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Continuum redundancy-PLS regression: A simple continuum approach

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  • Bougeard, S.
  • Hanafi, M.
  • Qannari, E.M.

Abstract

The relationships between two data sets are investigated. The aim is to predict one data set from the other. New formulations of Redundancy Analysis and Partial Least Square Regression (PLS) are discussed, clearly showing the connexions between these two popular methods. Moreover, it is shown that the Redundancy Analysis and PLS regression are the two end points of a continuum approach. Properties related to this continuum approach are discussed, showing how the multicolinearity problem is handled. The interest of the general strategy of analysis is illustrated on the basis of a data set pertaining to epidemiology.

Suggested Citation

  • Bougeard, S. & Hanafi, M. & Qannari, E.M., 2008. "Continuum redundancy-PLS regression: A simple continuum approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3686-3696, March.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3686-3696
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    References listed on IDEAS

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    1. Keith Muller, 1981. "Relationships between redundancy analysis, canonical correlation, and multivariate regression," Psychometrika, Springer;The Psychometric Society, vol. 46(2), pages 139-142, June.
    2. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    3. Arnold Wollenberg, 1977. "Redundancy analysis an alternative for canonical correlation analysis," Psychometrika, Springer;The Psychometric Society, vol. 42(2), pages 207-219, June.
    4. Takane, Yoshio & Hwang, Heungsun, 2007. "Regularized linear and kernel redundancy analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 394-405, September.
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    Cited by:

    1. Arthur Tenenhaus & Michel Tenenhaus, 2011. "Regularized Generalized Canonical Correlation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 257-284, April.
    2. Tenenhaus, Arthur & Philippe, Cathy & Frouin, Vincent, 2015. "Kernel Generalized Canonical Correlation Analysis," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 114-131.

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