IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v89y2024i2d10.1007_s11336-023-09942-5.html
   My bibliography  Save this article

Exploratory Procedure for Component-Based Structural Equation Modeling for Simple Structure by Simultaneous Rotation

Author

Listed:
  • Naoto Yamashita

    (Kansai University)

Abstract

Generalized structured component analysis (GSCA) is a structural equation modeling (SEM) procedure that constructs components by weighted sums of observed variables and confirmatorily examines their regressional relationship. The research proposes an exploratory version of GSCA, called exploratory GSCA (EGSCA). EGSCA is analogous to exploratory SEM (ESEM) developed as an exploratory factor-based SEM procedure, which seeks the relationships between the observed variables and the components by orthogonal rotation of the parameter matrices. The indeterminacy of orthogonal rotation in GSCA is first shown as a theoretical support of the proposed method. The whole EGSCA procedure is then presented, together with a new rotational algorithm specialized to EGSCA, which aims at simultaneous simplification of all parameter matrices. Two numerical simulation studies revealed that EGSCA with the following rotation successfully recovered the true values of the parameter matrices and was superior to the existing GSCA procedure. EGSCA was applied to two real datasets, and the model suggested by the EGSCA’s result was shown to be better than the model proposed by previous research, which demonstrates the effectiveness of EGSCA in model exploration.

