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A Note on Sufficient Conditions that a Common Factor will be Determinate in an Infinite Domain of Variables

Published online by Cambridge University Press:  01 January 2025

Stanley A. Mulaik
Stanley A. Mulaik*
Affiliation:
Georgia Institute of Technology
*
Requests for reprints should be sent to Dr. Stanley A. Mulaik, School of Psychology, Georgia Institute of Technology, Atlanta, GA 30332.
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Abstract

It is proved for the common factor model with r common factors that under certain condition s which maintain the distinctiveness of each common factor a given common factor will be determinate if there exists an unlimited number of variables in the model each having an absolute correlation with the factor greater than some arbitrarily small positive quantity.

Keywords

factor analysisfactor indeterminacy
Type
Notes And Comments
Information
Psychometrika , Volume 46 , Issue 1 , March 1981 , pp. 105 - 107
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

The author is indebted to R. P. McDonald for suggesting the proof of Guttman’s determinantal equation for the squared multiple correlation in predicting a factor from the observed variables used in the parenthetical note.

References

Guttman, L. Multiple rectilinear prediction and the resolution into components. Psychometrika, 1940, 5, 75–99.CrossRefGoogle Scholar
Mulaik, S. A. Inferring the communality of a variable in a universe of variables. Psychological Bulletin, 1966, 66, 119–124.CrossRefGoogle Scholar
Mulaik, S. A. & McDonald, R. P. The effect of additional variables on factor indeterminacy in models with a single common factor. Psychometrika, 1978, 43, 177–192.CrossRefGoogle Scholar
Piaggio, H. T. Three sets of conditions necessary for the existence of a g that is real and unique except for sign. British Journal of Psychology, 1933, 24, 88–105.Google Scholar