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The uniqueness and significance of simple structure demonstrated by contrasting organic “natural structure” and “random structure” data

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Abstract

The study compares the extent to which naturally structured data and artificial, relatively random data (both with the same basic parameters) produce simple structure factors which are uniquely determined. Two examples of unstructured matrices were compared with the ball problem matrix. The results show that an oblique position of maximum hyperplane count in the structured data differs from that in the unstructured by reaching a significantly more unique position in terms of the exactitude with which it is re-discoverable when starting from different positions, and by reaching (at the maximum) a significantly higher hyperplane count.

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References

  1. Bargmann, V. R. Signifikanzuntersuchugen der einfachen Strukture in der Factoranalyse.Mitteilungsblatt für Mathematische Statistik, Physiea-Verlag, Wursburg, 1954.

    Google Scholar 

  2. Burt, C. The factorial study of temperamental traits.Brit. J. Psychol, Statist. Sec., 1948,1, 178–203.

    Google Scholar 

  3. Cattell, R. B. A note of factor invariance and the identification of factors,Brit. J. Psychol., Statist. Sec., 1949,2, 134–139.

    Google Scholar 

  4. Cattell, R. B. Extracting the correct number of factors in factor analysis.Educ. psychol. Measmt, 1958,18, 791–838.

    Google Scholar 

  5. Cattell, R. B. The basis of recognition and interpretation of factors.Educ. psychol. Measmt, 1962,22, 667–697.

    Google Scholar 

  6. Cattell, R. B. and Baggaley, A. R. The salient variable similarity index for factor matching.Brit. J. statist. Psychol., 1960,8, 33–46.

    Google Scholar 

  7. Cattell, R. B. and Cattell, A. K. S. Factor rotation for proportional profiles: analytical solution and an example.Brit. J. statist. Psychol., 1955,8, 83–91.

    Google Scholar 

  8. Cattell, R. B. and Dickman, K. A dynamic model of physical influences demonstrating the necessity of oblique simple structure.Psychol. Bull., 1962,59, 389–400.

    Google Scholar 

  9. Cattell, R. B. and Foster, M. The rotoplot program for multiple single-plane, visually-guided rotation (up to 36 factors).Educ. psychol. Measmt, 1963, in press.

  10. Cattell, R. B. and Muerle, J. L. The “maxplane” program for factor rotation to oblique simple structure.Educ. psychol. Measmt, 1960,20, 569–590.

    Google Scholar 

  11. Cattell, R. B. and Sullivan, W. The scientific nature of factors: a demonstration by cups of coffee.Behav. Sci., 1962,7, 184–193.

    Google Scholar 

  12. Cattell, R. B. and White, O. Confactor rotation discussed and illustrated. Advanced Publication No. 17, Lab. of Personality Assessment, Univ. of Illinois, 1962.

  13. Guttman, L. Some necessary conditions for common-factor analysis.Psychometrika, 1954,19, 149–161.

    Google Scholar 

  14. Harman, H. H.Modern factor analysis. Chicago: Univ. Chicago Press, 1960.

    Google Scholar 

  15. Hurley, J. L. and Cattell, R. B. The Procrustes program, producing direct rotation to test an hypothesized factor structure.Behav. Sci., 1962,7, 258–262.

    Google Scholar 

  16. Kaiser, H. F. The varimax criterion for analytic rotation in factor analysis.Psychometrika, 1958,23, 187–200.

    Google Scholar 

  17. Kaiser, H. F. Relating factors between studies based upon different individuals. Preliminary unpublished manuscript, 1960.

  18. Landhal, H. D. Centroid orthogonal transformation.Psychometrika, 1940,5, 67–74.

    Google Scholar 

  19. Neuhaus, J. O. and Wrigley, C. The quartimax method.Brit. J. statist. Psychol., 1954,7, 81–91.

    Google Scholar 

  20. Pinzka, C. and Saunders, D. R. Analytic rotation to simple structure II. Princeton, N. J.: Educational Testing Service Research Bulletin, RB-54-31, 1954.

  21. Saunders, D. R. The rationale for an “oblimax” method of transformation in factor analysis.Psychometrika, 1961,26, 317–324.

    Google Scholar 

  22. Saunders, D. R. Factor analysis I. Some effects of chance.Psychometrika, 1948,13, 251–257.

    Google Scholar 

  23. Siegal, S.Nonparametric statistics for the behavioral sciences. New York: McGraw-Hill, 1956.

    Google Scholar 

  24. Sokol, R. R. A comparison of five tests for completeness of factor extraction.Transaction of the Kansas Acad. of Sci., 1959,62, 141–152.

    Google Scholar 

  25. Thurstone, L. L. Primary mental abilities.Psychometric Monogr., No. 1. Chicago: Univ. Chicago Press, 1938.

    Google Scholar 

  26. Thurstone, L. L.Multiple-factor analysis. Chicago: Univ. Chicago Press, 1947.

    Google Scholar 

  27. Tucker, L. R. A method for synthesis of factor analysis studies. Personnel Research Section Report, No. 984, Washington, D. C.: Dept. of the Army, 1951.

    Google Scholar 

  28. Wrigley, C. and Neuhaus, J. O. The matching of two sets of factors. Contract Memorandum Report, A-32, Urbana, Ill.: Univ. of Illinois, 1955.

    Google Scholar 

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Authors and Affiliations

  1. University of Illinois, USA

    Raymond B. Cattell & Richard L. Gorsuch

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  1. Raymond B. Cattell
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  2. Richard L. Gorsuch
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Cattell, R.B., Gorsuch, R.L. The uniqueness and significance of simple structure demonstrated by contrasting organic “natural structure” and “random structure” data. Psychometrika 28, 55–67 (1963). https://doi.org/10.1007/BF02289548

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  • DOI: https://doi.org/10.1007/BF02289548

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