IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v40y2015i6p579-603.html
   My bibliography  Save this article

Factor Rotation and Standard Errors in Exploratory Factor Analysis

Author

Listed:
  • Guangjian Zhang

    (University of Notre Dame)

  • Kristopher J. Preacher

    (Vanderbilt University)

Abstract

In this article, we report a surprising phenomenon: Oblique CF-varimax and oblique CF-quartimax rotation produced similar point estimates for rotated factor loadings and factor correlations but different standard error estimates in an empirical example. Influences of factor rotation on asymptotic standard errors are investigated using a numerical exploration method. The results are (a) CF-varimax, CF-quartimax, CF-equamax, and CF-parsimax produced similar asymptotic standard errors when the factor loading matrix is an independent cluster solution and (b) the four rotation methods produced different asymptotic standard errors when the factor loading matrix has a more complex structure. In addition, properties of the CF family are explored with a full range of κ values.

Suggested Citation

  • Guangjian Zhang & Kristopher J. Preacher, 2015. "Factor Rotation and Standard Errors in Exploratory Factor Analysis," Journal of Educational and Behavioral Statistics, , vol. 40(6), pages 579-603, December.
  • Handle: RePEc:sae:jedbes:v:40:y:2015:i:6:p:579-603
    DOI: 10.3102/1076998615606098
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998615606098
    Download Restriction: no

    File URL: https://libkey.io/10.3102/1076998615606098?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Charles Crawford & George Ferguson, 1970. "A general rotation criterion and its use in orthogonal rotation," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 321-332, September.
    2. Ke-Hai Yuan & Ying Cheng & Wei Zhang, 2010. "Determinants of Standard Errors of MLEs in Confirmatory Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 633-648, December.
    3. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(3), pages 187-200, September.
    4. R. Jennrich & P. Sampson, 1966. "Rotation for simple loadings," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 313-323, September.
    5. Robert Jennrich, 1973. "Standard errors for obliquely rotated factor loadings," Psychometrika, Springer;The Psychometric Society, vol. 38(4), pages 593-604, December.
    6. Claude Archer & Robert Jennrich, 1973. "Standard errors for rotated factor loadings," Psychometrika, Springer;The Psychometric Society, vol. 38(4), pages 581-592, December.
    Full references (including those not matched with items on IDEAS)

    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. Xinyi Liu & Gabriel Wallin & Yunxiao Chen & Irini Moustaki, 2023. "Rotation to Sparse Loadings Using $$L^p$$ L p Losses and Related Inference Problems," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 527-553, June.
    2. Liu, Xinyi Lin & Wallin, Gabriel & Chen, Yunxiao & Moustaki, Irini, 2023. "Rotation to sparse loadings using Lp losses and related inference problems," LSE Research Online Documents on Economics 118349, London School of Economics and Political Science, LSE Library.
    3. 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.
    4. Guangjian Zhang & Minami Hattori & Lauren A. Trichtinger, 2023. "Rotating Factors to Simplify Their Structural Paths," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 865-887, September.
    5. Guangjian Zhang & Michael Browne & Anthony Ong & Sy Chow, 2014. "Analytic Standard Errors for Exploratory Process Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 444-469, July.
    6. Guangjian Zhang & Kristopher Preacher & Robert Jennrich, 2012. "The Infinitesimal Jackknife with Exploratory Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 634-648, October.
    7. Yang Liu & Jan Hannig, 2016. "Generalized Fiducial Inference for Binary Logistic Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 81(2), pages 290-324, June.
    8. Douglas Clarkson & Robert Jennrich, 1988. "Quartic rotation criteria and algorithms," Psychometrika, Springer;The Psychometric Society, vol. 53(2), pages 251-259, June.
    9. Joost Ginkel & Pieter Kroonenberg, 2014. "Using Generalized Procrustes Analysis for Multiple Imputation in Principal Component Analysis," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 242-269, July.
    10. Thomas Despois & Catherine Doz, 2023. "Identifying and interpreting the factors in factor models via sparsity: Different approaches," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 533-555, June.
    11. Haruhiko Ogasawara, 2000. "Some relationships between factors and components," Psychometrika, Springer;The Psychometric Society, vol. 65(2), pages 167-185, June.
    12. Robert Boik, 2008. "Newton Algorithms for Analytic Rotation: an Implicit Function Approach," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 231-259, June.
    13. 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.
    14. Robert Jennrich & Peter Bentler, 2012. "Exploratory Bi-factor Analysis: The Oblique Case," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 442-454, July.
    15. James Heckman & Rodrigo Pinto & Peter Savelyev, 2013. "Understanding the Mechanisms through Which an Influential Early Childhood Program Boosted Adult Outcomes," American Economic Review, American Economic Association, vol. 103(6), pages 2052-2086, October.
    16. Kentaro Hayashi & Yiu-Fai Yung, 1999. "Standard errors for the class of orthomax-rotated factor loadings: Some matrix results," Psychometrika, Springer;The Psychometric Society, vol. 64(4), pages 451-460, December.
    17. Henk Kiers & Jos Berge, 1994. "The Harris-Kaiser independent cluster rotation as a method for rotation to simple component weights," Psychometrika, Springer;The Psychometric Society, vol. 59(1), pages 81-90, March.
    18. Henk Kiers, 1997. "Three-mode orthomax rotation," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 579-598, December.
    19. Lorenzo-Seva, Urbano & van de Velden, Michel & Kiers, Henk A. L., 2009. "CAR: A MATLAB Package to Compute Correspondence Analysis with Rotations," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i08).
    20. Kohei Adachi, 2011. "Three-Way Tucker2 Component Analysis Solutions of Stimuli × Responses × Individuals Data with Simple Structure and the Fewest Core Differences," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 285-305, April.

    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:sae:jedbes:v:40:y:2015:i:6:p:579-603. 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: SAGE Publications (email available below). General contact details of provider: .

    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.