IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i15p2580-d871050.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/15/2580/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/15/2580/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bastien, Philippe & Vinzi, Vincenzo Esposito & Tenenhaus, Michel, 2005. "PLS generalised linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 17-46, January.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Eric Melillanca & Milton Ramírez & Eric Forcael, 2023. "Model of Key Factors in the Sustainable Growth of Small and Medium-Sized Enterprises Belonging to the First Nations," Sustainability, MDPI, vol. 15(11), pages 1-27, May.

    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. Meisam Moghimbeygi & Anahita Nodehi, 2022. "Multinomial Principal Component Logistic Regression on Shape Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 578-599, November.
    2. Aziza Usmanova & Ahmed Aziz & Dilshodjon Rakhmonov & Walid Osamy, 2022. "Utilities of Artificial Intelligence in Poverty Prediction: A Review," Sustainability, MDPI, vol. 14(21), pages 1-39, October.
    3. Christopher J Greenwood & George J Youssef & Primrose Letcher & Jacqui A Macdonald & Lauryn J Hagg & Ann Sanson & Jenn Mcintosh & Delyse M Hutchinson & John W Toumbourou & Matthew Fuller-Tyszkiewicz &, 2020. "A comparison of penalised regression methods for informing the selection of predictive markers," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-14, November.
    4. André Altmann & Michal Rosen-Zvi & Mattia Prosperi & Ehud Aharoni & Hani Neuvirth & Eugen Schülter & Joachim Büch & Daniel Struck & Yardena Peres & Francesca Incardona & Anders Sönnerborg & Rolf Kaise, 2008. "Comparison of Classifier Fusion Methods for Predicting Response to Anti HIV-1 Therapy," PLOS ONE, Public Library of Science, vol. 3(10), pages 1-9, October.
    5. Janns Alvaro Patiño-Saucedo & Paola Patricia Ariza-Colpas & Shariq Butt-Aziz & Marlon Alberto Piñeres-Melo & José Luis López-Ruiz & Roberto Cesar Morales-Ortega & Emiro De-la-hoz-Franco, 2022. "Predictive Model for Human Activity Recognition Based on Machine Learning and Feature Selection Techniques," IJERPH, MDPI, vol. 19(19), pages 1-21, September.
    6. Markovsky, Ivan & Niranjan, Mahesan, 2010. "Approximate low-rank factorization with structured factors," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3411-3420, December.
    7. Orea, Luis & Zofío, José L., 2017. "A primer on the theory and practice of efficiency and productivity analysis," Efficiency Series Papers 2017/05, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    8. la Grange, Anthony & le Roux, Niël & Gardner-Lubbe, Sugnet, 2009. "BiplotGUI: Interactive Biplots in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 30(i12).
    9. František Dařena & Jan Přichystal, 2018. "Analysis of the Association between Topics in Online Documents and Stock Price Movements," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 66(6), pages 1431-1439.
    10. repec:wyi:journl:002122 is not listed on IDEAS
    11. Groenen, P.J.F. & Giaquinto, P. & Kiers, H.A.L., 2003. "Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models," Econometric Institute Research Papers EI 2003-09, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Wayne DeSarbo & Heungsun Hwang & Ashley Stadler Blank & Eelco Kappe, 2015. "Constrained Stochastic Extended Redundancy Analysis," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 516-534, June.
    13. Li Shaoyu & Lu Qing & Fu Wenjiang & Romero Roberto & Cui Yuehua, 2009. "A Regularized Regression Approach for Dissecting Genetic Conflicts that Increase Disease Risk in Pregnancy," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-30, October.
    14. ben Jabeur, Sami & Mefteh-Wali, Salma & Carmona, Pedro, 2021. "The impact of institutional and macroeconomic conditions on aggregate business bankruptcy," Structural Change and Economic Dynamics, Elsevier, vol. 59(C), pages 108-119.
    15. Sami Ben Jabeur & Youssef Fahmi, 2018. "Forecasting financial distress for French firms: a comparative study," Empirical Economics, Springer, vol. 54(3), pages 1173-1186, May.
    16. Basma Albanna & Julia Handl & Richard Heeks, 2021. "Publication outperformance among global South researchers: An analysis of individual-level and publication-level predictors of positive deviance," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(10), pages 8375-8431, October.
    17. Sami BEN JABEUR, 2014. "Prévision de la détresse financière des entreprises françaises: Approche par la régression logistique PLS," Working Papers 2014-321, Department of Research, Ipag Business School.
    18. G Johnes, 2005. "Nations will fall? Revisiting the economic determinants of attitudes to European integration," Working Papers 566772, Lancaster University Management School, Economics Department.
    19. Butaru, Florentin & Chen, Qingqing & Clark, Brian & Das, Sanmay & Lo, Andrew W. & Siddique, Akhtar, 2016. "Risk and risk management in the credit card industry," Journal of Banking & Finance, Elsevier, vol. 72(C), pages 218-239.
    20. Krijnen, Wim P., 2006. "Convergence of the sequence of parameters generated by alternating least squares algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 481-489, November.
    21. repec:lan:wpaper:4385 is not listed on IDEAS
    22. Matthew Herland & Richard A. Bauder & Taghi M. Khoshgoftaar, 2020. "Approaches for identifying U.S. medicare fraud in provider claims data," Health Care Management Science, Springer, vol. 23(1), pages 2-19, 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:gam:jmathe:v:10:y:2022:i:15:p:2580-:d:871050. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.