Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-08T09:56:27.264Z Has data issue: false hasContentIssue false
  • English
  • Français

A General Solution to Mosier's Oblique Procrustes Problem

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge  and
Klaas Nevels
Jos M. F. ten Berge*
Affiliation:
University of Groningen
Klaas Nevels
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Jos M. F. ten Berge, Psychology Department, University of Groningen, THE NETHERLANDS.
Get access Rights & Permissions [Opens in a new window]

Abstract

Browne provided a method for finding a solution to the normal equations derived by Mosier for rotating a factor matrix to a best least squares fit with a specified structure. Cramer showed that Browne's solution is not always valid, and proposed a modified algorithm. Both Browne and Cramer assumed the factor matrix to be of full rank. In this paper a general solution is derived, which takes care of rank deficient factor matrices as well. A new algorithm is offered.

Keywords

oblique Procrustes rotation
Type
Original Paper
Information
Psychometrika , Volume 42 , Issue 4 , December 1977 , pp. 593 - 600
Copyright
Copyright © 1977 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

The authors are indebted to Jan de Leeuw and Cees van der Laan for pointing this out.

References

Reference Note

Jöreskog, K. G. On rotation to a specified simple structure, 1965, Princeton, N. J.: Educational Testing Service.Google Scholar

References

Browne, M. W. On oblique Procrustes rotation. Psychometrika, 1967, 32, 125–132.CrossRefGoogle ScholarPubMed
Cramer, E. M. On Browne's solution for oblique Procrustes rotation. Psychometrika, 1974, 39, 159–163.CrossRefGoogle Scholar
Forsythe, G. F. & Golub, G. H. On the stationary values of a second-degree polynomial on the unit sphere. SIAM Journal of Applied Mathematics, 1965, 13, 1050–1068.CrossRefGoogle Scholar
Lawson, C. L. & Hanson, R. J. Solving least squares problems, 1974, Englewood Cliffs, N. J.: Prentice-Hall.Google Scholar
Macon, N. Numerical analysis, 1963, New York: Wiley.Google Scholar
Mosier, C. I. Determining a simple structure when loadings for certain tests are known. Psychometrika, 1939, 4, 149–162.CrossRefGoogle Scholar
Mulaik, S. A. The foundations of factor analysis, 1972, New York: McGraw-Hill.Google Scholar