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.
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Reference Notes
Brown, C. H. Missing Values in Factor Analysis. Technical Report #133, Department of Statistics, University of Chicago, 1981.
Dear, R. E. A Principal-Component Missing Data Method for Multiple Regression Models.System Development Corporation, Technical Report SP-86, 1959.
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.
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.
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.
Anderson, T. W.An introduction to multivariate statistical analysis. New York: John Wiley, 1958.
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.
Beale, E. M. L. & Little, R. J. A. Missing values in multivariate analysis,Journal of the Royal Statistical Society, Series B, 1975, 129–146.
Dempster, A. P.Elements of continuous multivariate analysis. Menlo Park, California: Addison-Wesley, 1969.
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.
Dixon, W. J. & Brown, M. B.BMDP Biomedical Computer Programs P-Series 1977. Berkeley: University of California, 1977.
Finkbeiner, C. Estimation for the multiple factor model when data are missing.Psychometrika, 1979,44, 409–420.
Gleason, Terry C. & Staelin, Richard. A proposal for handling missing data.Psychometrika, 1975,40, 229–252.
Haitovsky, V. Missing data in regression analysis.Journal of the Royal Statistical Society, Series B, 1968,30, 67–82.
Harman, Harry H.Modern factor analysis. Chicago: University of Chicago Press, 1967.
Heiberger, R. M. Regression with the pairwise-present covariance matrix: A dangerous practice. InProceedings of the Statistical Computing Section, 1977, Washington: American Statistical Association.
Jöreskog, K. G. & Sörbom, D.Advances in factor analysis and structural equation models. Boston: Abt Association, 1979.
Lawley, D. N., & Maxwell, A. E.Factor analysis as a statistical method. London: Butterworth, 1963.
Marini, M. M., Olsen, A. R., & Rubin, D. B. Maximum likelihood estimation in panel studies with missing data. InSociological Methodology 1980, Karl Schuessler, ed. San Francisco: Jossey Bass, 1979.
Orchard, T. & Woodbury, M. A. A missing information principle: Theory and practice. InProceedings of Sixth Berkeley Symposium on Multivariate Statistics and Probability, 1972, Vol. I, LeCam, L. M., Neyman, J. & Scott, E. L. ed.
Rao, C. R.Linear statistical inference and its applications. New York: John Wiley, 1973.
Ratkowsky, D. A. Maximum likelihood in small incomplete samples from the bivariate normal distribution.Applied Statistics, 1974,23, 180–189.
Rubin, D. B. Characterizing the estimation of parameters in complete data problems.Journal of the American Statistical Association, 1974,69, 467–474.
Rubin, D. B. Inference and missing data.Biometrika, 1976,63, 581–592.
Timm, Neil H. The estimation of variance-covariance and correlation matrices from incomplete data.Psychometrika, 1970,35, 417–437.
Wilks, S. S. Moments and distributions of estimates of population parameters from fragmentary samples.Annals of Mathematical Statistics, 1932,3, 163–195.
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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.
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Hendricks Brown, C. Asymptotic comparison of missing data procedures for estimating factor loadings. Psychometrika 48, 269–291 (1983). https://doi.org/10.1007/BF02294022
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DOI: https://doi.org/10.1007/BF02294022