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The Square Root Method and Multiple Group Methods of Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Harry H. Harman
Harry H. Harman*
Affiliation:
Personnel Research Branch, the Adjutant General's Office*
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Abstract

The square root method for the solution of a set of simultaneous linear equations or the reduction of a matrix has been known for some time under a variety of names. Because of its usefulness in statistical work, especially in factor analysis, the square root method is presented in general terms and an example given. Several independently developed “multiple group methods” for factor analysis are compared and synthesized. Their fundamental concepts are set forth and an appropriate system of notation developed. Detailed computational procedures are outlined, and the square root method is emphasized as a computing aid in multiple group analysis.

Type
Original Paper
Information
Psychometrika , Volume 19 , Issue 1 , March 1954 , pp. 39 - 55
Copyright
Copyright © 1954 Psychometric Society

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Footnotes

*

The opinions expressed in this paper are those of the author and do not necessarily reflect official Department of the Army policy. The author is now with The RAND Corporation, Santa Monica, Calif.

References

Banachiewicz, T. Méthode de résolution numerique des équations linéaires, du calcul de déterminants et des inverses et de réduction des formes quadratiques. Bull. Int. Acad. Polonaise des Sciences et Lettres, Series A: Sci. Math., Cracovie 1938, pp. 393–404.Google Scholar
Banachiewicz, T.. An outline of the Cracovian algorithm of the method of least squares. Astr. Jour., 1942, 50, 38–41CrossRefGoogle Scholar
Benoit, Commandant. Note sur une méthode de résolution des équations normales. Bulletin Géodésique, Paris, 1924, pp. 67–77.Google Scholar
Dwyer, Paul S.. A matrix presentation of least squares and correlation theory with matrix justification of improved methods of solution. Annals math. Statist., 1944, 15, 82–89CrossRefGoogle Scholar
Dwyer, Paul S.. The square root method and its use in correlation and regression. J. Amer. statist. Assn., 1945, 40, 493–503CrossRefGoogle Scholar
Dwyer, Paul S.. Linear Computations, New York: Wiley, 1951Google Scholar
Guttman, Louis. General theory and methods for matrix factoring. Psychometrika, 1944, 9, 1–16CrossRefGoogle Scholar
Guttman, Louis. Multiple group methods for common-factor analysis: their basis, computation, and interpretation. Psychometrika, 1952, 17, 209–222CrossRefGoogle Scholar
Harman, Harry H. and Dwyer, Paul S. The relative efficacy and economy of various test selection methods. (Presented at Fifty-Ninth Annual Convention of the American Psychological Association, Chicago, 1951.)Google Scholar
Holzinger, Karl J.. Preliminary report on Spearman-Holzinger unitary trait study, No. 5, Chicago: Dept. of Education, University of Chicago, 1935Google Scholar
Holzinger, Karl J.. A simple method of factor analysis. Psychometrika, 1944, 9, 257–262CrossRefGoogle Scholar
Holzinger, Karl J., Harman, Harry H.. Factor analysis, Chicago: Univ. Chicago Press, 1941Google Scholar
Horst, Paul. A method of factor analysis by means of which all coordinates of the factor matrix are given simultaneously. Psychometrika, 1937, 2, 225–236CrossRefGoogle Scholar
McMahon, James. Hyperspherical goniometry; and its application to correlation theory for n variables. Biometrika, 1923, 15, 173–208CrossRefGoogle Scholar
Thurstone, L. L.. The vectors of mind, Chicago: Univ. Chicago Press, 1935Google Scholar
Thurstone, L. L.. A multiple group method of factoring the correlation matrix. Psychometrika, 1945, 10, 73–78CrossRefGoogle Scholar
Thurstone, L. L.. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947Google Scholar
Thurstone, L. L.. Note about the multiple group method. Psychometrika, 1949, 14, 43–45CrossRefGoogle ScholarPubMed