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The Geometry of Factorial Indeterminancy

Published online by Cambridge University Press:  01 January 2025

Emil F. Heermann
Emil F. Heermann*
Affiliation:
University of Maryland
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Abstract

The N-dimensional geometry of a Spearman-Thurstone factor solution reveals two sources for the indeterminancy of factor scores: indeterminancy of total factor space and a rotational indeterminancy within a given total factor space. The analytical papers of Ledermann [4] and Guttman [2] on indeterminancy of factor scores are related to these findings and a simple vector model is developed to reveal the properties of rotational indeterminancy. The significance of factor-score indeterminancy is discussed in light of these findings.

Type
Original Paper
Information
Psychometrika , Volume 29 , Issue 4 , December 1964 , pp. 371 - 381
Copyright
Copyright © 1964 Psychometric Society

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References

Guttman, L. General theory and methods of matric factoring. Psychometrika, 1944, 9, 1–16.CrossRefGoogle Scholar
Guttman, L. The determinancy of factor score matrices with implications for five other basic problems of common factor theory. Brit. J. statist. Psychol., 1955, 8, 65–81.CrossRefGoogle Scholar
Harman, H. Modern factor analysis, Chicago: Univ. Chicago Press, 1960.Google Scholar
Ledermann, W. The orthogonal transformation of a factorial matrix into itself. Psychometrika, 1938, 3, 181–187.CrossRefGoogle Scholar
Sommerville, D. M. Y. An introduction to the geometry of N dimensions, New York: Dover Publications, 1958.Google Scholar
Thomson, G. H. The definition and measurement ofg. J. educ. Psychol., 1935, 26, 241–262.CrossRefGoogle Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar