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The relationship between external variables and common factors

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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.

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Reference note

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 Unpublished doctoral dissertation, Purdue University, 1976.

References

  • Green, B. F. On the factor score controversy.Psychometrika, 1976,41, 263–266.

    Google Scholar 

  • McDonald, R. P. The measurement of factor indeterminacy.Psychometrika, 1974,39, 203–221.

    Google 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.

    Google 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.

    Google Scholar 

  • Mulaik, S. A. Comments on ‘the measurement of factorial indeterminacy.’Psychometrika, 1976,41, 249–262.

    Google 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.

    Google Scholar 

  • Schönemann, P. H. The minimum average correlation between equivalent sets of uncorrelated factors.Psychometrika, 1971,36, 21–30.

    Google Scholar 

  • Schönemann, P. H. & Steiger, J. H. Regression component analysis.British Journal of Mathematical and Statistical Psychology, 1976,29, 175–189.

    Google Scholar 

  • Schönemann, P. H., & Steiger, J. H. On the validity of indeterminate factor scores.Bulletin of the Psychonomic Society, 1978,12, 287–290.

    Google Scholar 

  • Schönemann, P. H., & Wang, M. M. Some new results on factor indeterminacy.Psychometrika, 1972,37, 61–91.

    Google Scholar 

  • Steiger J. H. & Schönemann; P. H. A history of factor score indeterminary. In Shye, S. (ed)Theory construction and data analysis in the behavioral Sciences, San Francisco: Jossey-Bass, 1978.

    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.

    Google Scholar 

Download references

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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.

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Steiger, J.H. The relationship between external variables and common factors. Psychometrika 44, 93–97 (1979). https://doi.org/10.1007/BF02293788

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  • DOI: https://doi.org/10.1007/BF02293788

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