Skip to main content

On the validity of indeterminate factor scores

Abstract

A partition of the vector space of all deviation score vectors for fixed sample size N is used to show that the (indeterminate) factors of the factor model can always be constructed so as to predict any criterion perfectly, including all those that are entirely uncorrected with the observed variables.

References

  1. 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.

    Article  Google Scholar 

  2. Kestelman, H. The fundamental equation of factor analysis. British Journal of Psychology, Statistical Section, 1952, 5, 1–6.

    Article  Google Scholar 

  3. Pease, M. C. III. Methods of matrix algebra. New York and London: Academic Press, 1965.

    Google Scholar 

  4. Piaggio, H. T. H. The general factor in Spearman’s theory of intelligence. Nature, 1931, 127, 56–57.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  7. Searle, S. R. Matrix algebra for the biological sciences. New York: Wiley, 1966.

    Google Scholar 

  8. Seber, G. A. F. The linear hypothesis: A general theory. New York: Hafner, 1966.

    Google Scholar 

  9. Spearman, C. The abilities of man. New York: McMillan, 1927.

    Google Scholar 

  10. Steiger, J. H., & SchÖnemann, P. H. A history of factor indeterminacy. In Shye,S. (Ed.), Theory construction and data analysis. San Francisco: Jossey-Bass, in press.

  11. Tucker, L. Relations of factor score estimates to their use. Psychometrika, 1971, 36, 427–436.

    Article  Google Scholar 

  12. Wilson, E. B. On hierarchical correlation system. Proceedings of the National Academy of Sciences, 1928, 14, 283–291.

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Peter H. SchÖnemann.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

SchÖnemann, P.H., Steiger, J.H. On the validity of indeterminate factor scores. Bull. Psychon. Soc. 12, 287–290 (1978). https://doi.org/10.3758/BF03329685

Download citation

Keywords

  • Deviation Score
  • Factor Model
  • Factor Score
  • Null Space
  • Test Space