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

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  • 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
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    References listed on IDEAS

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    1. TENENHAUS, Michel, 2008. "Component-based structural equation modelling," HEC Research Papers Series 887, HEC Paris.
    2. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(3), pages 187-200, September.
    3. Coen Bernaards & Robert Jennrich, 2003. "Orthomax rotation and perfect simple structure," Psychometrika, Springer;The Psychometric Society, vol. 68(4), pages 585-588, December.
    4. 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.
    5. 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.
    6. Urbano Lorenzo-Seva, 2003. "A factor simplicity index," Psychometrika, Springer;The Psychometric Society, vol. 68(1), pages 49-60, March.
    7. Michel Tenenhaus, 2008. "Component-based Structural Equation Modelling," Working Papers hal-00580149, HAL.
    8. Nickolay Trendafilov, 2014. "From simple structure to sparse components: a review," Computational Statistics, Springer, vol. 29(3), pages 431-454, June.
    9. 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.
    10. Nickolay T. Trendafilov & Sara Fontanella & Kohei Adachi, 2017. "Sparse Exploratory Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 778-794, September.
    11. 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.
    12. Stanley Mulaik, 1986. "Factor analysis and Psychometrika: Major developments," Psychometrika, Springer;The Psychometric Society, vol. 51(1), pages 23-33, March.
    13. Heungsun Hwang & Yoshio Takane, 2004. "Generalized structured component analysis," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 81-99, March.
    14. Tenenhaus, Michel & Vinzi, Vincenzo Esposito & Chatelin, Yves-Marie & Lauro, Carlo, 2005. "PLS path modeling," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 159-205, January.
    15. Henry Kaiser, 1974. "An index of factorial simplicity," Psychometrika, Springer;The Psychometric Society, vol. 39(1), pages 31-36, March.
    16. Kohei Adachi, 2013. "Generalized joint Procrustes analysis," Computational Statistics, Springer, vol. 28(6), pages 2449-2464, December.
    17. Chester Harris & Henry Kaiser, 1964. "Oblique factor analytic solutions by orthogonal transformations," Psychometrika, Springer;The Psychometric Society, vol. 29(4), pages 347-362, December.
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