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Alternating Least Squares Algorithms for Simultaneous Components Analysis with Equal Component Weight Matrices in Two or More Populations

Published online by Cambridge University Press:  01 January 2025

Henk A. L. Kiers  and
Jos M. F. ten Berge
Henk A. L. Kiers*
Affiliation:
University of Groningen
Jos M. F. ten Berge
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Henk A. L. Kiers, Department of Psychology, Grote Markt 31/32, 9712 HV Groningen, THE NETHERLANDS.
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Abstract

Millsap and Meredith (1988) have developed a generalization of principal components analysis for the simultaneous analysis of a number of variables observed in several populations or on several occasions. The algorithm they provide has some disadvantages. The present paper offers two alternating least squares algorithms for their method, suitable for small and large data sets, respectively. Lower and upper bounds are given for the loss function to be minimized in the Millsap and Meredith method. These can serve to indicate whether or not a global optimum for the simultaneous components analysis problem has been attained.

Keywords

simultaneous components analysisalternating least squaresprincipal components analysislongitudinal datacross-sectional datastationary component weights
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 3 , September 1989 , pp. 467 - 473
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

Financial support by the Netherlands organization for scientific research (NWO) is gratefully acknowledged.

References

Meredith, W., & Millsap, R. E. (1985). On component analysis. Psychometrika, 50, 495–507.CrossRefGoogle Scholar
Millsap, R. E., & Meredith, W. (1988). Component analysis in cross-sectional and longitudinal data. Psychometrika, 53, 123–134.CrossRefGoogle Scholar
ten Berge, J. M. F. (1986). Rotation to perfect congruence and the cross-validation of component weights across populations. Multivariate Behavioral Research, 21, 41–64.CrossRefGoogle ScholarPubMed