IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

On the estimators of model-based and maximal reliability

  • Ogasawara, Haruhiko
Registered author(s):

    Four estimators of the reliability for a composite score based on the factor analysis model and five estimators of the maximal reliability for the composite are presented. When the Wishart maximum likelihood is used for the estimation of the model parameters, it is shown that the five estimators of maximal reliability are the same. Asymptotic cumulants of the estimators and their logarithmic transformations are derived under arbitrary distributions with possible model misspecification. The theoretical results considering model misspecification when a model does not hold are shown to be closer to their simulated values than those neglecting model misspecification. Simulations of the confidence intervals using the normal approximation based on the asymptotically distribution-free theory and the asymptotic expansion by Hall's method with variable transformation are performed.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.sciencedirect.com/science/article/B6WK9-4V1663B-3/2/41efef457b0bf26ba9d5ed3ac06c480e
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 100 (2009)
    Issue (Month): 6 (July)
    Pages: 1232-1244

    as
    in new window

    Handle: RePEc:eee:jmvana:v:100:y:2009:i:6:p:1232-1244
    Contact details of provider: Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description

    Order Information: Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
    Web: https://shop.elsevier.com/order?id=622892&ref=622892_01_ooc_1&version=01

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. C. Rao, 1955. "Estimation and tests of significance in factor analysis," Psychometrika, Springer, vol. 20(2), pages 93-111, June.
    2. Heng Li, 1997. "A unifying expression for the maximal reliability of a linear composite," Psychometrika, Springer, vol. 62(2), pages 245-249, June.
    3. 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.
    4. Haruhiko Ogasawara, 2007. "Higher-order approximations to the distributions of fit indexes under fixed alternatives in structural equation models," Psychometrika, Springer, vol. 72(2), pages 227-243, June.
    5. 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.
    6. Charles Mosier, 1943. "On the reliability of a weighted composite," Psychometrika, Springer, vol. 8(3), pages 161-168, September.
    7. Ogasawara, Haruhiko, 2006. "Asymptotic expansion of the sample correlation coefficient under nonnormality," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 891-910, February.
    8. Karl Jöreskog & Arthur Goldberger, 1972. "Factor analysis by generalized least squares," Psychometrika, Springer, vol. 37(3), pages 243-260, September.
    9. Bert Green, 1950. "A note on the calculation of weights for maximum battery reliability," Psychometrika, Springer, vol. 15(1), pages 57-61, March.
    10. P. Bentler, 1968. "Alpha-maximized factor analysis (alphamax): Its relation to alpha and canonical factor analysis," Psychometrika, Springer, vol. 33(3), pages 335-345, September.
    11. M. Knott & D. Bartholomew, 1993. "Constructing measures with maximum reliability," Psychometrika, Springer, vol. 58(2), pages 331-338, June.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:100:y:2009:i:6:p:1232-1244. 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: (Zhang, Lei)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.