, Volume 79, Issue 1, pp 20–50

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

  • Kenneth A. Bollen
  • Stanislav Kolenikov
  • Shawn Bauldry

DOI: 10.1007/s11336-013-9335-3

Cite this article as:
Bollen, K.A., Kolenikov, S. & Bauldry, S. Psychometrika (2014) 79: 20. doi:10.1007/s11336-013-9335-3


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.

Key words

structural equation models latent variables generalized method of moments instrumental variables factor analysis 

Copyright information

© The Psychometric Society 2013

Authors and Affiliations

  • Kenneth A. Bollen
    • 1
  • Stanislav Kolenikov
    • 2
  • Shawn Bauldry
    • 3
  1. 1.Department of SociologyUniversity of North Carolina at Chapel HillChapel HillUSA
  2. 2.Abt SRBICambridgeUSA
  3. 3.Department of SociologyUniversity of Alabama at BirminghamBirminghamUSA

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