Abstract
A least squares method is presented for fitting a given matrixA to another given matrixB 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, T. W.An introduction to multivariate statistical analysis. New York: Wiley, 1958.
Bargmann, R. Review ofOn the unified factor theory of mind by Yrjö Ahmavaara.Psychometrika, 1960,25, 105–108.
Carroll, R. M. A Monte Carlo comparison of nonmetric multidimensional scaling and factor analysis. Doctoral dissertation, The Ohio State University, 1969.
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.
Green, B. F. The orthogonal approximation of an oblique simple structure in factor analysis.Psychometrika, 1952,17, 429–440.
Guttman, L. A general nonmetric technique for finding the smallest coordinate space for a configuration of points.Psychometrika, 1968,33, 469–506.
Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika, 1964a,29, 1–27.
Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method.Psychometrika, 1964b,29, 115–129.
Lingoes, J. C. & Guttman, L. Nonmetric factor analysis: A rank reducing alternative to linear factor analysis.Multivariate Behavioral Research, 1967,2, 485–505.
McGee, V. E. The multidimensional analysis of ‘elastic’ distances.The British Journal of Mathematical and Statistical Psychology, 1966,19, 181–196.
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.
Schönemann, P. H. On the formal matrix differentiation of traces and determinants. Research Memorandum No. 27, Chapel Hill: University of North Carolina Psychometric Laboratory, 1965.
Schönemann, P. H. A generalized solution of the orthogonal Procrustes problem.Psychometrika, 1966,31, 1–10.
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function. I, II.Psychometrika, 1962,27, 125–139, 219–246.
Author information
Authors and Affiliations
Additional information
Part of this work was done while the senior author held a visiting research fellowship at the Educational Testing Service, Princeton, New Jersey.
Rights and permissions
About this article
Cite this article
Schönemann, P.H., Carroll, R.M. Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika 35, 245–255 (1970). https://doi.org/10.1007/BF02291266
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02291266