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Partial Least Squares Regression for Binary Responses and Its Associated Biplot Representation

Author

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  • Laura Vicente-Gonzalez

    (Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain)

  • Jose Luis Vicente-Villardon

    (Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain)

Abstract

In this paper, we propose a generalization of Partial Least Squares Regression (PLS-R) for a matrix of several binary responses and a a set of numerical predictors. We call the method Partial Least Squares Binary Logistic Regression (PLS-BLR). That is equivalent to a PLS-2 model for binary responses. Biplot and even triplot graphical representations for visualizing PLS-BLR models are described, and an application to real data is presented. Software packages for the calculation of the main results are also provided. We conclude that the proposed method and its visualization using triplots are powerful tools for the interpretation of the relations among predictors and responses.

Suggested Citation

  • Laura Vicente-Gonzalez & Jose Luis Vicente-Villardon, 2022. "Partial Least Squares Regression for Binary Responses and Its Associated Biplot Representation," Mathematics, MDPI, vol. 10(15), pages 1-23, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2580-:d:871050
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    References listed on IDEAS

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    1. Opeoluwa F. Oyedele & Sugnet Lubbe, 2015. "The construction of a partial least-squares biplot," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(11), pages 2449-2460, November.
    2. Bastien, Philippe & Vinzi, Vincenzo Esposito & Tenenhaus, Michel, 2005. "PLS generalised linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 17-46, January.
    3. Sugnet Gardner-Lubbe & Niël Le Roux & John Gowers, 2008. "Measures of fit in principal component and canonical variate analyses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(9), pages 947-965.
    4. Jose Giovany Babativa-Márquez & José Luis Vicente-Villardón, 2021. "Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    5. Kiers, Henk A. L., 2002. "Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 157-170, November.
    6. Contreras-Reyes, Javier E. & López Quintero, Freddy O. & Wiff, Rodrigo, 2018. "Bayesian modeling of individual growth variability using back-calculation: Application to pink cusk-eel (Genypterus blacodes) off Chile," Ecological Modelling, Elsevier, vol. 385(C), pages 145-153.
    7. Michel Jose Anzanello & Flavio Sanson Fogliatto, 2014. "A review of recent variable selection methods in industrial and chemometrics applications," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 8(5), pages 619-645.
    8. S. le Cessie & J. C. van Houwelingen, 1992. "Ridge Estimators in Logistic Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 191-201, March.
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    Cited by:

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