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Asymptotic Comparison of Missing Data Procedures for Estimating Factor Loadings

Published online by Cambridge University Press:  01 January 2025

C. Hendricks Brown
C. Hendricks Brown*
Affiliation:
The Johns Hopkins University
*
Reprint requests should be addressed to C. Hendricks Brown, Department of Biostatistics, School of Hygiene and Public Health, 615 North Wolfe Street, The Johns Hopkins University, Baltimore, Maryland 21205.
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Abstract

Large sample properties of four methods of handling multivariate missing data are compared. The criterion for comparison is how well the loadings from a single factor model can be estimated. It is shown that efficiencies of the methods depend on the pattern or arrangement of missing data, and an evaluation study is used to generate predictive efficiency equations to guide one's choice of an estimating procedure. A simple regression-type estimator is introduced which shows high efficiency relative to the maximum likelihood method over a large range of patterns and covariance matrices.

Keywords

EM algorithm
Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 2 , June 1983 , pp. 269 - 291
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

The author wishes to thank Professor David Wallace of the Statistics Department, University of Chicago, for providing valuable suggestions, guidance, and stimulus during the writing of the dissertation from which this work is drawn.

References

Reference Notes

Brown, C. H. Missing Values in Factor Analysis. Technical Report #133, Department of Statistics, University of Chicago, 1981.Google Scholar
Dear, R. E. A Principal-Component Missing Data Method for Multiple Regression Models. System Development Corporation, Technical Report SP-86, 1959.Google Scholar

References

Afifi, 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
Afifi, A. & Elashoff, R. M. Missing observations in multivariate statistics II. Point estimation in simple linear regression. Journal of the American Statistical Association, 1967, 62, 10–29.Google Scholar
Anderson, T. W. Maximum likelihood estimates for a multivariate normal distribution when some observations are missing. Journal of the American Statistical Association, 1957, 52, 200–204.CrossRefGoogle Scholar
Anderson, T. W. An introduction to multivariate statistical analysis, New York: John Wiley, 1958.Google Scholar
Barr, A. J., Goodnight, J. H., Sall, J. P., Blair, W. H., & Hilko, D. M. SAS User's guide 1979 edition. Raleigh, North Carolina: SAS Institute, 1979.Google Scholar
Beale, E. M. L. & Little, R. J. A. Missing values in multivariate analysis, Journal of the Royal Statistical Society, Series B, 1975, 129–146.CrossRefGoogle Scholar
Dempster, A. P. Elements of continuous multivariate analysis, Menlo Park, California: Addison-Wesley, 1969.Google Scholar
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, 1–22.CrossRefGoogle Scholar
Dixon, W. J. & Brown, M. B. BMDP Biomedical Computer Programs P-Series 1977, Berkeley: University of California, 1977.Google Scholar
Finkbeiner, C. Estimation for the multiple factor model when data are missing. Psychometrika, 1979, 44, 409–420.CrossRefGoogle Scholar
Gleason, Terry C. & Staelin, Richard A proposal for handling missing data. Psychometrika, 1975, 40, 229–252.CrossRefGoogle Scholar
Haitovsky, V. Missing data in regression analysis. Journal of the Royal Statistical Society, 1968, 30, 67–82.CrossRefGoogle Scholar
Harman, Harry H. Modern factor analysis, Chicago: University of Chicago Press, 1967.Google Scholar
Heiberger, R. M. Regression with the pairwise-present covariance matrix: A dangerous practice. Proceedings of the Statistical Computing Section, Washington: American Statistical Association, 1977.Google Scholar
Jöreskog, K. G. & Sörbom, D. Advances in factor analysis and structural equation models, Boston: Abt Association, 1979.Google Scholar
Lawley, D. N. & Maxwell, A. E. Factor analysis as a statistical method, London: Butterworth, 1963.Google Scholar
Marini, M. M., Olsen, A. R., & Rubin, D. B. Maximum likelihood estimation in panel studies with missing data. In Karl, Schuessler (Eds.), Sociological Methodology 1980, San Francisco: Jossey Bass, 1979.Google Scholar
Orchard, T. & Woodbury, M. A. A missing information principle: Theory and practice. In Proceedings of Sixth Berkeley Symposium on Multivariate Statistics and Probability, 1972, Vol. I, LeCam, L. M., Neyman, J. & Scott, E. L. ed.Google Scholar
Rao, C. R. Linear statistical inference and its applications, New York: John Wiley, 1973.CrossRefGoogle Scholar
Ratkowsky, D. A. Maximum likelihood in small incomplete samples from the bivariate normal distribution. Applied Statistics, 1974, 23, 180–189.CrossRefGoogle Scholar
Rubin, D. B. Characterizing the estimation of parameters in complete data problems. Journal of the American Statistical Association, 1974, 69, 467–474.CrossRefGoogle Scholar
Rubin, D. B. Inference and missing data. Biometrika, 1976, 63, 581–592.CrossRefGoogle Scholar
Timm, Neil H. The estimation of variance-covariance and correlation matrices from incomplete data. Psychometrika, 1970, 35, 417–437.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