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Scale Freeness in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Hariharan Swaminathan and
James Algina
Hariharan Swaminathan*
Affiliation:
University of Massachusetts
James Algina
Affiliation:
University of Pittsburgh
*
Requests for reprints should be sent to H. Swaminathan, School of Education, University of Massachusetts, Amherst, MA 01002.
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Abstract

The notion of scale freeness does not seem to have been well understood in the factor analytic literature. It has been believed that if the loss function that is minimized to obtain estimates of the parameters in the factor model is scale invariant, then the estimates are scale free. It is shown that scale invariance of the loss function is neither a necessary nor a sufficient condition for scale freeness. A theorem that ensures scale freeness in the orthogonal factor model is given in this paper.

Keywords

factor modelprincipal componentsscale free estimatesmaximum likelihoodgeneralized least squaresleast squaresloss functionidentification

Information

Type
Notes And Comments
Information
Psychometrika , Volume 43 , Issue 4 , December 1978, pp. 581 - 583
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

The authors are grateful for the suggestions of the referees.

References

Reference Notes

McDonald, R. P., & Swaminathan, H. Structural analysis of dispersion matrices based on a very general model with a rapidly convergent procedure for the estimation of parameters, 1972, Toronto, Canada: Ontario Institute for Studies in Education.Google Scholar
Jöreskog, K. G., Gruvaeus, G. T., & van Thillo, M. A general computer program for analysis of covariance structures, 1970, Princeton, N.J.: Educational Testing Service.CrossRefGoogle Scholar

References

Anderson, T. W. An introduction to multivariate statistics, 1958, New York: Wiley.Google Scholar
Anderson, T. W., & Rubin, H. Statistical inference in factor analysis. Proceedings of the third Berkeley symposium on mathematical statistics and probability, 1956, V, 111–150.Google Scholar
Harris, C. W. Some recent developments in factor analysis. Educational and Psychological Measurement, 1964, 24, 193–206.CrossRefGoogle Scholar
Jöreskog, K. G., & Goldberger, A. S. Factor analysis by generalized least squares. Psychometrika, 1972, 37, 243–260.CrossRefGoogle Scholar
Lawley, D. N., & Maxwell, A. E. Factor analysis as a statistical method, 1971, New York: American Elsevier Publishing Co..Google Scholar
McDonald, R. P. A unified treatment of the weighting problem. Psychometrika, 1968, 33, 351–381.CrossRefGoogle ScholarPubMed
McDonald, R. P. The theoretical foundations of principal factor analysis, canonical factor analysis, and alpha factor analysis. British Journal of Mathematical and Statistical Psychology, 1970, 23, 1–21.CrossRefGoogle Scholar
Morrison, D. F. Multivariate statistical methods, 1976, New York: McGraw Hill Book Co..Google Scholar
Press, S. J. Applied multivariate analysis, 1972, New York: Holt, Rinehart and Winston, Inc..Google Scholar
Swain, A. J. A class of factor analysis estimation procedures with common asymptotic sampling properties. Psychometrika, 1975, 40, 315–335.CrossRefGoogle Scholar