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Generalized Structured Component Analysis Accommodating Convex Components: A Knowledge-Based Multivariate Method with Interpretable Composite Indexes

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  • Gyeongcheol Cho

    (The Ohio State University)

  • Heungsun Hwang

    (McGill University)

Abstract

Generalized structured component analysis (GSCA) is a multivariate method for examining theory-driven relationships between variables including components. GSCA can provide the deterministic component score for each individual once model parameters are estimated. As the traditional GSCA always standardizes all indicators and components, however, it could not utilize information on the indicators’ scale in parameter estimation. Consequently, its component scores could just show the relative standing of each individual for a component, rather than the individual’s absolute standing in terms of the original indicators’ measurement scales. In the paper, we propose a new version of GSCA, named convex GSCA, which can produce a new type of unstandardized components, termed convex components, which can be intuitively interpreted in terms of the original indicators’ scales. We investigate the empirical performance of the proposed method through the analyses of simulated and real data.

Suggested Citation

  • Gyeongcheol Cho & Heungsun Hwang, 2024. "Generalized Structured Component Analysis Accommodating Convex Components: A Knowledge-Based Multivariate Method with Interpretable Composite Indexes," Psychometrika, Springer;The Psychometric Society, vol. 89(1), pages 241-266, March.
    • Handle: RePEc:spr:psycho:v:89:y:2024:i:1:d:10.1007_s11336-023-09944-3
    DOI: 10.1007/s11336-023-09944-3
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    References listed on IDEAS

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    1. Hariharan Swaminathan & James Algina, 1978. "Scale freeness in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 581-583, December.
    2. Heungsun Hwang & Yoshio Takane, 2004. "Generalized structured component analysis," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 81-99, March.
    3. 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.
    4. Gyeongcheol Cho & Heungsun Hwang & Marko Sarstedt & Christian M. Ringle, 2020. "Cutoff criteria for overall model fit indexes in generalized structured component analysis," Journal of Marketing Analytics, Palgrave Macmillan, vol. 8(4), pages 189-202, December.
    5. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
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