IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v88y2023i3d10.1007_s11336-022-09877-3.html
   My bibliography  Save this article

Rotating Factors to Simplify Their Structural Paths

Author

Listed:
  • Guangjian Zhang

    (University of Notre Dame)

  • Minami Hattori

    (Soka University)

  • Lauren A. Trichtinger

    (Simmons University)

Abstract

Applications of structural equation modeling (SEM) may encounter issues like inadmissible parameter estimates, nonconvergence, or unsatisfactory model fit. We propose a new factor rotation method that reparameterizes the factor correlation matrix in exploratory factor analysis (EFA) such that factors can be either exogenous or endogenous. The proposed method is an oblique rotation method for EFA, but it allows directional structural paths among factors. We thus referred it to as FSP (factor structural paths) rotation. In particular, we can use FSP rotation to “translate” an SEM model to incorporate theoretical expectations on both factor loadings and structural parameters. We illustrate FSP rotation with an empirical example and explore its statistical properties with simulated data. The results include that (1) EFA with FSP rotation tends to fit data better and encounters fewer Heywood cases than SEM does when there are cross-loadings and many small nonzero loadings, (2) FSP rotated parameter estimates are satisfactory for small models, and (3) FSP rotated parameter estimates are more satisfactory for large models when the structural parameter matrices are sparse.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:88:y:2023:i:3:d:10.1007_s11336-022-09877-3
    DOI: 10.1007/s11336-022-09877-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-022-09877-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-022-09877-3?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
    ---><---

    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. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(3), pages 187-200, September.
    2. Robert Jennrich, 2002. "A simple general method for oblique rotation," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 7-19, March.
    3. Douglas Clarkson, 1979. "Estimating the standard errors of rotated factor loadings by jackknifing," Psychometrika, Springer;The Psychometric Society, vol. 44(3), pages 297-314, September.
    4. 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.
    5. 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.
    6. A. Swain, 1975. "A class of factor analysis estimation procedures with common asymptotic sampling properties," Psychometrika, Springer;The Psychometric Society, vol. 40(3), pages 315-335, September.
    7. 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.
    8. 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.
    9. Robert Jennrich, 1973. "Standard errors for obliquely rotated factor loadings," Psychometrika, Springer;The Psychometric Society, vol. 38(4), pages 593-604, December.
    10. Robert Jennrich, 2004. "Derivative free gradient projection algorithms for rotation," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 475-480, September.
    11. 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. 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.
    2. Haruhiko Ogasawara, 2002. "Concise formulas for the standard errors of component loading estimates," Psychometrika, Springer;The Psychometric Society, vol. 67(2), pages 289-297, June.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Robert Boik, 2008. "Newton Algorithms for Analytic Rotation: an Implicit Function Approach," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 231-259, June.
    10. 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.
    11. Robert Jennrich & Peter Bentler, 2012. "Exploratory Bi-factor Analysis: The Oblique Case," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 442-454, July.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Haruhiko Ogasawara, 2000. "Some relationships between factors and components," Psychometrika, Springer;The Psychometric Society, vol. 65(2), pages 167-185, June.
    17. 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.
    18. 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.
    19. 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.
    20. Henk Kiers, 1997. "Three-mode orthomax rotation," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 579-598, December.

    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:spr:psycho:v:88:y:2023:i:3:d:10.1007_s11336-022-09877-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.