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The Relationship between External Variables and Common Factors

Published online by Cambridge University Press:  01 January 2025

James H. Steiger
James H. Steiger*
Affiliation:
University of British Columbia
*
Requests for reprints should be sent to Dr. James H. Steiger, Department of Psychology, University of British Columbia, Vancouver, B.C., CANADA V6T 1W5.
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Abstract

A theorem is presented which gives the range of possible correlations between a common factor and an external variable (i.e., a variable not included in the test battery factor analyzed). Analogous expressions for component (and regression component) theory are also derived. Some situations involving external correlations are then discussed which dramatize the theoretical differences between components and common factors.

Keywords

factor analysisfactor indeterminacyexternal variables

Information

Type
Original Paper
Information
Psychometrika , Volume 44 , Issue 1 , March 1979 , pp. 93 - 97
Copyright
Copyright © 1979 The Psychometric Society

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Footnotes

Support by the National Research Council of Canada (NRC Grant No. A4640) and the University of British Columbia (UBC Humanities and Social Sciences Grant 26-9718) is gratefully acknowledged.

This paper is based in part on the author's Ph.D. dissertation. I am particularly grateful to my dissertation advisor, Dr. Peter H. Schönemann. Thanks also to the editor and the anonymous reviewers, who contributed many helpful comments and suggestions.

References

Reference Note

Steiger, J. H. The relationship between external variables and indeterminate factors. Unpublished doctoral dissertation, Purdue University, 1976.Google Scholar

References

Green, B. F. On the factor score controversy. Psychometrika, 1976, 41, 263–266.CrossRefGoogle Scholar
McDonald, R. P. The measurement of factor indeterminacy. Psychometrika, 1974, 39, 203–221.CrossRefGoogle Scholar
McDonald, R. P. The indeterminacy of components and the definition of common factors. British Journal of Mathematical and Statistical Psychology, 1977, 30, 165–176.CrossRefGoogle Scholar
Meyer, E. P. On the relationship between ratio of number of variables to number of factors and factorial indeterminacy. Psychometrika, 1973, 38, 375–378.CrossRefGoogle Scholar
Mulaik, S. A. Comments on ‘the measurement of factorial indeterminacy.’. Psychometrika, 1976, 41, 249–262.CrossRefGoogle Scholar
Mulaik, S. A., & McDonald, R. P. The effect of additional variables on factor indeterminacy in models with a single common factor. Psychometrika, 1978, 43, 177–192.CrossRefGoogle Scholar
Schönemann, P. H. The minimum average correlation between equivalent sets of uncorrelated factors. Psychometrika, 1971, 36, 21–30.CrossRefGoogle Scholar
Schönemann, P. H. & Steiger, J. H. Regression component analysis. British Journal of Mathematical and Statistical Psychology, 1976, 29, 175–189.CrossRefGoogle Scholar
Schönemann, P. H., & Steiger, J. H. On the validity of indeterminate factor scores. Bulletin of the Psychonomic Society, 1978, 12, 287–290.CrossRefGoogle Scholar
Schönemann, P. H. & Wang, M. M. Some new results on factor indeterminacy. Psychometrika, 1972, 37, 61–91.CrossRefGoogle Scholar
Steiger, J. H. & Schönemann;, P. H. A history of factor score indeterminary. In Shye, S.(Eds.), Theory construction and data analysis in the behavioral Sciences, 1978, San Francisco: Jossey-Bass.Google Scholar
Williams, J. S. A definition for the common factor model and the elimination of problems of factor score indeterminacy. Psychometrika, 1978, 43, 293–306.CrossRefGoogle Scholar