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A Definition for the Common-Factor Analysis Model and the Elimination of Problems of Factor Score Indeterminacy

Published online by Cambridge University Press:  01 January 2025

James S. Williams
James S. Williams*
Affiliation:
Colorado State University
*
Requests for reprints should be sent to J. S. Williams, Statistics Department, Colorado State University, Fort Collins, Colorado 80523.
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Abstract

A factor analysis model consists of a random sequence of variates defined on a probability space and satisfying the usual descriptive equations of the common-factor analysis in which the common-factor scores are dimensionally independent. Necessary and sufficient conditions are given for a model to exist with essentially unique and hence determinate common factor scores. Parallel results are given for the existence of models with nonunique and hence indeterminate scores. It is then próved that two models cannot exist with essentially unique but different scores for the same common factors. The meaning and application of these results are discussed.

Keywords

existence of a factor analysis modeluniqueness of common-factor scoresdeterminateness of factor scores
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 3 , September 1978 , pp. 293 - 306
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

Research reported in this paper was supported by Grant CTR-1066 from the Council for Tobacco Research.

References

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