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Descriptive Axioms for Common Factor Theory, Image Theory and Component Theory

Published online by Cambridge University Press:  01 January 2025

Roderick P. McDonald
Roderick P. McDonald*
Affiliation:
The Ontario Institute for Studies in Education
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Abstract

Through an extension of work by Guttman, common factor theory, image theory, and component theory are derived from distinct minimum subsets of assumptions chosen out of a set of five possible assumptions. It is thence shown that the problem of indeterminacy of factor scores in the common factor model is precisely reflected in the problem of the non-orthogonality of anti-images. Indeed, image scores are determinate for the same reason that the usual estimates of factor scores are determinate, and image scores cannot be used as though they were factor scores for the same reason that factor score estimates cannot be used as though they were factor scores.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 2 , June 1975 , pp. 137 - 152
Copyright
Copyright © 1975 The Psychometric Society

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