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Factor Indeterminacy in the 1930’s and the 1970’s Some Interesting Parallels

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 James H. Steiger, Department of Psychology, University of British Columbia, Vancouver, B.C., CANADA V6T 1W5.
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Abstract

The issue of factor indeterminacy, and its meaning and significance for factor analysis, has been the subject of considerable debate in recent years. Interestingly, the identical issue was discussed widely in the literature of the late 1920's and early 1930's, but this early discussion was somehow lost or forgotten during the development and popularization of multiple factor analysis. There are strong parallels between the arguments in the early literature, and those which have appeared in recent papers. Here I review the history of this early literature, briefly survey the more recent work, and discuss these parallels where they are especially illuminating.

Keywords

factor analysisfactor indeterminacy
Type
Original Paper
Information
Psychometrika , Volume 44 , Issue 2 , June 1979 , pp. 157 - 167
Copyright
Copyright © 1979 The Psychometric Society

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Footnotes

Support by the NRC (Grant No. A4640) and the University of British Columbia (UBC Humanities and Social Sciences Grant 26-9508) is gratefully acknowledged.

References

Camp, B. H. The converse of Spearman's two-factor theorem. Biometrika, 1932, 24, 418–427.CrossRefGoogle Scholar
Camp, B. H. Spearman's general factor again. Biometrika, 1934, 26, 260–261.Google Scholar
Dodd, S. C. The theory of factors, I. Psychological Review, 1928, 35, 211–234.CrossRefGoogle Scholar
Dodd, S. C. The theory of factors, II. Psychological Review, 1928, 35, 261–279.CrossRefGoogle Scholar
Garnett, J. C. General ability, cleverness, and purpose. British Journal of Psychology, 1919, 9, 345–366.Google Scholar
Garnett, J. C. The single general factor in dissimilar mental measurements. British Journal of Psychology, 1920, 10, 242–258.Google Scholar
Gorsuch, R. L. Factor analysis, 1974, Philadelphia: Saunders.Google Scholar
Green, B. F. On the factor score controversy. Psychometrika, 1976, 41, 263–266.CrossRefGoogle Scholar
Guttman, L. The determinacy of factor score matrices with implications for five other basic problems of common factor theory. British Journal of Statistical Psychology, 1955, 8, 65–81.CrossRefGoogle Scholar
Guttman, L. “Best possible” systematic estimates of communalities. Psychometrika, 1956, 21, 273–285.CrossRefGoogle Scholar
Harman, H. H. Modern factor analysis, 2nd ed., Chicago: University of Chicago Press, 1967.Google Scholar
Harris, C. W. On factors and factor scores. Psychometrika, 1967, 32, 363–379.CrossRefGoogle Scholar
Hart, B. Spearman, C. General ability, its existence and nature. British Journal of Psychology, 1912, 5, 51–84.Google Scholar
Heermann, E. F. The geometry of factorial indeterminancy. Psychometrika, 1964, 29, 371–381.CrossRefGoogle Scholar
Heermann, E. F. The algebra of factorial indeterminancy. Psychometrika, 1966, 31, 539–543.CrossRefGoogle ScholarPubMed
Heywood, H. B. On finite sequences of real numbers. Proceedings of the Royal Society of London, 1931, 134, 486–501.Google Scholar
Holzinger, K. J., & Harman, H. H. Factor analysis, 1941, Chicago: University of Chicago Press.Google Scholar
Irwin, J. O. On the uniqueness of the factor g for general intelligence. British Journal of Psychology, 1932, 22, 359–363.Google Scholar
Irwin, J. O. On the indeterminacy in the estimate of g. British Journal of Psychology, 1935, 25, 393–394.Google Scholar
Kestelman, H. The fundamental equation of factor analysis. British Journal of Psychology, Statistical Section, 1952, 5, 1–6.CrossRefGoogle Scholar
