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A Non-Graphical Method for Transforming an Arbitrary Factor Matrix into a Simple Structure Factor Matrix

Published online by Cambridge University Press:  01 January 2025

Paul Horst
Paul Horst*
Affiliation:
The Procter & Gamble Company
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Abstract

The most commonly used method of factoring a matrix of intercorrelations is the centroid method developed by L. L. Thurstone. It is, however, necessary to transform the centroid matrix of factor loadings into a simple structure matrix in order to facilitate the interpretation of the factor loadings. Current methods for effecting this transformation are chiefly graphical and require considerable experience and personal judgment. This paper presents a new method for transforming an arbitrary factor matrix into a simple structure matrix by methods almost completely objective. The theory underlying the method is developed and approximation procedures are derived. The method is applied to a matrix of factor loadings previously analyzed by Thurstone.

Type
Original Paper
Information
Psychometrika , Volume 6 , Issue 2 , April 1941 , pp. 79 - 99
Copyright
Copyright © 1941 The Psychometric Society

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Footnotes

*

We shall not here consider how the correlation matrix is reproduced by the factor matrix, as this relationship is extensively discussed in numerous published works.

References

Hotelling, H. Analysis of a complex of statistical variables into principle components, Baltimore: Warwick and York, 1933.Google Scholar
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Tucker, L. R. A Rotational method based upon the mean principal axis of a subgroup of tests. Psychological Bulletin, 1940, 37, 578–578.Google Scholar