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On the Co-Inertia(-PLS) analysis with linear constraints

Author

Listed:
  • Pietro Amenta

    (University of Sannio)

  • Antonello D’Ambra

    (University of Campania L. Vanvitelli)

Abstract

This paper presents a theoretical framework based on Co-Inertia Analysis (Chessel and Mercier, in: Lebreton, Asselain (eds) Biométrie et Environnement, Masson, Paris, 1993), which has been enhanced by incorporating the Restricted Eigenvalue Problem principle (Rao in Linear statistical inference and its application, Wiley, New York, 1973). This modified framework includes external information as a linear restrictions on parameters from both sets of variables, introducing two new constrained methods. One method is an extension of Wold’s two-block “Mode A” Partial Least Squares (Wegelin in A survey of partial least squares (PLS) methods with emphasis on the two-block case, 2000; Wold, in: Joreskog, Wold (eds) Systems under indirect observations: part II, North-Holland, Amsterdam, 1982; in: Kotz, Johnson (eds) Encyclopedia of statistical sciences, Wiley, New York, 1985), while the other applies linear constraints to the coefficients of Partial Least Squares Regression (Höskuldsson in J Chemom 2:211–228, 1988; Tenenhaus in La Régression PLS: Théorie et pratique, 1998) that is a popular technique that generalizes and combines features from principal component analysis and multiple regression. The paper also discusses the mathematical and geometrical properties of these approaches.

Suggested Citation

  • Pietro Amenta & Antonello D’Ambra, 2025. "On the Co-Inertia(-PLS) analysis with linear constraints," Quality & Quantity: International Journal of Methodology, Springer, vol. 59(3), pages 1979-1998, June.
    • Handle: RePEc:spr:qualqt:v:59:y:2025:i:3:d:10.1007_s11135-024-02019-0
    DOI: 10.1007/s11135-024-02019-0
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    References listed on IDEAS

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    1. Yoshio Takane & Haruo Yanai & Shinichi Mayekawa, 1991. "Relationships among several methods of linearly constrained correspondence analysis," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 667-684, December.
    2. John Geer, 1984. "Linear relations amongk sets of variables," Psychometrika, Springer;The Psychometric Society, vol. 49(1), pages 79-94, March.
    3. Yoshio Takane & Tadashi Shibayama, 1991. "Principal component analysis with external information on both subjects and variables," Psychometrika, Springer;The Psychometric Society, vol. 56(1), pages 97-120, March.
    4. Ledyard Tucker, 1958. "An inter-battery method of factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(2), pages 111-136, June.
    5. Norman Cliff, 1966. "Orthogonal rotation to congruence," Psychometrika, Springer;The Psychometric Society, vol. 31(1), pages 33-42, March.
    6. Martens, Harald & Anderssen, Endre & Flatberg, Arnar & Gidskehaug, Lars Halvor & Hoy, Martin & Westad, Frank & Thybo, Anette & Martens, Magni, 2005. "Regression of a data matrix on descriptors of both its rows and of its columns via latent variables: L-PLSR," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 103-123, January.
    7. Takane, Yoshio & Yanai, Haruo & Hwang, Heungsun, 2006. "An improved method for generalized constrained canonical correlation analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 221-241, January.
    8. Yoshio Takane & Henk Kiers & Jan Leeuw, 1995. "Component analysis with different sets of constraints on different dimensions," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 259-280, June.
    9. Pietro Amenta & Antonio Lucadamo & Antonello D’Ambra, 2021. "Restricted Common Component and Specific Weight Analysis: A Constrained Explorative Approach for the Customer Satisfaction Evaluation," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 156(2), pages 409-427, August.
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