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Fitting One Matrix to Another Under Choice of a Central Dilation and a Rigid Motion

Published online by Cambridge University Press:  01 January 2025

Peter H. Schönemann  and
Robert M. Carroll
Peter H. Schönemann
Affiliation:
The Ohio State University
Robert M. Carroll
Affiliation:
The Ohio State University
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Abstract

A least squares method is presented for fitting a given matrix A to another given matrix B under choice of an unknown rotation, an unknown translation, and an unknown central dilation. The procedure may be useful to investigators who wish to compare results obtained with nonmetric scaling techniques across samples or who wish to compare such results with those obtained by conventional factor analytic techniques on the same sample.

Type
Original Paper
Information
Psychometrika , Volume 35 , Issue 2 , June 1970 , pp. 245 - 255
Copyright
Copyright © 1970 The Psychometric Society

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Footnotes

*

Now at Purdue University. Part of this work was done while the senior author held a visiting research fellowship at the Educational Testing Service, Princeton, New Jersey.

†

Now at the University of Maryland.

References

Anderson, T. W. An introduction to multivariate statistical analysis, 1958, New York: Wiley.Google Scholar
Bargmann, R. Review of On the unified factor theory of mind by Yrjö Ahmavaara. Psychometrika, 1960, 25, 105–108.CrossRefGoogle Scholar
Carroll, R. M. A Monte Carlo comparison of nonmetric multidimensional scaling and factor analysis. Doctoral dissertation, The Ohio State University, 1969.Google Scholar
Cliff, N. Orthogonal rotation to congruence. Psychometrika, 1966, 31, 33–42.CrossRefGoogle Scholar
Eckart, C. & Young, G. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211–218.CrossRefGoogle Scholar
Green, B. F. The orthogonal approximation of an oblique simple structure in factor analysis. Psychometrika, 1952, 17, 429–440.CrossRefGoogle Scholar
Guttman, L. A general nonmetric technique for finding the smallest coordinate space for a configuration of points. Psychometrika, 1968, 33, 469–506.CrossRefGoogle Scholar
Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 1964, 29, 1–27.CrossRefGoogle Scholar
Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method. Psychometrika, 1964, 29, 115–129.CrossRefGoogle Scholar
Lingoes, J. C. & Guttman, L. Nonmetric factor analysis: A rank reducing alternative to linear factor analysis. Multivariate Behavioral Research, 1967, 2, 485–505.CrossRefGoogle Scholar
McGee, V. E. The multidimensional analysis of ‘elastic’ distances. The British Journal of Mathematical and Statistical Psychology, 1966, 19, 181–196.CrossRefGoogle Scholar
Prien, E. P. & Liske, R. E. Assessments of higher-level personnel: III Rating criteria: A comparative analysis of supervisor ratings and incumbent self-ratings of job performance. Personnel Psychology, 1962, 15, 187–194.CrossRefGoogle Scholar
Schönemann, P. H. On the formal matrix differentiation of traces and determinants, 1965, Chapel Hill: University of North Carolina Psychometric Laboratory.Google Scholar
Schönemann, P. H. A generalized solution of the orthogonal Procrustes problem. Psychometrika, 1966, 31, 1–10.CrossRefGoogle Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function. I, II. Psychometrika, 1962, 27, 125–139.CrossRefGoogle Scholar