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A Note on Lower Bounds for the Number of Common Factors

Published online by Cambridge University Press:  01 January 2025

Michael W. Browne
Michael W. Browne*
Affiliation:
Educational Testing Service
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Abstract

It is shown that the lower bounds for the number of common factors, established by Guttman [1954] and modified by Kaiser [1961], cannot decrease as the number of observed variates is increased. The result implies that the lower bounds cannot become weaker if the number of observed variates is increased and the number of factors remains constant.

Type
Original Paper
Information
Psychometrika , Volume 33 , Issue 2 , June 1968 , pp. 233 - 236
Copyright
Copyright © 1968 The Psychometric Society

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Footnotes

*

This paper is based on a section of a thesis submitted to the Department of Statistics of the University of the Witwatersrand in fulfillment of the requirements for a M.Sc. degree.

†

Presently at the National Institute for Personnel Research, Johannesburg, South Africa.

References

Guttman, L. Multiple rectilinear prediction and the resolution into components. Psychometrika, 1940, 5, 75–99.CrossRefGoogle Scholar
Guttman, L. Some necessary conditions for common factor analysis. Psychometrika, 1954, 19, 149–161.CrossRefGoogle Scholar
Guttman, L. Inequalities for sign frequencies of latent roots. Jerusalem: The Israel Institute of Applied Social Research, 1961, Technical Note No. 7.Google Scholar
Kaiser, H. F. A note on Guttman's lower bounds for the number of common factors. British Journal of Statistical Psychology, 1961, 14, 1–2.CrossRefGoogle Scholar
Ostrowski, A. M. A quantitative formulation of Sylvester's Law of Inertia. Proceedings of the National Academy of Sciences of the United States, 1959, 65, 740–744.CrossRefGoogle Scholar