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Oblique Factor Analytic Solutions by Orthogonal Transformations

Published online by Cambridge University Press:  01 January 2025

Chester W. Harris  and
Henry F. Kaiser
Chester W. Harris
Affiliation:
University of Wisconsin
Henry F. Kaiser
Affiliation:
University of Wisconsin
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Abstract

A general framework for obtaining all possible factor analytic solutions, orthogonal and oblique, for a given common factor space is developed in detail. Interestingly, and seemingly paradoxically, any one of these solutions may be obtained by orthogonal transformations of selected matrices; thus an oblique solution may be determined by orthogonal transformations. Within the possible oblique solutions, two distinct categories of solutions emerge, a special case of the simpler of which apparently provides a definitive solution to the problem of independent, but correlated, clusters. Possible further specializations of the general approach to specific problems are discussed.

Type
Original Paper
Information
Psychometrika , Volume 29 , Issue 4 , December 1964 , pp. 347 - 362
Copyright
Copyright © 1964 Psychometric Society

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References

Harman, H. Modern factor analysis, Chicago: Univ. Chicago Press, 1960.Google Scholar
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Horst, P. A non-graphical method for transforming an arbitrary factor matrix into a simple structure factor matrix. Psychometrika, 1941, 6, 79–99.CrossRefGoogle Scholar