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Simple Proofs of Relations Between the Communality Problem and Multiple Correlation

Published online by Cambridge University Press:  01 January 2025

Louis Guttman
Louis Guttman*
Affiliation:
The Israel Institute of Applied Social Research and The Hebrew University in Jerusalem
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Abstract

Solutions of the communality problem and of the problem of meaning of common and unique factors have been shown previously to depend intimately on certain relations with ordinary multiple correlation. To make these basic propositions more accessible, simple proofs of some of them are provided here, avoiding any matrix algebra. New results are also obtained, with no extra work, that extend the previously known propositions to a more general class of coefficients than that of communalities.

Type
Original Paper
Information
Psychometrika , Volume 22 , Issue 2 , June 1957 , pp. 147 - 157
Copyright
Copyright © 1957 Psychometric Society

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Footnotes

*

Revised from a paper written while on leave at the Center for Advanced Study in the Behavioral Sciences.

References

Guttman, L. Multiple rectilinear prediction and the resolution into components. Psychometrika, 1940, 5, 75–99CrossRefGoogle Scholar
Guttman, L. A basis for analyzing test-retest reliability. Psychometrika, 1945, 10, 255–282CrossRefGoogle ScholarPubMed
Guttman, L. Image theory for the structure of quantitative variates. Psychometrika, 1953, 18, 277–296CrossRefGoogle Scholar
Guttman, L. A. new appraoch to factor analysis: the radex. In Lazarsfeld, P. F. (Eds.), Mathematical thinking in the social sciences (pp. 308–309). Glencoe, Ill.: The Free Press, 1954Google Scholar
Guttman, L. The determinacy of factor score matrices with implications for five other basic problems of common-factor theory. Brit. J. statist. Psychol., 1955, 8, 65–81CrossRefGoogle Scholar
Guttman, L. “Best possible” systematic estimates for communalities. Psychometrika, 1956, 21, 273–285CrossRefGoogle Scholar
Roff, M. Some properties of the communality in multiple-factor theory. Psychometrika, 1936, 1, 1–6CrossRefGoogle Scholar