IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v52y2008i10p4842-4858.html
   My bibliography  Save this article

Structural equation modeling with near singular covariance matrices

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00201-6
    Download Restriction: Full text for ScienceDirect subscribers only.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    3. Masanori Ichikawa & Sadanori Konishi, 1995. "Application of the bootstrap methods in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 60(1), pages 77-93, March.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:52:y:2008:i:10:p:4842-4858. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/csda .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.