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“Best Possible” Systematic Estimates of Communalities

Published online by Cambridge University Press:  01 January 2025

Louis Guttman
Louis Guttman*
Affiliation:
The Israel Institute of Applied Social Research
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Abstract

At least four approaches have been used to estimate communalities that will leave an observed correlation matrix R Gramian and with minimum rank. It has long been known that the square of the observed multiple-correlation coefficient is a lower bound to any communality of a variable of R. This lower bound actually provides a “best possible” estimate in several senses. Furthermore, under certain conditions basic to the Spearman-Thurstone common-factor theory, the bound must equal the communality in the limit as the number of observed variables increases. Otherwise, this type of theory cannot hold for R.

Keywords

Public PolicyStatistical TheoryVariable IncreaseSystematic EstimateMinimum Rank
Type
Original Paper
Information
Psychometrika , Volume 21 , Issue 3 , September 1956 , pp. 273 - 285
Copyright
Copyright © 1956 The Psychometric Society

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Footnotes

*

This research was facilitated by a grant from the Lucius N. Littauer Foundation to the American Committee for Social Research in Israel in order to promote methodological work of the Israel Institute of Applied Social Research.

References

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