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Structural equation modeling with near singular covariance matrices


  • Yuan, Ke-Hai
  • Chan, Wai


Conventional structural equation modeling involves fitting a structural model to the sample covariance matrix . Due to collinearity or small samples with practical data, nonconvergences often occur in the estimation process. For a small constant a, this paper proposes to fit the structural model to the covariance matrix . When treating as the sample covariance matrix in the maximum likelihood (ML) procedure, consistent parameter estimates are still obtained. The asymptotic distributions of the parameter estimates and the corresponding likelihood ratio statistic are studied and compared to those by the conventional ML. Two rescaled statistics for the overall model evaluation with modeling are constructed. Empirical results imply that the estimates from modeling are more efficient than those of fitting the structural model to even when data are normally distributed. Simulations and real data examples indicate that modeling allows us to evaluate the overall model structure even when is literally singular. Implications of modeling in a broader context are discussed.

Suggested Citation

  • Yuan, Ke-Hai & Chan, Wai, 2008. "Structural equation modeling with near singular covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4842-4858, June.
  • Handle: RePEc:eee:csdana:v:52:y:2008:i:10:p:4842-4858

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    References listed on IDEAS

    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Ke-Hai Yuan & Linda Marshall & Peter Bentler, 2002. "A unified approach to exploratory factor analysis with missing data, nonnormal data, and in the presence of outliers," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 95-121, March.
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    4. Franklin Satterthwaite, 1941. "Synthesis of variance," Psychometrika, Springer;The Psychometric Society, vol. 6(5), pages 309-316, October.
    5. Yuan, Ke-Hai & Hayashi, Kentaro & Bentler, Peter M., 2007. "Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1262-1282, July.
    6. Vinod, H. D., 1982. "Maximum entropy measurement error estimates of singular covariance matrices in undersized samples," Journal of Econometrics, Elsevier, vol. 20(2), pages 163-174, November.
    7. S. Lee & R. Jennrich, 1979. "A study of algorithms for covariance structure analysis with specific comparisons using factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 44(1), pages 99-113, March.
    8. Yuan, Ke-Hai & Bentler, Peter M., 1997. "Improving parameter tests in covariance structure analysis," Computational Statistics & Data Analysis, Elsevier, vol. 26(2), pages 177-198, December.
    9. Anne Boomsma, 1985. "Nonconvergence, improper solutions, and starting values in lisrel maximum likelihood estimation," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 229-242, June.
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    Cited by:

    1. Jon Poynter & James Winder & Tzu Tai, 2015. "An analysis of co-movements in industrial sector indices over the last 30 years," Review of Quantitative Finance and Accounting, Springer, vol. 44(1), pages 69-88, January.
    2. 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.
    3. repec:spr:aistmt:v:69:y:2017:i:3:d:10.1007_s10463-016-0552-2 is not listed on IDEAS

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