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General Resolution of Correlation Matrices into Components and its Utilization in Multiple and Partial Regression

Published online by Cambridge University Press:  01 January 2025

John A. Creager
John A. Creager*
Affiliation:
Air Force Personnel and Training Research Center
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Abstract

The derivation of multiple and partial regression statistics from uniqueness-augmented factor loadings, presented in the literature for orthogonal factor solutions, is generalized to oblique solutions. A mathematical rationale for the general case, without restriction to uncorrelated factors, is presented. Use of the general formulation is illustrated with a two-factor, seven-variable example.

Type
Original Paper
Information
Psychometrika , Volume 23 , Issue 1 , March 1958 , pp. 1 - 8
Copyright
Copyright © 1958 The Psychometric Society

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Footnotes

*

This report is based on work done under ARDC Project 7702, in support of the research and development program of the Air Force Personnel and Training Research Center, Lackland Air Force Base, Texas. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.

References

Dwyer, P. S. The evaluation of multiple and partial correlation coefficients from the factorial matrix. Psychometrika, 1940, 5, 211–232CrossRefGoogle Scholar
Dwyer, P. S. The relative efficacy and economy of various test selection methods. PRS Report 957, AGO. 12 June 1952.Google Scholar
Guttman, L. Multiple rectilinear prediction and the resolution into components. Psychometrika, 1940, 5, 75–99CrossRefGoogle Scholar
Guttman, L. and Cohen, J. Multiple rectilinear prediction and the resolution into components: II. Psychometrika, 1943, 8, 169–183CrossRefGoogle Scholar
Horst, P. The prediction of personal adjustment. SSRC Bull., 1941, 48, 437ffGoogle Scholar
Thorndike, R. L. Personnel selection, New York: Wiley, 1949Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947Google Scholar