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Behavior Research Methods, Instruments, & Computers

, Volume 32, Issue 3, pp 389–395 | Cite as

Determining the number of factors to retain: Q windows-based FORTRAN-IMSL program for parallel analysis

  • Jennifer D. KaufmanEmail author
  • William P. Dunlap
Article

Abstract

Parallel analysis (PA; Horn, 1965) is a technique for determining the number of factors to retain in exploratory factor analysis that has been shown to be superior to more widely known methods (Zwick & Velicer, 1986). Despite its merits, PA is not widely used in the psychological literature, probably because the method is unfamiliar and because modern, Windows-compatible software to perform PA is unavailable. We provide a FORTRAN-IMSL program for PA that runs on a PC under Windows; it is interactive and designed to suit the range of problems encountered in most psychological research. Furthermore, we provide sample output from the PA program in the form of tabled values that can be used to verify the program operation; or, they can be used either directly or with interpolation to meet specific needs of the researcher.

Keywords

Exploratory Factor Analysis Parallel Analysis Scree Plot Nitr Multivariate Behavioral Research 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supplementary material

Kaufman-BRM-2000.zip (3 kb)
Supplementary material, approximately 340 KB.

References

  1. Allen, S. J., &Hubbard, R. (1986). Regression equations for the latent roots of random data correlation matrices with unities on the diagonal.Multivariate Behavioral Research,21, 393–398.CrossRefGoogle Scholar
  2. Cattell, R. B. (1966). The scree tests for the number of factors.Multivariate Behavioral Research,1, 245–276.CrossRefGoogle Scholar
  3. Comrey, A. L., &Lee, H. B. (1992).A first course in factor analysis. Hillsdale, NJ: Erlbaum.Google Scholar
  4. Cota, A. A., Longman, R. S., Holden, R. R., Fekken, C., &Xinaris, S. (1993). Interpolating 95th percentile eigenvalues from random data: An empirical example.Educational & Psychological Measurement,53, 585–596.CrossRefGoogle Scholar
  5. Everitt, B. S. (1975). Multivariate analysis: The need for data, and other problems.British Journal of Psychiatry,126, 237–240.CrossRefPubMedGoogle Scholar
  6. Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., &Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research.Psychological Methods,3, 272–299.CrossRefGoogle Scholar
  7. Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis.Psychometrica,30, 179–185.CrossRefGoogle Scholar
  8. Humphreys, L. G., &Montanelli, R. G., Jr. (1975). An investigation of the parallel analysis criterion for determining the number of common factors.Multivariate Behavioral Research,10, 193–205.CrossRefGoogle Scholar
  9. International Mathematical and Statistical Libraries (1982).International mathematics and statistical libraries reference manual (9th ed.). Houston: Author.Google Scholar
  10. Kaiser, H. F. (1960). The application of electronic computers to factor analysis.Education & Psychological Measurement,20, 141–151.CrossRefGoogle Scholar
  11. Lautenschlager, G. J. (1989). A comparison of alternatives to conducting Monte Carlo analyses for determining parallel analysis criteria.Multivariate Behavioral Research,24, 365–395.CrossRefGoogle Scholar
  12. Lautenschlager, G. J., Lance, C. E., &Flaherty, V. L. (1989). Parallel analysis criteria: Revised equations for estimating the latent roots of random data correlation matrices.Educational & Psychological Measurement,49, 339–345.CrossRefGoogle Scholar
  13. Lawley, D. N., &Maxwell, A. E. (1963).Factor analysis as a statistical method. London: Butterworth.Google Scholar
  14. Longman, R. S., Cota, A. A., Holden, R. R., &Fekken, G. C. (1989). PAN: A double precision FORTRAN routine for the parallel analysis method in principal components analysis.Behavior Research Methods, Instruments, & Computers,21, 477–480.CrossRefGoogle Scholar
  15. MacCallum, R. C., Widaman, K. F., Zhang, S., &Hong, S. (1999). Sample size in factor analysis.Psychological Methods,4, 84–99.CrossRefGoogle Scholar
  16. Montanelli, R. G., Jr., &Humphreys, L. G. (1976). Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A Monte Carlo study.Psychometrika,41, 341–348.CrossRefGoogle Scholar
  17. O’Connor, B. P. (2000). SPSS and SAS programs for determining the number of components using parallel analysis and Velicer’s MAP test.Behavior Research Methods, Instruments, & Computers,32, 396–402.CrossRefGoogle Scholar
  18. Sharma, S. (1996).Applied multivariate techniques. New York: Wiley.Google Scholar
  19. Tabachnick, B. G., &Fidell, L. S. (1996).Using multivariate statistics. New York: HarperCollins.Google Scholar
  20. Turner, N. E. (1998). The effect of common variance and structure pattern on random data eigenvalues: Implications for the accuracy of parallel analysis.Educational & Psychological Measurement,58, 541–568.CrossRefGoogle Scholar
  21. Velicer, W. F. (1976). Determining the number of components from the matrix of partial correlations.Psychometrika,41, 321–327.CrossRefGoogle Scholar
  22. Zwick, W. R., &Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain.Psychological Bulletin,99, 432–442.CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 2000

Authors and Affiliations

  1. 1.Department of PsychologyTulane UniversityNew Orleans

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