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Influence of Chance Error on Simple Structure: An Empirical Investigation of the Effect of Chance Error and Estimated Communalities on Simple Structure in Factorial Analysis

Published online by Cambridge University Press:  01 January 2025

Charles I. Mosier
Charles I. Mosier*
Affiliation:
University of Florida
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Abstract

Correlation coefficients derived from an hypothetical simple structure for twenty tests and four factors were “loaded” with chance error components. Centroid analyses and rotations to give least square determinations of the hypothetical simple structure were made for several conditions. It is concluded that the experimental situation of inaccurate coefficients and estimated communalities permits accurate determination of primary trait loadings provided that the rank of the centroid matrix is equal to or greater than that of the underlying primary trait matrix. Of several criteria for the completeness of factorization which were tested, none was wholly satisfactory.

Type
Original Paper
Information
Psychometrika , Volume 4 , Issue 1 , March 1939 , pp. 33 - 44
Copyright
Copyright © 1939 The Psychometric Society

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References

Eckhart, Car, and Young, Gal, The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211–218.CrossRefGoogle Scholar
Mosier, C. I., “On rotation to a known simple structure,” to appear in Psychometrika.Google Scholar
Thurstone, L. L., The Vectors of Mind. Chicago: Univ. of Chicago Press. 1935, xv–xv.Google Scholar