Ledermann, W. The orthogonal transformation of a factorial matrix into itself. Psychometrika, 1938, 3, 181–187.CrossRefGoogle Scholar
McDonald, R. P. The measurement of factor indeterminacy. Psychometrika, 1974, 39, 203–221.CrossRefGoogle Scholar
McDonald, R. P., & Burr, E. J. A comparison of four methods of constructing factor scores. Psychometrika, 1967, 32, 381–401.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. The foundations of factor analysis, 1972, New York: McGraw-Hill.Google 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 indeterminancy in models with a single common factor. Psychometrika, 1978, 43, 177–192.CrossRefGoogle Scholar
Piaggio, H. T. H. The general factor in Spearman's theory of intelligence. Nature, 1931, 127, 56–57.CrossRefGoogle Scholar
Piaggio, H. T. H. Three sets of conditions necessary for the existence of a g that is real and unique except in sign. British Journal of Psychology, 1933, 24, 88–105.Google Scholar
Piaggio, H. T. H. Approximate general and specific factors without indeterminate parts. British Journal of Psychology, 1935, 25, 485–489.Google Scholar
Piaggio, H. T. H., & Dallas, A. E. M. N. An analysis of recent tests of the two-factor theory. British Journal of Psychology, 1934, 25, 217–220.Google Scholar
Schönemann, P. H. The minimum average correlation between equivalent sets of uncorrelated factors. Psychometrika, 1971, 36, 21–30.CrossRefGoogle Scholar
Schönemann, P. H., & Wang, M. M. Some new results on factor indeterminacy. Psychometrika, 1972, 37, 61–91.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
Spearman, C. General intelligence, objectively determined and measured. American Journal of Psychology, 1904, 15, 201–293.CrossRefGoogle Scholar
Spearman, C. Correlation between arrays in a table of correlations. Proceedings of the Royal Society, Series A, 1922, 101, 94–100.Google Scholar
Spearman, C. The abilities of man, 1927, New York: MacMillan.Google Scholar
Spearman, C. The uniqueness of ‘g’. Journal of Educational Psychology, 1933, 24, 106–108.Google Scholar
Spearman, C. The factor theory and its troubles. IV. Uniqueness of g. Journal of Educational Psychology, 1934, 25, 142–153.CrossRefGoogle Scholar
Steiger, J. H. The relationship between external variables and indeterminate factors. Psychometrika, 1979, 44, 93–97.CrossRefGoogle Scholar
Thomson, G. H. A hierarchy without a general factor. British Journal of Psychology, 1916, 8, 271–281.Google Scholar
Thomson, G. H. The hierarchy of abilities. British Journal of Psychology, 1919, 9, 337–344.Google Scholar
Thomson, G. H. The meaning of ‘i’ in the measurement of ‘g’ (general intelligence). Journal of Educational Psychology, 1935, 26, 241–262.CrossRefGoogle Scholar
Thurstone, L. L. The vectors of mind, 1935, Chicago: University of Chicago Press.Google Scholar
Thurstone, L. L. Multiple factor analysis, 1947, Chicago: University of Chicago Press.Google Scholar
Williams, J. S. A definition for the common factor model and the elimination of problems of factor score indeterminancy. Psychometrika, 1978, 43, 293–306.CrossRefGoogle Scholar
Wilson, E. B. Review of ‘The abilities of man, their nature and measurement’ by C. Spearman. Science, 1928, 67, 244–248.CrossRefGoogle Scholar
Wilson, E. B. On hierarchical correlation systems. Proceedings of the National Academy of Sciences, 1928, 14, 283–291.CrossRefGoogle ScholarPubMed
Wilson, E. B. Review of ‘Crossroads in the mind of man: A study of differentiable mental abilities’ by T. L. Kelley. Journal of General Psychology, 1929, 2, 153–169.Google Scholar
Wilson, E. B. Comments on Professor Spearman's note. Journal of Educational Psychology, 1929, 20, 217–223.CrossRefGoogle Scholar
Wolfle, D. Factor analysis to 1940. Psychometric Monographs, No. 3, 1940, Chicago: University of Chicago Press.Google Scholar