their finite sample properties and find that they perform well across a range of sample sizes.

Keywords

structural equation modelslatent variablesgeneralized method of momentsinstrumental variablesfactor analysis
Type
Original Paper
Information
Psychometrika , Volume 79 , Issue 1 , January 2014 , pp. 20 - 50
Copyright
Copyright © 2013 The Psychometric Society

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