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A Set of Inequalities in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

J. N. Darroch
J. N. Darroch*
Affiliation:
University of Michigan
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Abstract

Inequalities relating the communalities to the multiple-correlation coefficients are derived. They are stronger than the well-known inequalities which have played an important role in factor analysis for the past thirty years. Necessary and sufficient conditions for equality are obtained.

Type
Original Paper
Information
Psychometrika , Volume 30 , Issue 4 , December 1965 , pp. 449 - 453
Copyright
Copyright © 1965 Psychometric Society

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References

Dwyer, P. S. The contribution of an orthogonal multiple factor solution to multiple correlation. Psychometrika, 1939, 4, 163–171.CrossRefGoogle Scholar
Guttman, L. “Best possible” systematic estimates of communalities. Psychometrika, 1956, 21, 273–285.CrossRefGoogle Scholar
Roff, M. Some properties of the communality in multiple factor theory. Psychometrika, 1935, 1, 1–6.CrossRefGoogle Scholar