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Testing the Significance of the Successive Components in Redundancy Analysis

Published online by Cambridge University Press:  01 January 2025

Aziz Lazraq  and
Robert Cléroux
Aziz Lazraq
Affiliation:
École Nationale de L'Industrie Minérale, Rabat, Morrocco
Robert Cléroux*
Affiliation:
Department of Mathematics and Statistics, University of Montreal
*
Requests for reprints should be sent to Robert Cléroux, Department de Mathematiques et de Statistique, Universite de Montreal, P.O. Box 6128, Succursale Centre-Ville, Montreal, Quebec, CANADA H3C 3J7. E-Mail: cleroux@dms.umontreal.ca
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Abstract

In this paper we study the interrelationships between two sets of data measured on the same subjects via redundancy analysis. We consider redundancy analysis from an inferential point of view. Under the hypothesis of multinormality, tests of significance are obtained for each successive redundancy component so that only the significant factors are retained for prediction purposes. An example illustrates the method.

Keywords

redundancy analysissignificant factorstests of significancecanonical correlationmultivariate linear regression

Information

Type
Articles
Information
Psychometrika , Volume 67 , Issue 3 , September 2002 , pp. 411 - 419
Copyright
Copyright © 2002 The Psychometric Society

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Footnotes

The authors would like to thank the Editor and the referees for their helpful comments. This research has been partly financed by NSERC (Canada).

References

Anderson, R.L., & Bancroft, T.A. (1952). Statistical theory in research. New York, NY: McGraw-Hill.Google Scholar
Bry, X. (1996). Analyses factorielles multiples. Paris, France: Economica.Google Scholar
Buzas, T.E., Fornell, C., & Byong-Duk, Rhee (1989). Conditions under which canonical correlation and redundancy maximization produce identical results. Biometrika, 76, 618–621.CrossRefGoogle Scholar
Cramer, E.M., & Nicewander, W.A. (1979). Some symmetric, invariant measures of multivariate association. Psychometrika, 44, 43–54.CrossRefGoogle Scholar
Dawson-Saunders, B.K., & Tatsuoka, M.M. (1983). The effect of affine transformation on redundancy analysis. Psychometrika, 48, 299–302.CrossRefGoogle Scholar
DeSarbo, W.S. (1981). Canonical/Redundancy factoring analysis. Psychometrika, 46, 307–329.CrossRefGoogle Scholar
Fornell, C. (1979). External single-set component analysis of multiple criterion/multiple predictor variables. Multivariate Behavioral Research, 14, 323–338.CrossRefGoogle ScholarPubMed
Gleason, T. (1976). On redundancy in canonical analysis. Psychological Bulletin, 83, 1004–1006.CrossRefGoogle Scholar
Imhof, P. (1961). Computing the distribution of quadratic forms in normal variates. Biometrika, 48, 419–426.CrossRefGoogle Scholar
Israëls, A.Z. (1984). Redundancy analysis for qualitative variables. Psychometrika, 49, 331–346.CrossRefGoogle Scholar
Johansson, J.K. (1981). An extension of Wollenberg's redundancy analysis. Psychometrika, 46, 93–103.CrossRefGoogle Scholar
Koertz, J., & Abrahamse, A.P.J. (1969). On the theory and application of the general linear model. Rotterdam, Netherlands: Rotterdam University Press.Google Scholar
Lazraq, A., & Cléroux, R. (1988). Étude comparative de différentes mesures de liaison entre deux vecteurs alatoires. Statistique et Analyse des donnes, 13, 15–38.Google Scholar
Lazraq, A., & Cléroux, R. (1988). Un algorithme pas à pas de sélection de variables en régression linéaire multivariée. Statistique et Analyse des donnes, 13, 39–58.Google Scholar
Mardia, K.V., Kent, J.T., & Bibby, J.M. (1979). Multivariate analysis. London, U.K.: Academic Press.Google Scholar
Muller, K.E. (1981). Relationships between redundancy analysis, canonical correlation and multivariate regression. Psychometrika, 46, 139–142.CrossRefGoogle Scholar
Rao, C.R. (1964). The use and interpretation of principal component analysis in applied research. Sankhya, 26, 329–358.Google Scholar
Rao, C.R. (1973). Linear statistical inference and its applications 2nd ed., New York, NY: John Wiley & Sons.CrossRefGoogle Scholar
Stewart, D., & Love, W. (1968). A general canonical correlation index. Psychological Bulletin, 70, 160–163.CrossRefGoogle ScholarPubMed
Tyler, D.E. (1982). On the optimality of the simultaneous redundancy transformations. Psychometrika, 47, 77–86.CrossRefGoogle Scholar
van den Wollenberg, A.L. (1977). Redundancy analysis, an alternative for canonical correlation analysis. Psychometrika, 42, 207–219.CrossRefGoogle Scholar
van de Geer, J.P. (1984). Linear relationships amongK sets of variables. Psychometrika, 49, 79–94.CrossRefGoogle Scholar