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The Uniqueness and Significance of Simple Structure Demonstrated by Contrasting Organic “Natural Structure” and “Random Structure” Data

Published online by Cambridge University Press:  01 January 2025

Raymond B. Cattell  and
Richard L. Gorsuch
Raymond B. Cattell
Affiliation:
University of Illinois
Richard L. Gorsuch
Affiliation:
University of Illinois
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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.

Type
Original Paper
Information
Psychometrika , Volume 28 , Issue 1 , March 1963 , pp. 55 - 67
Copyright
Copyright © 1963 The Psychometric Society

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References

Bargmann, V. R. Signifikanzuntersuchugen der einfachen Strukture in der Factoranalyse. Mitteilungsblatt für Mathematische Statistik, Wursburg: Physiea-Verlag, 1954.Google Scholar
Burt, C. The factorial study of temperamental traits. Brit. J. Psychol, Statist. Sec., 1948, 1, 178–203.CrossRefGoogle Scholar
Cattell, R. B. A note of factor invariance and the identification of factors. Brit. J. Psychol., Statist. Sec., 1949, 2, 134–139.CrossRefGoogle Scholar
Cattell, R. B. Extracting the correct number of factors in factor analysis. Educ. psychol. Measmt, 1958, 18, 791–838.CrossRefGoogle Scholar
Cattell, R. B. The basis of recognition and interpretation of factors. Educ. psychol. Measmt, 1962, 22, 667–697.CrossRefGoogle Scholar
Cattell, R. B. and Baggaley, A. R. The salient variable similarity index for factor matching. Brit. J. statist. Psychol., 1960, 8, 33–46.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.Google Scholar
Cattell, R. B. and Muerle, J. L. The “maxplane” program for factor rotation to oblique simple structure. Educ. psychol. Measmt, 1960, 20, 569–590.CrossRefGoogle Scholar
Cattell, R. B. and Sullivan, W. The scientific nature of factors: a demonstration by cups of coffee. Behav. Sci., 1962, 7, 184–193.CrossRefGoogle Scholar
Cattell, R. B. and White, O. Confactor rotation discussed and illustrated. Advanced Publication No. 17, Lab. of Personality Assessment, Univ. of Illinois, 1962.Google Scholar
Guttman, L. Some necessary conditions for common-factor analysis. Psychometrika, 1954, 19, 149–161.CrossRefGoogle Scholar
Harman, H. H. Modern factor analysis, Chicago: Univ. Chicago Press, 1960.Google Scholar
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.CrossRefGoogle Scholar
Kaiser, H. F. The varimax criterion for analytic rotation in factor analysis. Psychometrika, 1958, 23, 187–200.CrossRefGoogle Scholar
Kaiser, H. F. Relating factors between studies based upon different individuals. Preliminary unpublished manuscript, 1960.Google Scholar
Landhal, H. D. Centroid orthogonal transformation. Psychometrika, 1940, 5, 67–74.Google Scholar
Neuhaus, J. O. and Wrigley, C. The quartimax method. Brit. J. statist. Psychol., 1954, 7, 81–91.CrossRefGoogle Scholar
Pinzka, C. and Saunders, D. R. Analytic rotation to simple structure II. Princeton, N. J.: Educational Testing Service Research Bulletin, RB-54-31, 1954.CrossRefGoogle Scholar
Saunders, D. R. The rationale for an “oblimax” method of transformation in factor analysis. Psychometrika, 1961, 26, 317–324.CrossRefGoogle Scholar
Saunders, D. R. Factor analysis I. Some effects of chance. Psychometrika, 1948, 13, 251–257.CrossRefGoogle ScholarPubMed
Siegal, S. Nonparametric statistics for the behavioral sciences, New York: McGraw-Hill, 1956.Google Scholar
Sokol, R. R. A comparison of five tests for completeness of factor extraction. Transaction of the Kansas Acad. of Sci., 1959, 62, 141–152.CrossRefGoogle Scholar
Thurstone, L. L. Primary mental abilities. Psychometric Monogr., No. 1, Chicago: Univ. Chicago Press, 1938.Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Tucker, L. R. A method for synthesis of factor analysis studies, Washington, D. C.: Dept. of the Army, 1951.CrossRefGoogle Scholar
Wrigley, C. and Neuhaus, J. O. The matching of two sets of factors, Urbana, Ill.: Univ. of Illinois, 1955.Google Scholar