Summary
Influence measures based on the sample influence curves for the initial and rotated loadings are discussed and some scalar influence measures based on the Cook’s distance are proposed. Large values of influence measures may not necessarily imply a large influence on the factor loadings but a minor change of the variances explained leading to the change of the ordering of the factors. Therefore, the sample influence curves may, in fact, measure the difference between two different factors, instead of the change of one factor before and after an observation is omitted. The switching problem is studied by investigating the factor loadings pattern, variances explained and factor scores.
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References
Archer, CO and Jennrich, RI (1973). Standard errors for rotated factor loadings. Psychometrika, 38, 581–592.
Castano-Tostado, E and Tanaka, Y (1991). Sensitivity measures of influence on the loading matrix in exploratory factor analysis. Communications in Statistics–Theory and Methods, 20, 1329–1343.
Cook, RD and Weisberg S (1982). Residuals and Influence in Regression. London: Chapman and Hall.
Fung, WK and Kwan, CW (1995). Sensitivity analysis in factor analysis: Difference between using covariance and correlation matrices. Pyschometrika, 60, 607–614.
Hampel, FR (1974) The influence curve and its role in robust estimation. Journal of American Statistics Association, 69, 383–393.
Harman, HH (1967). Modern Factor Analysis. Chicago: University of Chicago Press.
Jennrich, RI and Thayer, DT, (1973). A note on lawley’s formulas for standard errors in maximum likelihood factor analysis. Psychometrika, 38, 571–580.
Johnson, RA and Wichem, DW (1998) Applied Multivariate Statistical Analysis, 46’ ed, London: Prentice-Hall.
Lawley, DN and Maxwell, AE (1971). Factor Analysis as a Statistical Method. London: Butterworths.
Kwan, CW and Fung, WK (1998). Assessing local influence for specific restricted likelihood: application to factor analysis. Psychometrika, 63, 35–46.
Pack, P, Jolliffe, IT and Morgan, BJT (1987). Influential observations in principal component analysis: A case study. Journal of Applied Statistics, 15, 39–50.
Tanaka, Y and Odaka, Y (1989). Sensitivity analysis in maximum likelihood factor analysis. Communications in Statistics–Theory and Methods, 18, 4067–4084.
Tanaka, Y and Watadani, Y(1992). Sensitivity analysis in covariance structure analysis with equality constraints. Communications in Statistics–Theory and Methods, 21, 1501–1515.
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© 2003 Springer Japan
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Fung, W.K., Kwan, C.W. (2003). Identifying Influential Observations for Loadings in Factor Analysis. In: Yanai, H., Okada, A., Shigemasu, K., Kano, Y., Meulman, J.J. (eds) New Developments in Psychometrics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-66996-8_17
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DOI: https://doi.org/10.1007/978-4-431-66996-8_17
Publisher Name: Springer, Tokyo
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