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Robustness of normal theory statistics in structural equation models

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  • A. Mooijaart
  • P.M. Bentler

Abstract

A condition is given by which optimal normal theory methods, such as the maximum likelihood methods, are robust against violation of the normality assumption in a general linear structural equation model. Specifically, the estimators and the goodness of fit test are robust. The estimator is efficient within some defined class, and its standard errors can be obtained by a correction formula applied to the inverse of the information matrix. Some special models, like the factor analysis model and path models, are discussed in more detail. A method for evaluating the robustness condition is given.

Suggested Citation

  • A. Mooijaart & P.M. Bentler, 1991. "Robustness of normal theory statistics in structural equation models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 45(2), pages 159-171, June.
    • Handle: RePEc:bla:stanee:v:45:y:1991:i:2:p:159-171
    DOI: 10.1111/j.1467-9574.1991.tb01301.x
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    Cited by:

    1. Ke-Hai Yuan & Peter M. Bentler & Wei Zhang, 2005. "The Effect of Skewness and Kurtosis on Mean and Covariance Structure Analysis," Sociological Methods & Research, , vol. 34(2), pages 240-258, November.
    2. Prokhorov, Artem, 2009. "On relative efficiency of quasi-MLE and GMM estimators of covariance structure models," Economics Letters, Elsevier, vol. 102(1), pages 4-6, January.
    3. Albert Satorra, 1992. "Multi-sample analysis of moment-structures: Asymptotic validity of inferences based on second-order moments," Economics Working Papers 16, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Yutaka Kano & Masamori Ihara, 1994. "Identification of inconsistent variates in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 59(1), pages 5-20, March.
    5. Hildebrandt, Lutz & Görz, Nicole, 1999. "Zum Stand der Kausalanalyse mit Strukturgleichungsmodellen: Methodische Trends und Software-Entwicklungen," SFB 373 Discussion Papers 1999,46, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Terje Skjerpen, 2008. "Engel elasticities, pseudo-maximum likelihood estimation and bootstrapped standard errors. A case study," Discussion Papers 532, Statistics Norway, Research Department.
    7. Satorra, Albert & Neudecker, Heinz, 1994. "On the Asymptotic Optimality of Alternative Minimum-Distance Estimators in Linear Latent-Variable Models," Econometric Theory, Cambridge University Press, vol. 10(5), pages 867-883, December.
    8. Ogasawara, Haruhiko, 2005. "Asymptotic robustness of the asymptotic biases in structural equation modeling," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 771-783, June.
    9. Kano, Yutaka & Takai, Keiji, 2011. "Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1241-1255, October.
    10. Yuan, Ke-Hai & Bentler, Peter M., 2005. "Asymptotic robustness of the normal theory likelihood ratio statistic for two-level covariance structure models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 328-343, June.
    11. Mijke Rhemtulla & Victoria Savalei & Todd Little, 2016. "On the Asymptotic Relative Efficiency of Planned Missingness Designs," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 60-89, March.
    12. Ke-Hai Yuan & Yubin Tian & Hirokazu Yanagihara, 2015. "Empirical Correction to the Likelihood Ratio Statistic for Structural Equation Modeling with Many Variables," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 379-405, June.
    13. Pison, Greet & Rousseeuw, Peter J. & Filzmoser, Peter & Croux, Christophe, 2003. "Robust factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 145-172, January.

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