Abstract
A common problem for both principal component analysis and image component analysis is determining how many components to retain. A number of solutions have been proposed, none of which is totally satisfactory. An alternative solution which employs a matrix of partial correlations is considered. No components are extracted after the average squared partial correlation reaches a minimum. This approach gives an exact stopping point, has a direct operational interpretation, and can be applied to any type of component analysis. The method is most appropriate when component analysis is employed as an alternative to, or a first-stage solution for, factor analysis.
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Howe, W. G.Some contributions to factor analysis (Report No. ONRL-1919). Oak Ridge, Tenn.: Oak Ridge National Laboratory, 1955.
References
Bartlett, M. S. Tests of significance in factor analysis.The British Journal of Psychology, 1950,3 (Part II), 77–85.
Bartlett, M. S. A further note on tests of significance in factor analysis.The British Journal of Psychology, 1951,4 (Part I), 1–2.
Bechtoldt, H. P. An empirical study of the factor analysis stability hypothesis.Psychometrika, 1961,26, 405–432.
Cattell, R. B. The scree test for the number of factors.Multivariate Behavioral Research, 1966,1, 245–276.
Emmett, W. C. Factor analysis by Lawley's method of maximum likelihood.British Journal of Psychology, Statistical Section, 1949, 2, 90–97.
Gorsuch, R. L. Using Bartlett's significance test to determine the number of factors to extract.Educational and Psychological Measurement, 1973,33, 361–364.
Harman, H. H.Modern factor analysis. Chicago: University of Chicago Press, 1960.
Harman, H. H., & Jones, W. H. Factor analysis by minimizing residuals (minres).Psychometrika, 1966,31, 351–368.
Horst, P.Factor analysis of data matrices. New York: Holt, Rinehart, and Winston, 1965.
Jöreskog, K. G. Some contributions to maximum likelihood factor analysis.Psychometrika, 1967,32, 443–482.
Kaiser, H. F. The application of electronic computers to factor analysis.Educational and Psychological Measurement, 1960,20, 141–151.
Lord, F. M. A study of speed factors in tests and academic grades.Psychometrika, 1956,21, 31–50.
Maxwell, E. A. Recent trends in factor analysis.Journal of the Royal Statistical Society, Series A, 1961,124, 49–59.
Schönemann, P. H., & Wang, M. Some new results on factor indeterminacy.Psychometrika, 1972,37, 61–91.
Thurstone, L. L. The dimensions of temperament.Psychometrika, 1951,16, 11–20.
Van de Geer, J. P.Introduction to multivariate analysis for the social sciences. San Francisco: Freeman, 1971.
Velicer, W. F. An empirical comparison of the stability of factor analysis, principal component analysis, and image analysis.Educational and Psychological Measurement, 1974,34, 563–572.
Velicer, W. F. The relation between factor score estimates, image scores, and principal component scores.Educational and Psychological Measurement, 1976,36, 149–159.
Velicer, W. F. An empirical comparison of the similarity of principal component, image, and factor patterns.Multivariate Behavioral Research, in press.
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Velicer, W.F. Determining the number of components from the matrix of partial correlations. Psychometrika 41, 321–327 (1976). https://doi.org/10.1007/BF02293557
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DOI: https://doi.org/10.1007/BF02293557