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Generalized Canonical Correlation Analysis of Matrices with Missing Rows: a Simulation Study

Published online by Cambridge University Press:  01 January 2025

Michel van de Velden  and
Tammo H. A. Bijmolt
Michel van de Velden*
Affiliation:
Erasmus University Rotterdam
Tammo H. A. Bijmolt
Affiliation:
University of Groningen
*
Requests for reprints should be sent to M. van de Velden, Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands. E-mail: vandevelden@few.eur.nl
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Abstract

A method is presented for generalized canonical correlation analysis of two or more matrices with missing rows. The method is a combination of Carroll’s (1968) method and the missing data approach of the OVERALS technique (Van der Burg, 1988). In a simulation study we assess the performance of the method and compare it to an existing procedure called GENCOM, proposed by Green and Carroll (1988). We find that the proposed method outperforms the GENCOM algorithm both with respect to model fit and recovery of the true structure.

Keywords

generalized canonical correlation analysisOVERALSmissing valuesMonte carlo simulation
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 2 , June 2006 , pp. 323 - 331
Copyright
Copyright © 2006 The Psychometric Society

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Footnotes

The research of Michel van de Velden was partly funded through EU Grant HPMF-CT-2000-00664. The authors would like to thank the associate editor and three anonymous referees for their constructive comments and suggestions that led to a considerable improvement of the paper.

References

Alpert, M.I., & Peterson, R.A. (1972). On the interpretation of canonical analysis. Journal of Marketing Research, 9, 187–492.CrossRefGoogle Scholar
Bijmolt, T.H.A., & Wedel, M. (1999). A comparison of multidimensional scaling methods for perceptual mapping. Journal of Marketing Research, 36, 277–285.CrossRefGoogle Scholar
Borg, I., & Leutner, D. (1985). Measuring the similarity between MDS configurations. Multivariate Behavioral Research, 20, 325–334.CrossRefGoogle ScholarPubMed
Carroll, J.D. (1968). Generalization of canonical correlation analysis to three or more sets of variables. Proceedings of the 76th Annual Convention of the Psychological Association, 3, 227–228.Google Scholar
Commandeur, J.J.F. (1991). Matching configurations. Leiden: DSWO Press.Google Scholar
Gifi, A. (1990). Nonlinear multivariate analysis. Chichester, UK: Wiley.Google Scholar
Gleason, T.C. (1976). On redundancy in canonical analysis. Psychological Bulletin, 83, 1004–1006.CrossRefGoogle Scholar
Green, P.E., & Carroll, J.D. (1988). A simple procedure for finding a composite of several multidimensional scaling solutions. Journal of the Academy of Marketing Science, 16, 25–35.CrossRefGoogle Scholar
Greenacre, M.J. (1984). Theory and applications of correspondence analysis. London: Academic Press.Google Scholar
Hotelling, H. (1936). Filiations between two sets of variates. Biometrika, 28, 321–377.CrossRefGoogle Scholar
Lazraq, A., & Cléroux, R. (2001). Statistical inference concerning several redundancy indices. Journal of Multivariate Analysis, 79, 71–88.CrossRefGoogle Scholar
Lazraq, A., Cléroux, R., & Kiers, H.A.L. (1992). Mesures de liaison vectorielle et generalisation de l'analyse canonique. Revue de Statistique Appliquee, XXXIX(1), 23–35.Google Scholar
Meulman, J. (1982). Homogeneity analysis of incomplete data. Leiden: DSWO Press.Google Scholar
Steenkamp, J.-B.E.M., Van Trijp, H.C.M., & Ten Berge, J.M.F. (1994). Perceptual mapping based on idiosyncratic sets of attributes. Journal of Marketing Research, 31, 15–27.CrossRefGoogle Scholar
Stewart, D., & Love, W. (1968). A general canonical correlation index. Psychological Bulletin, 70, 160–463.CrossRefGoogle ScholarPubMed
Van der Burg, E. (1988). Nonlinear canonical correlation and some related techniques. Leiden: + DSWO Press.Google Scholar
Van der Burg, E., De Leeuw, J., & Dijksterhuis, G. (1994). OVERALS, nonlinear canonical correlation with k sets of variables. Computational Statistics and Data Analysis, 18, 141–463.CrossRefGoogle Scholar
Van der Burg, E., De Leeuw, J., & Verdegaal, R. (1988). Homogeneity analysis with k sets of variables: An alternating least squares method with optimal scaling features. Psychometrika, 53, 177–197.CrossRefGoogle Scholar