Research Article

The PLS multivariate regression model: testing the significance of successive PLS components

  1. Aziz Lazraq1,
  2. Robert Cléroux2,*

Article first published online: 8 JUN 2001

DOI: 10.1002/cem.641

Issue

Journal of Chemometrics

Journal of Chemometrics

Volume 15, Issue 6, pages 523–536, July 2001

Additional Information

How to Cite

Lazraq, A. and Cléroux, R. (2001), The PLS multivariate regression model: testing the significance of successive PLS components. Journal of Chemometrics, 15: 523–536. doi: 10.1002/cem.641

Author Information

  1. 1

    École Nationale de l'Industrie Minérale, Rabat, Morocco

  2. 2

    Department of Mathematics and Statistics, University of Montreal, Montreal, Quebec, Canada

*Department of Mathematics and Statistics, University of Montreal, Montreal, Quebec, Canada.

Publication History

  1. Issue published online: 8 JUN 2001
  2. Article first published online: 8 JUN 2001
  3. Manuscript Accepted: 8 MAY 2000
  4. Manuscript Received: 6 DEC 1999

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Keywords:

  • partial least squares;
  • PLS components;
  • stepwise selection;
  • redundancy index

Abstract

In this paper we write the PLS multivariate regression model in terms of a redundancy index and obtain some properties of the successive PLS components. We study their significance in the model and build tests of hypotheses to this effect. A stopping rule is given to obtain the right number of PLS components, and a numerical measure is defined to assess the overall quality of the PLS regression. Finally, an algorithm is given explicitly as it was coded in S-Plus and is applied in some chosen examples. Copyright © 2001 John Wiley & Sons, Ltd.

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