Hostname: page-component-5f745c7db-2kk5n Total loading time: 0 Render date: 2025-01-06T07:02:25.697Z Has data issue: true hasContentIssue false

A Note on the Tryon-Kaiser Solution for the Communalities

Published online by Cambridge University Press:  01 January 2025

Henry F. Kaiser*
Affiliation:
University of Illinois

Abstract

The Tryon-Kaiser solution for the communalities is reviewed. Numerical investigation suggests that the procedure is applicable if and only if the correlation matrix has unique minimum rank communalities. This implies that this approach to the communality problem is not general enough to be of practical use.

Type
Original Paper
Copyright
Copyright © 1959 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albert, A. A. The minimum rank of a correlation matrix. Proc. nat. Acad. Sci., 1944, 30, 144148.CrossRefGoogle ScholarPubMed
Guttman, L. “Best possible” systematic estimates of communalities. Psychometrika, 1956, 21, 273285.CrossRefGoogle Scholar
Kaiser, H. F. Solution for the communalities: a preliminary report. Rep. No. 5, Contract No. AF 41(657)-76, Univ. California, 1956.Google Scholar
Ledermann, W. On the rank of the reduced correlational matrix in multiple factor analysis. Psychometrika, 1937, 2, 8593.CrossRefGoogle Scholar
Scarborough, J. B. Numerical mathematical analysis (2nd ed.), Baltimore: Johns Hopkins, 1950.Google Scholar
Tryon, R. C. Communality of a variable: formulation by cluster analysis. Psychometrika, 1957, 22, 241260.Google Scholar