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A Semi-Orthogonal Dependent Factor Solution

Published online by Cambridge University Press:  01 January 2025

Olgierd R. Porebski
Olgierd R. Porebski*
Affiliation:
University of New South Wales*
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Abstract

The paper presents a general framework for the dependent factor method in which judgmental as well as analytic criteria may be employed. The procedure involves a semi-orthogonal transformation of an oblique solution comprising a number of reference factors and a number of experimental factors (composites). It determines analytically the residual factors in the experimental field keeping the reference field constant. The method is shown to be a generalization of the multiple factor procedure [Thurstone, 1947] in so far as it depends on the use of generalized inverse in deriving partial structure from total pattern. It is also shown to provide an example of the previously empty category (Case III) of the Harris-Kaiser generalization [1964]. A convenient computational procedure is provided. It is based on an extension of Aitken's [1937] method of pivotal condensation of a triple-product matrix to the evaluation of a matrix of the form H − VA−1U' (for a nonsingular A).

Keywords

Public PolicyStatistical TheoryGeneral FrameworkAnalytic CriterionExperimental Factor

Information

Type
Original Paper
Information
Psychometrika , Volume 33 , Issue 4 , December 1968 , pp. 451 - 468
Copyright
Copyright © 1968 Psychometric Society

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Footnotes

*

Now at the University of Ottawa

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