Orthogonal procrustes rotation for two or more matrices
- Jos M. F. Ten Berge
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
Necessary and sufficient conditions for rotating matrices to maximal agreement in the least-squares sense are discussed. A theorem by Fischer and Roppert, which solves the case of two matrices, is given a more straightforward proof. A sufficient condition for a best least-squares fit for more than two matrices is formulated and shown to be not necessary. In addition, necessary conditions suggested by Kristof and Wingersky are shown to be not sufficient. A rotation procedure that is an alternative to the one by Kristof and Wingersky is presented. Upper bounds are derived for determining the extent to which the procedure falls short of attaining the best least-squares fit. The problem of scaling matrices to maximal agreement is discussed. Modifications of Gower's method of generalized Procrustes analysis are suggested.
- Haven, S.Empirical comparison of two methods of simultaneous Procrustes rotation (Heymans Bulletin 76-245 EX). Groningen, the Netherlands: University of Groningen, Department of Psychology, 1976.
- Schonemann, P. H., Bock, R. D., & Tucker, L. R.Some notes on a theorem by Eckart and Young (Res. Memorandum No. 25). Chapel Hill, North Carolina: University of North Carolina Psychometric Laboratory, 1965.
- Tucker, L. R.A method for synthesis of factor analytic studies (Personnel Research Section Report No. 984). Washington, D. C.: Department of the Army, 1951.
- Cliff, N. Orthogonal rotation to congruence.Psychometrika, 1966,31, 33–42.
- Eckart, C. & Young, G. The approximation of one matrix by another of lower rank.Psychometrika, 1936,1, 211–218.
- Fischer, G. H. & Roppert, J. Ein Verfahren der Transformationsanalyse faktorenanalytischer Ergebnisse. In J. Roppert and G. H. Fischer,Lineare Strukturen in Mathematik und Statistik. Wien/Würzburg: Physika-Verlag, 1965.
- Gower, J. C. Generalized Procrustes analysis.Psychometrika, 1975,40, 33–51.
- Green, B. F. The orthogonal approximation of an oblique structure in factor analysis.Psychometrika, 1952,17, 429–440.
- Kettenring, J. R. Canonical analysis of several sets of variables.Biometrika, 1971,58, 433–451.
- Kristof, W. Die beste orthogonale Transformation zur gegenseitigen Ueberfuehrung zweier Faktormatrizen.Diagnostica, 1964,10, 87–90.
- Kristof, W. & Wingersky, B. Generalization of the orthogonal Procrustes rotation procedure for more than two matrices.Proceedings of the 79th Annual Convention of the American Psychological Association, 1971, 89–90.
- Schönemann, P. H. A generalized solution of the orthogonal Procrustes problem.Psychometrika, 1966,31, 1–10.
- Orthogonal procrustes rotation for two or more matrices
Volume 42, Issue 2 , pp 267-276
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- factor matching
- least-squares rotation
- Industry Sectors
- Author Affiliations
- 1. Psychology Department, University of Groningen, Groningen, the Netherlands