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Iterative Least Squares Estimates of Communality: Initial Estimate Need not Affect Stabilized Value

Published online by Cambridge University Press:  01 January 2025

Keith F. Widaman  and
Lawrence G. Herringer
Keith F. Widaman*
Affiliation:
University of California at Riverside
Lawrence G. Herringer
Affiliation:
University of California at Riverside
*
Requests for reprints should be sent to Keith Widaman, Department of Psychology, University of California, Riverside, CA 92521.
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Abstract

A common criticism of iterative least squares estimates of communality is that method of initial estimation may influence stabilized values. As little systematic research on this topic has been performed, the criticism appears to be based on cumulated experience with empirical data sets. In the present paper, two studies are reported in which four types of initial estimate (unities, squared multiple correlations, highest r, and zeroes) and four levels of convergence criterion were employed using four widely available computer packages (BMDP, SAS, SPSS, and SOUPAC). The results suggest that initial estimates have no effect on stabilized communality estimates when a stringent criterion for convergence is used, whereas initial estimates appear to affect stabilized values employing rather gross convergence criteria. There were no differences among the four computer packages for matrices without Heywood cases.

Keywords

communality estimationcommon factor analysisiterative estimation
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 4 , December 1985 , pp. 469 - 477
Copyright
Copyright © 1985 The Psychometric Society

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Footnotes

The present study was supported, in part, by grants HD-14688 and HD-04612 from the National Institute of Child Health and Human Development, and by intramural grants from the Academic Computing Center and the Academic Senate of the University of California at Riverside. The helpful comments by the editor, by four anonymous reviewers, and by Robert MacCallum to a previous draft of this manuscript are gratefully acknowledged.

References

Cattell, R. B. (1954). Growing points in factor analysis. Australian Journal of Psychology, 6, 105–140.CrossRefGoogle Scholar
Cattell, R. B. (1978). The scientific use of factor analysis in behavioral and life sciences, New York: Plenum Press.CrossRefGoogle Scholar
Comrey, A. L. (1962). The minimum residual method of factor analysis. Psychological Reports, 11, 15–18.CrossRefGoogle Scholar
Comrey, A. L. (1973). A first course in factor analysis, New York: Academic Press.Google Scholar
Dixon, W. J. (1981). BMDP statistical software—1981, Berkeley, CA: University of California Press.Google Scholar
Gorsuch, R. L. (1974). Factor analysis, Philadelphia, PA: W. B. Saunders.Google Scholar
Guttman, L. (1956). “Best possible” systematic estimates of communality. Psychometrika, 21, 273–285.CrossRefGoogle Scholar
Harman, H. H. (1976). Modern factor analysis 3rd ed. rev.,, Chicago, IL: University of Chicago Press.Google Scholar
Hull, C. H., Nie, N. H. (1981). SPSS update 7–9, New York: McGraw-Hill.Google Scholar
Jöreskog, K. G., van Thillo, M. (1971). New rapid algorithms for factor analysis by unweighted least squares, generalized least squares and maximum likelihood, Princeton, NJ: Educational Testing Service.Google Scholar
Kale, B. K. (1962). On the solution of likelihood equations by iteration processes: The multiparametric case. Biometrika, 49, 479–486.CrossRefGoogle Scholar
Nie, N. H., Hull, C. H., Jenkins, J. G., Steinbrenner, K., Bent, D. H. (1975). SPSS statistical package for the social sciences, New York: McGraw-Hill.Google Scholar
Nunnally, J. C. (1978). Psychometric theory 2nd ed.,, New York: McGraw-Hill.Google Scholar
Rummel, R. J. (1970). Applied factor analysis, Evanston, IL: Northwestern University Press.Google Scholar
SAS Institute (1979). SAS user's guide 1979 ed.,, Cary, NC: Author.Google Scholar
Schönemann, P. H. (1971). The minimum average correlation between equivalent sets of uncorrelated factors. Psychometrika, 36, 21–30.CrossRefGoogle Scholar
Schönemann, P. H., Steiger, J. H. (1978). On the validity of indeterminate factor scores. Bulletin of the Psychonomic Society, 12, 287–290.CrossRefGoogle Scholar
Schönemann, P. H., Wang, M. M. (1972). Some new results on factor indeterminacy. Psychometrika, 37, 61–91.CrossRefGoogle Scholar
Thurstone, L. L. (1947). Multiple factor analysis, Chicago, IL: University of Chicago Press.Google Scholar
Tucker, L. R., Koopman, R. F., Linn, R. L. (1969). Evaluation of factor analytic research procedures by means of simulated correlation matrices. Psychometrika, 34, 421–459.CrossRefGoogle Scholar
Tyler, F., Michael, W. B. (1958). An empirical study of the comparability of factor structure when unities and communality estimates are used. Educational and Psychological Measurement, 18, 347–354.CrossRefGoogle Scholar
University of Illinois at Urbana-Champaign Computing Services (1976). SOUPAC program descriptions, Urbana, IL: Author.Google Scholar
Wherry, R. J. (1949). A new iterative method for correcting erroneous communality estimates in factor analysis. Psychometrika, 14, 231–241.CrossRefGoogle ScholarPubMed
Wrigley, C., Neuhaus, J. O. (1955). The use of an electronic computer in principal axis factor analysis. Journal of Educational Psychology, 46, 31–41.CrossRefGoogle Scholar
Wrigley, C., & Twery, R. (1953, September). The estimation of communalities in factor analysis by an iterative procedure. Paper presented at the annual meeting of the American Psychological Association, Cleveland, OH.Google Scholar