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Sensitivity Analysis in Factor Analysis: Difference Between Using Covariance and Correlation Matrices

Published online by Cambridge University Press:  01 January 2025

W. K. Fung  and
C. W. Kwan
W. K. Fung*
Affiliation:
Department of Statistics, The University of Hong Kong
C. W. Kwan
Affiliation:
Department of Statistics, The University of Hong Kong
*
Requests for reprints should be sent to W.K. Fung, Department of Statistics, The University of Hong Kong, Pokfulam Road, HONG KONG.
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Abstract

Influence curves of some parameters under various methods of factor analysis have been given in the literature. These influence curves depend on the influence curves for either the covariance or the correlation matrix used in the analysis. The differences between the influence curves based on the covariance and the correlation matrices are derived in this paper. Simple formulas for the differences of the influence curves, based on the two matrices, for the unique variance matrix, factor loadings and some other parameter are obtained under scale-invariant estimation methods, though the influence curves themselves are in complex forms.

Keywords

sensitivity analysisinfluential observationsinfluence curvescorrelation matrixcovariance matrixstandardization

Information

Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 4 , December 1995 , pp. 607 - 614
Copyright
Copyright © 1995 The Psychometric Society

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Footnotes

The authors are most grateful to the referees, the Associate Editor, the Editor and Raymond Lam for helpful suggestions for improving the clarity of the paper.

References

Critchley, F. (1985). Influence in principal component analysis. Biometrika, 72, 627–636.CrossRefGoogle Scholar
Hampel, F. R. (1974). The influence curve and its role in robust estimation. Journal of the American Statistical Association, 69, 383–393.CrossRefGoogle Scholar
Lawley, D. N., Maxwell, A. E. (1971). Factor analysis as a statistical method, London: Butterworths.Google Scholar
Mardia, K. V., Kent, J. T., Bibby, J. M. (1979). Multivariate analysis, London: Academic Press.Google Scholar
Pack, P., Jolliffe, I. T., Morgan, B. J. T. (1987). Influential observations in principal component analysis: A case study. Journal of Applied Statistics, 15, 39–50.CrossRefGoogle Scholar
Radhakrishnan, R., Kshirsagar, A. M. (1981). Influence functions for certain parameters in multivariate analysis. Communications in Statistics-Theory and Methods, 10, 515–529.CrossRefGoogle Scholar
Tanaka, Y., Odaka, Y. (1989). Influential observations in principal factor analysis. Psychometrika, 54, 475–485.CrossRefGoogle Scholar
Tanaka, Y., Odaka, Y. (1989). Sensitivity analysis in maximum likelihood factor analysis. Communications in Statistics-Theory and Methods, 18, 4067–4084.CrossRefGoogle Scholar
Tanaka, Y., Odaka, Y. (1989). Sensitivity analysis in least squares factor analysis. In Diday, E. (Eds.), Data analysis, learning symbolic and numeric knowledge (pp. 141–148). New York, Budapest: Nova Science Publishers.Google Scholar