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On Oblique Procrustes Rotation

Published online by Cambridge University Press:  01 January 2025

Michael W. Browne
Michael W. Browne*
Affiliation:
Educational Testing Service
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Abstract

The equations involved in the rotation of an arbitrary factor matrix to a least squares fit to a specified factor structure have been known for many years. These equations, in general, cannot be solved by purely algebraic means, and an approximate solution has previously been used in practical applications.

In this paper an effective iterative method for obtaining the exact solution is developed. By algebraic manipulation the set of equations is expressed in the form of one polynomial equation in one unknown. Newton's method is suggested for solving this equation. Practical applications of the procedure indicate that convergence within small tolerance limits is generally attained after few iterations.

Type
Original Paper
Information
Psychometrika , Volume 32 , Issue 2 , June 1967 , pp. 125 - 132
Copyright
Copyright © 1967 The Psychometric Society

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Footnotes

*

Part of this research was carried out at the National Institute for Personnel Research (South Africa). It was completed while the author was a Visiting Research Psychologist at Educational Testing Service.

References

Green, B. F. The orthogonal approximation of an oblique structure in factor analysis. Psychometrika, 1952, 17, 429–440.CrossRefGoogle Scholar
Lanczos, C. Applied analysis, Englewood Cliffs, N. J.: Prentice Hall, 1956.Google Scholar
Mosier, C. I. Determining a simple structure when loadings for certain tests are known. Psychometrika, 1939, 4, 149–162.CrossRefGoogle Scholar