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

Listed author(s):
  • Kenneth Bollen

    ()

  • Stanislav Kolenikov

    ()

  • Shawn Bauldry

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. Copyright The Psychometric Society 2014

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File URL: http://hdl.handle.net/10.1007/s11336-013-9335-3
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Article provided by Springer & The Psychometric Society in its journal Psychometrika.

Volume (Year): 79 (2014)
Issue (Month): 1 (January)
Pages: 20-50

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Handle: RePEc:spr:psycho:v:79:y:2014:i:1:p:20-50
DOI: 10.1007/s11336-013-9335-3
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Web page: https://www.psychometricsociety.org/

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  1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
  2. Albert Madansky, 1964. "Instrumental variables in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 105-113, June.
  3. Masamori Ihara & Yutaka Kano, 1986. "A new estimator of the uniqueness in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 51(4), pages 563-566, December.
  4. Albert Satorra, 1990. "Robustness issues in structural equation modeling: a review of recent developments," Quality & Quantity: International Journal of Methodology, Springer, vol. 24(4), pages 367-386, November.
  5. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  6. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
  7. Kenneth Bollen, 1996. "An alternative two stage least squares (2SLS) estimator for latent variable equations," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 109-121, March.
  8. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
  9. James Anderson & David Gerbing, 1984. "The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 49(2), pages 155-173, June.
  10. Stanislav Kolenikov & Kenneth A. Bollen, 2012. "Testing Negative Error Variances," Sociological Methods & Research, , vol. 41(1), pages 124-167, February.
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