Hostname: page-component-6bf8c574d5-h6jzd Total loading time: 0.001 Render date: 2025-02-23T13:56:49.046Z Has data issue: false hasContentIssue false
  • English
  • Français

Evaluation of Factor Analytic Research Procedures by means of Simulated Correlation Matrices

Published online by Cambridge University Press:  01 January 2025

Ledyard R Tucker ,
Raymond F. Koopman  and
Robert L. Linn
Ledyard R Tucker
Affiliation:
University of Illinois
Raymond F. Koopman
Affiliation:
Simon Fraser University
Robert L. Linn
Affiliation:
Educational Testing Service
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In order to study the effectiveness of factor analytic methods, a procedure was developed for computing simulated correlation matrices which are more similar to real data correlation matrices than are those matrices computed from the factor analysis structural model. In the present investigation, three methods of factor extraction were studied as applied to 54 simulated correlation matrices which varied in proportion of variance derived from a major factor domain, number of factors in the major domain, and closeness of the simulation procedure to the factor analysis structural model. While the factor extraction methods differed little from one another in quality of results for matrices more dissimilar to the factor analytic model, major differences in quality of results were associated with fewer factors in the major domain, higher proportion of variance from the major domain, and closeness of the simulation procedure to the factor analysis structural model.

Type
Original Paper
Information
Psychometrika , Volume 34 , Issue 4 , December 1969 , pp. 421 - 459
Copyright
Copyright © 1969 The Psychometric Society

Footnotes

*

The research was jointly supported by the University of Illinois and the office of Naval Research under contracts Nonr 1834(39) and N00014-67-A-0305-0003.

References

Burt, C. Factor analysis and canonical correlations. British Journal of Statistical Psychology, 1949, 1, 95–106.CrossRefGoogle Scholar
Cattell, R. B. and Dickman, K. A dynamic model of physical influences demonstrating the necessity of oblique simple structure. Psychological Bulletin, 1962, 59, 389–400.CrossRefGoogle ScholarPubMed
Cattell, R. B. and Sullivan, W. The scientific nature of factors: a demonstration by cups of coffee. Behavioral Sciences, 1962, 7, 184–193.CrossRefGoogle Scholar
Cliff, N. and Hamburger, C. D. The study of sampling errors in factor analysis by means of artificial experiments. Psychological Bulletin, 1967, 68, 430–445.CrossRefGoogle Scholar
Guttman, L. Image theory for the structure of quantitative variates. Psychometrika, 1953, 18, 277–296.CrossRefGoogle Scholar
Guttman, L. Some necessary conditions for common-factor analysis. Psychometrika, 1954, 19, 149–161.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. To what extent can communalities reduce rank?. Psychometrika, 1958, 23, 297–308.CrossRefGoogle Scholar
Harris, C. W. Some Rao-Guttman relationships. Psychometrika, 1962, 27, 247–263.CrossRefGoogle Scholar
Holzinger, K. J. and Harman, H. H. Comparison of two factorial analyses. Psychometrika, 1938, 3, 45–60.CrossRefGoogle Scholar
Hotelling, H. Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 1933, 24, 417–441.CrossRefGoogle Scholar
Kaiser, H. F. Varimax solution for primary mental abilities. Psychometrika, 1960, 25, 153–158.CrossRefGoogle Scholar
Kaiser, H. F. A note on Guttman's lower bound for the number of common factors. British Journal of Statistical Psychology, 1961, 14, 1–2.CrossRefGoogle Scholar
Kaiser, H. F. and Caffrey, J. Alpha factor analysis. Psychometrika, 1965, 30, 1–14.CrossRefGoogle ScholarPubMed
Kelley, T. L. Essential traits of mental life. Harvard Studies in Education,26, 1935, Cambridge, Mass.: Harvard Univ. Press.Google Scholar
Lawley, D. N. The estimation of factor loadings by the method of maximum likelihood. Proceedings of the Royal Society of Edinborough, 1940, A40, 64–82.CrossRefGoogle Scholar
Linn, R. L. A Monte Carlo approach to the number of factors problem. Psychometrika, 1968, 33, 37–71.CrossRefGoogle Scholar
Loevinger, Jane Person and population as psychometric concepts. Psychological Review, 1965, 72, 143–155.CrossRefGoogle ScholarPubMed
Odell, P. L. and Feiveson, A. H. A numerical procedure to generate a sample covariance matrix. Journal of the American Statistics Association, 1966, 61, 199–203.CrossRefGoogle Scholar
Rao, C. R. Estimation and tests of significance in factor analysis. Psychometrika, 1955, 20, 93–111.CrossRefGoogle Scholar
Spearman, C. Thurstone's work “reworked”. Journal of Educational Psychology, 1939, 30, 1–16.CrossRefGoogle Scholar
Thurstone, L. L. Primary mental abilities, 1938, Chicago: Univ. of Chicago Press.Google Scholar
Thurstone, L. L. Current issues in factor analysis. Psychological Bulletin, 1940, 37, 189–236.CrossRefGoogle Scholar
Tryon, R. C. Communality of a variable: formulation by cluster analysis. Psychometrika, 1957, 22, 241–260.CrossRefGoogle Scholar
Tryon, R. C. Reliability and behavior domain validity: reformulation and historical critique. Psychological Bulletin, 1957, 54, 229–249.CrossRefGoogle ScholarPubMed
Tryon, R. C. Cumulative communality cluster analysis. Educ. Psychol. Measurement, 1958, 18, 3–35.CrossRefGoogle Scholar
Tucker, L. R. A method for synthesis of factor analysis studies, 1951, Washington, D. C.: Department of the Army.CrossRefGoogle Scholar
Wrigley, C. S. and Neuhaus, J. O. The matching of two sets of factors. American Psychologist, 1955, 10, 418–419.Google Scholar
Zimmerman, W. S. A revised orthogonal rotational solution for Thurstone's original Primary Mental Abilities test battery. Psychometrika, 1953, 18, 77–93.CrossRefGoogle Scholar