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Matrix Reduction and Approximation to Principal Axes

Published online by Cambridge University Press:  01 January 2025

Paul Horst
Paul Horst*
Affiliation:
University of Washington
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Abstract

A modification of Hotelling’s iteration method of factor analysis is presented which is much more rapid and almost as accurate. At any stage of the approximation for a factor vector its major product moment reduces the rank of the residual matrix by precisely one. Each approximation to an eigenvalue is larger than the preceding one. By observing the decline in these increments one can often stop the iterations at early stages without serious loss. If subsequent rotational procedures are used, the method gives practically the same results as the more exact methods and in a small fraction of the time.

Type
Original Paper
Information
Psychometrika , Volume 27 , Issue 2 , June 1962 , pp. 169 - 178
Copyright
Copyright © 1962 The Psychometric Society

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Footnotes

*

This study was supported in part by Office of Naval Research Contract Nonr-477(08) and Public Health Research Grant M-743 (C6).

References

Bodewig, E. Matrix calculus, New York: Interscience Publishers, 1959.Google Scholar
Burk, H. W. The effect of limiting the number of iterations on a principal axes factor analysis solution. Technical Report, Office of Naval Research Contract Nonr-477(08), and Public Health Research Grant M-743(C4), Univ. Washington Division of Counseling and Testing Services, February 1960.Google Scholar
Campbell, M. M. The primary dimensions of item ratings on scales designed to measure 24 of Murray’s Manifest Needs. Technical Report, Public Health Research Grant M-743(C4), Univ. Washington Division of Counseling and Testing Services, December 1959.Google Scholar
Guttman, L. General theory and methods for matric factoring. Psychometrika, 1944, 9, 1–16.CrossRefGoogle Scholar
Horst, P. Servant of the human sciences, Seattle: Division of Counseling and Testing Services, Univ. Washington, 1953.Google Scholar
Hotelling, H. Analysis of a complex of statistical variables into principal components. J. educ. Psychol., 1933, 24, 417–441.CrossRefGoogle Scholar
Hotelling, H. Analysis of a complex of statistical variables into principal components (Concluded). J. educ. Psychol., 1933, 24, 498–520.CrossRefGoogle Scholar
Lunneborg, C. E. and Wright, C. E. A modified principal axes factor analysis solution programmed for the IBM Type 650. Technical Report, Office of Naval Research Contract Nonr-477(08), and Public Health Research Grant M-743(C3), Univ. Washington Division of Counseling and Testing Services, August, 1958.Google Scholar
Murray, H. A. et al. Explorations in personality, New York: Oxford Univ. Press, 1938.Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Thurstone, L. L. and Thurstone, T. G. Factorial studies of intelligence, Chicago: Univ. Chicago Press, 1941.Google Scholar
Wright, C. E. Relations between normative and ipsative measures of personality Technical Report, Office of Naval Research Contract Nonr-477(08), and Public Health Research Grant M-743(C2), Univ. Washington Division of Counseling and Testing Services, December, 1957.Google Scholar