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A Note Concerning the Creager—Valentine Paper

Published online by Cambridge University Press:  01 January 2025

Aart Hazewinkel
Aart Hazewinkel*
Affiliation:
Netherlands Institute for Preventive Medicine, Leiden
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Abstract

The Ui statistic, discussed by Creager and Valentine in a recent paper, is defined as a standard error of estimate for the regression of a composite, consisting of n components, on the n − 1 components, exclusive of the jth component. It is shown that this standard error equals the standard error of estimate for the prediction of the jth component from the other n − 1 components. This equality is used to suggest an efficient procedure to compute all primary uniquenesses Ui.

Type
Original Paper
Information
Psychometrika , Volume 28 , Issue 1 , March 1963 , pp. 105 - 108
Copyright
Copyright © 1963 The Psychometric Society

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References

Creager, J. A. General resolution of correlation matrices into components and its utilization in multiple and partial regression. Psychometrika, 1958, 23, 1–8.CrossRefGoogle Scholar
Creager, J. A. and Valentine, L. D. Jr. Regression analysis of linear composite variance. Psychometrika, 1962, 27, 31–37.CrossRefGoogle Scholar
Fruchter, B. and Anderson, H. E. Geometrical representation of two methods of linear least squares multiple correlation. Psychometrika, 1961, 26, 433–442.CrossRefGoogle Scholar
Guttman, L. A note on the derivation of formulae for multiple and partial correlation. Ann. math. Statist., 1938, 9, 305–308.CrossRefGoogle Scholar