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Estimation for the Multiple Factor Model when Data are Missing

Published online by Cambridge University Press:  01 January 2025

Carl Finkbeiner
Carl Finkbeiner*
Affiliation:
The Procter & Gamble Company
*
Requests for reprints should be sent to C. T. Finkbeiner, Ivorydale Technical Center, 3W76, The Procter & Gamble Co., Cincinnati, Ohio 45217.
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Abstract

A maximum likelihood method of estimating the parameters of the multiple factor model when data are missing from the sample is presented. A Monte Carlo study compares the method with 5 heuristic methods of dealing with the problem. The present method shows some advantage in accuracy of estimation over the heuristic methods but is considerably more costly computationally.

Keywords

factor analysismissing data

Information

Type
Original Paper
Information
Psychometrika , Volume 44 , Issue 4 , December 1979 , pp. 409 - 420
Copyright
Copyright © 1979 The Psychometric Society

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Footnotes

This paper is based on the author’s doctoral dissertation at the Department of Psychology, University of Illinois at Urbana-Champaign. The author gratefully acknowledges the aid of Drs. Robert Bohrer, Charles Lewis, Robert Linn, Maurice Tatsuoka, and Ledyard Tucker.

References

Reference Notes

Finkbeiner, C. T. Estimation for the multiple common factor model when data are missing. Unpublished dissertation, University of Illinois at Urbana—Champaign, 1976.Google Scholar
Gruvaeus, G. T. & Jöreskog, K. G. A computer program for minimizing a function of several variables (E. T. S. Res. Bull. RB70-14), 1970, Princeton, N. J.: Educational Testing Service.Google Scholar
Lewis, P. A., Goodman, A. S., & Miller, J. M. A pseudo-random number generator for the System/360. IBM System Journal, No. 2, 1969, pp. 136–146.CrossRefGoogle Scholar

References

Afifi, A. A. & Elashoff, R. M. Missing observations in multivariate statistics I. Review of the literature. Journal of the American Statistical Association, 1966, 61, 595–604.Google Scholar
Anderson, T. W. & Rubin, H. Statistical inference in factor analysis. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1956, 5, 111–150.Google Scholar
Box, G. E. P. & Muller, S. A. A note on the generation of random normal deviates. Annals of Mathematical Statistics, 1958, 29, 610–611.CrossRefGoogle Scholar
Browne, M. W. A comparison of factor analytic techniques. Psychometrika, 1968, 33, 267–334.CrossRefGoogle ScholarPubMed
Cattell, R. B. Factor analysis: An introduction to essentials. Biometrics, 1965, 21, 190–215.CrossRefGoogle ScholarPubMed
Dempster, A. P., Laird, N. M. & Rubin, D. B. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 1977, 39, 1–22.CrossRefGoogle Scholar
Dorans, N. & Drasgow, F. Alternative weighting schemes for linear prediction. Organizational Behavior and Human Performance, 1978, 21, 316–345.CrossRefGoogle Scholar
Gleason, T. C. & Staelin, R. A proposal for handling missing data. Psychometrika, 1975, 40, 229–252.CrossRefGoogle Scholar
Hoadley, B. Asymptotic properties of maximum likelihood estimators for the independent not identically distributed case. Annals of Mathematical Statistics, 1971, 42, 1977–1991.CrossRefGoogle Scholar
Jöreskog, K. G. Analyzing psychological data by structural analysis of covariance matrices. In Krantz, D. H., Atkinson, R. C., Luce, R. D. & Suppes, P. (Eds.), Contemporary developments of mathematical psychology, Vol. II, 1974, San Francisco: Freeman.Google Scholar
Jöreskog, K. G. & Goldberger, A. S. Factor analysis by generalized least squares. Psychometrika, 1972, 37, 243–260.CrossRefGoogle Scholar
Kendall, M. G. & Stuart, A. The Advanced Theory of Statistics, Vol. 2, 1973, New York: Hafner.Google Scholar
Korth, B. & Tucker, L. R. The distribution of chance congruence coefficients from simulated data. Psychometrika, 1975, 40, 361–372.CrossRefGoogle Scholar
Lawley, D. N. & Maxwell, A. E. Factor analysis as a statistical method, 1971, New York: American Elsevier.Google Scholar
Orchard, T. & Woodbury, M. A. A missing information principle: Theory and applications. Proceedings of the Sixth Berkley Symposium on Mathematical Statistics and Probability, 1970, 1, 697–715.Google Scholar
Rubin, D. B. Inference and missing data. Biometrika, 1976, 63, 581–592.CrossRefGoogle Scholar
Thurstone, L. L. Multiple factor analysis, 1947, Chicago: University of Chicago Press.Google Scholar
Tucker, L. R., Koopman, R. F., & Linn, R. L. Evaluation of factor analytic research procedures by means of simulated correlation matrices. Psychometrika, 1969, 34, 421–459.CrossRefGoogle Scholar
Wilks, S. S. Moments and distributions of estimates of population parameters from fragmentary samples. Annals of Mathematical Statistics, 1932, 3, 163–195.CrossRefGoogle Scholar