IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i5p902-912.html
   My bibliography  Save this article

Asymptotic expansions in mean and covariance structure analysis

Author

Listed:
  • Ogasawara, Haruhiko

Abstract

Asymptotic expansions of the distributions of parameter estimators in mean and covariance structures are derived. The parameters may be common to, or specific in means and covariances of observable variables. The means are possibly structured by the common/specific parameters. First, the distributions of the parameter estimators standardized by the population asymptotic standard errors are expanded using the single- and the two-term Edgeworth expansions. In practice, the pivotal statistic or the Studentized estimator with the asymptotically distribution-free standard error is of interest. An asymptotic distribution of the pivotal statistic is also derived by the Cornish-Fisher expansion. Simulations are performed for a factor analysis model with nonzero factor means to see the accuracy of the asymptotic expansions in finite samples.

Suggested Citation

  • Ogasawara, Haruhiko, 2009. "Asymptotic expansions in mean and covariance structure analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 902-912, May.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:902-912
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00188-7
    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. Ke-Hai Yuan & Peter Bentler, 2006. "Mean Comparison: Manifest Variable Versus Latent Variable," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 139-159, March.
    2. Ogasawara, Haruhiko, 2008. "Errata and supplement to the paper "Higher-order asymptotic cumulants of Studentized estimators in covariance structures"," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 59(2/3), pages 95-107.
    3. Ogasawara, Haruhiko, 2007. "Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1726-1750, October.
    4. Ogasawara, Haruhiko, 2006. "Asymptotic expansion of the sample correlation coefficient under nonnormality," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 891-910, February.
    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. Haruhiko Ogasawara, 2004. "Asymptotic biases in exploratory factor analysis and structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 235-256, June.
    7. Ogasawara, Haruhiko, 2007. "Higher-order Estimation Error in Structural Equation Modeling," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 57(4), pages 131-160.
    8. Haruhiko Ogasawara, 2001. "Standard errors of fit indices using residuals in structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 66(3), pages 421-436, September.
    9. Boik, Robert J., 2008. "An implicit function approach to constrained optimization with applications to asymptotic expansions," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 465-489, March.
    10. Yiu-Fai Yung & Peter M. Bentler, 1999. "On Added Information for ML Factor Analysis with Mean and Covariance Structures," Journal of Educational and Behavioral Statistics, , vol. 24(1), pages 1-20, March.
    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. Shimizu, Hiroaki & Wakaki, Hirofumi, 2011. "Asymptotic expansions for a class of tests for a general covariance structure under a local alternative," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1080-1089, July.
    2. Ogasawara, Haruhiko, 2012. "Cornish-Fisher expansions using sample cumulants and monotonic transformations," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 1-18, January.
    3. Ogasawara, Haruhiko, 2009. "Supplement to Ogasawara's papers on "the ADF pivotal statistic", "mean and covariance structure analysis", and "maximal reliability"," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 60(1), pages 21-44.
    4. Ogasawara, Haruhiko, 2017. "Expected predictive least squares for model selection in covariance structures," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 151-164.
    5. Ogasawara, Haruhiko, 2016. "Bias correction of the Akaike information criterion in factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 144-159.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ogasawara, Haruhiko, 2016. "Bias correction of the Akaike information criterion in factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 144-159.
    2. Ogasawara, Haruhiko, 2009. "On the estimators of model-based and maximal reliability," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1232-1244, July.
    3. Ogasawara, Haruhiko, 2010. "Accurate distribution and its asymptotic expansion for the tetrachoric correlation coefficient," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 936-948, April.
    4. Hao Wu & Michael Browne, 2015. "Random Model Discrepancy: Interpretations and Technicalities (A Rejoinder)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 619-624, September.
    5. Tsukada, Shin-ichi, 2014. "Asymptotic expansion for distribution of the trace of a covariance matrix under a two-step monotone incomplete sample," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 206-219.
    6. 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.
    7. Ogasawara, Haruhiko, 2010. "Supplement to the paper "Asymptotic expansions of the distributions of the chi-square statistic based on the asymptotically distribution-free theory in covariance structures"," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 60(4), pages 187-200.
    8. Chun, So Yeon & Alexander, Shapiro, 2009. "Normal versus Noncentral Chi-square Asymptotics of Misspecified Models," MPRA Paper 17310, University Library of Munich, Germany.
    9. Prokhorov, Artem, 2012. "Second order bias of quasi-MLE for covariance structure models," Economics Letters, Elsevier, vol. 114(2), pages 195-197.
    10. Shapiro, Alexander, 2009. "Asymptotic normality of test statistics under alternative hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 936-945, May.
    11. Najarzadeh, Dariush, 2020. "A simple test for zero multiple correlation coefficient in high-dimensional normal data using random projection," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    12. 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.
    13. Ogasawara, Haruhiko, 2007. "Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1726-1750, October.
    14. Sandip Sinharay & Peter W. van Rijn, 2020. "Assessing Fit of the Lognormal Model for Response Times," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 534-568, October.
    15. 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.
    16. Yingbin Zhang & Zhaoxi Yang & Yehui Wang, 2022. "The Impact of Extreme Response Style on the Mean Comparison of Two Independent Samples," SAGE Open, , vol. 12(2), pages 21582440221, June.
    17. Denis Agniel & Tianxi Cai, 2017. "Analysis of multiple diverse phenotypes via semiparametric canonical correlation analysis," Biometrics, The International Biometric Society, vol. 73(4), pages 1254-1265, December.
    18. Feinian Chen & Patrick J. Curran & Kenneth A. Bollen & James Kirby & Pamela Paxton, 2008. "An Empirical Evaluation of the Use of Fixed Cutoff Points in RMSEA Test Statistic in Structural Equation Models," Sociological Methods & Research, , vol. 36(4), pages 462-494, May.
    19. Peter M. Robinson & Francesca Rossi, 2014. "Improved Lagrange multiplier tests in spatial autoregressions," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 139-164, February.
    20. Ogasawara, Haruhiko, 2017. "Expected predictive least squares for model selection in covariance structures," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 151-164.

    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:jmvana:v:100:y:2009:i:5:p:902-912. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.