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Structural equation modeling with near singular covariance matrices

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  • Yuan, Ke-Hai
  • Chan, Wai

Abstract

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

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    Cited by:

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    4. 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.
    5. Ke-Hai Yuan & Peter M. Bentler, 2017. "Improving the convergence rate and speed of Fisher-scoring algorithm: ridge and anti-ridge methods in structural equation modeling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 571-597, June.
    6. Ke-Hai Yuan & Hongyun Liu & Yuting Han, 2021. "Differential Item Functioning Analysis Without A Priori Information on Anchor Items: QQ Plots and Graphical Test," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 345-377, June.

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