Suggested Citation

  • Naoto Yamashita, 2024. "Exploratory Procedure for Component-Based Structural Equation Modeling for Simple Structure by Simultaneous Rotation," Psychometrika, Springer;The Psychometric Society, vol. 89(2), pages 411-438, June.
    • Handle: RePEc:spr:psycho:v:89:y:2024:i:2:d:10.1007_s11336-023-09942-5
    DOI: 10.1007/s11336-023-09942-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-023-09942-5
    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/s11336-023-09942-5?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. Coen Bernaards & Robert Jennrich, 2003. "Orthomax rotation and perfect simple structure," Psychometrika, Springer;The Psychometric Society, vol. 68(4), pages 585-588, December.
    2. Kohei Adachi, 2013. "Generalized joint Procrustes analysis," Computational Statistics, Springer, vol. 28(6), pages 2449-2464, December.
    3. P. Bentler, 1986. "Structural modeling and psychometrika: An historical perspective on growth and achievements," Psychometrika, Springer;The Psychometric Society, vol. 51(1), pages 35-51, March.
    4. Henk Kiers, 1994. "Simplimax: Oblique rotation to an optimal target with simple structure," Psychometrika, Springer;The Psychometric Society, vol. 59(4), pages 567-579, December.
    5. Nickolay T. Trendafilov & Sara Fontanella & Kohei Adachi, 2017. "Sparse Exploratory Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 778-794, September.
    6. Stanley Mulaik, 1986. "Factor analysis and Psychometrika: Major developments," Psychometrika, Springer;The Psychometric Society, vol. 51(1), pages 23-33, March.
    7. TENENHAUS, Michel, 2008. "Component-based structural equation modelling," HEC Research Papers Series 887, HEC Paris.
    8. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(3), pages 187-200, September.
    9. Heungsun Hwang & Wayne Desarbo & Yoshio Takane, 2007. "Fuzzy Clusterwise Generalized Structured Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 181-198, June.
    10. Urbano Lorenzo-Seva, 2003. "A factor simplicity index," Psychometrika, Springer;The Psychometric Society, vol. 68(1), pages 49-60, March.
    11. Nickolay Trendafilov, 2014. "From simple structure to sparse components: a review," Computational Statistics, Springer, vol. 29(3), pages 431-454, June.
    12. Kohei Adachi, 2009. "Joint Procrustes Analysis for Simultaneous Nonsingular Transformation of Component Score and Loading Matrices," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 667-683, December.
    13. Henry Kaiser, 1974. "An index of factorial simplicity," Psychometrika, Springer;The Psychometric Society, vol. 39(1), pages 31-36, March.
    14. Heungsun Hwang & Yoshio Takane, 2004. "Generalized structured component analysis," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 81-99, March.
    15. Chester Harris & Henry Kaiser, 1964. "Oblique factor analytic solutions by orthogonal transformations," Psychometrika, Springer;The Psychometric Society, vol. 29(4), pages 347-362, 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. Kei Hirose & Yoshikazu Terada, 2023. "Sparse and Simple Structure Estimation via Prenet Penalization," Psychometrika, Springer;The Psychometric Society, vol. 88(4), pages 1381-1406, December.
    2. Giovanni Franco, 2014. "Toward a simple structure: a comparison of different rotation techniques," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(3), pages 1785-1797, May.
    3. Naoto Yamashita, 2023. "Principal component analysis constrained by layered simple structures," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 347-367, June.
    4. Urbano Lorenzo-Seva, 2000. "The weighted oblimin rotation," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 301-318, September.
    5. Jin, Shaobo & Moustaki, Irini & Yang-Wallentin, Fan, 2018. "Approximated penalized maximum likelihood for exploratory factor analysis: an orthogonal case," LSE Research Online Documents on Economics 88118, London School of Economics and Political Science, LSE Library.
    6. Rosember Guerra-Urzola & Katrijn Van Deun & Juan C. Vera & Klaas Sijtsma, 2021. "A Guide for Sparse PCA: Model Comparison and Applications," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 893-919, December.
    7. Urbano Lorenzo-Seva, 2003. "A factor simplicity index," Psychometrika, Springer;The Psychometric Society, vol. 68(1), pages 49-60, March.
    8. Ikemoto, Hiroki & Adachi, Kohei, 2016. "Sparse Tucker2 analysis of three-way data subject to a constrained number of zero elements in a core array," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 1-18.
    9. Heungsun Hwang & Moon-Ho Ho & Jonathan Lee, 2010. "Generalized Structured Component Analysis with Latent Interactions," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 228-242, June.
    10. 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.
    11. 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.
    12. Guerra Urzola, Rosember & Van Deun, Katrijn & Vera, J. C. & Sijtsma, K., 2021. "A guide for sparse PCA : Model comparison and applications," Other publications TiSEM 4d35b931-7f49-444b-b92f-a, Tilburg University, School of Economics and Management.
    13. Shaobo Jin & Irini Moustaki & Fan Yang-Wallentin, 2018. "Approximated Penalized Maximum Likelihood for Exploratory Factor Analysis: An Orthogonal Case," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 628-649, September.
    14. 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.
    15. Urbano Lorenzo-Seva & Antoni Rodríguez-Fornells, 2006. "Acquiescent Responding in Balanced Multidimensional Scales and Exploratory Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 769-777, December.
    16. Rodríguez-Fuentes, Carlos Javier & Hernández-López, Montserrat, 1997. "Análisis de diferencias estructurales interregionales determinantes en el impacto de la política monetaria," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 7, pages 141-157, Junio.
    17. 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.
    18. Hauck, Jana & Suess-Reyes, Julia & Beck, Susanne & Prügl, Reinhard & Frank, Hermann, 2016. "Measuring socioemotional wealth in family-owned and -managed firms: A validation and short form of the FIBER Scale," Journal of Family Business Strategy, Elsevier, vol. 7(3), pages 133-148.
    19. Tina Vohra & Mandeep Kaur, 2018. "Determining Reasons for Lower Participation of Women in Indian Stock Market: A Comparative Study of Stock Investors and Non-investors," Jindal Journal of Business Research, , vol. 7(2), pages 87-102, December.
    20. Lyndon Lim & Elaine Chapman, 2022. "Development and Preliminary Validation of the Moral Reasoning Questionnaire for Secondary School Students," SAGE Open, , vol. 12(1), pages 21582440221, March.

    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:89:y:2024:i:2:d:10.1007_s11336-023-09942-5. 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.