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.
Similar content being viewed by others
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 Unpublished dissertation, University of Illinois at Urbana—Champaign, 1976.
Gruvaeus, G. T. & Jöreskog, K. G.A computer program for minimizing a function of several variables (E. T. S. Res. Bull. RB70-14). Princeton, N. J.: Educational Testing Service, 1970.
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.
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.
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.
Box, G. E. P. & Muller, S. A. A note on the generation of random normal deviates.Annals of Mathematical Statistics, 1958,29, 610–611.
Browne, M. W. A comparison of factor analytic techniques.Psychometrika, 1968,33, 267–334.
Cattell, R. B. Factor analysis: An introduction to essentials.Biometrics, 1965,21, 190–215, 405–435.
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.
Dorans, N. & Drasgow, F. Alternative weighting schemes for linear prediction.Organizational Behavior and Human Performance, 1978,21, 316–345.
Gleason, T. C. & Staelin, R. A proposal for handling missing data.Psychometrika, 1975,40, 229–252.
Hoadley, B. Asymptotic properties of maximum likelihood estimators for the independent not identically distributed case.Annals of Mathematical Statistics, 1971,42, 1977–1991.
Jöreskog, K. G. Analyzing psychological data by structural analysis of covariance matrices. In D. H. Krantz, R. C. Atkinson, R. D. Luce & P. Suppes (Eds.)Contemporary developments of mathematical psychology, Vol. II. San Francisco, Freeman, 1974.
Jöreskog, K. G. & Goldberger, A. S. Factor analysis by generalized least squares.Psychometrika, 1972,37, 243–260.
Kendall, M. G. & Stuart, A.The Advanced Theory of Statistics, Vol. 2. New York, Hafner, 1973.
Korth, B. & Tucker, L. R. The distribution of chance congruence coefficients from simulated data.Psychometrika, 1975,40, 361–372.
Lawley, D. N. & Maxwell, A. E.Factor analysis as a statistical method. New York, American Elsevier, 1971.
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.
Rubin, D. B. Inference and missing data.Biometrika, 1976,63, 581–592.
Thurstone, L. L.Multiple factor analysis. Chicago, University of Chicago Press, 1947.
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.
Wilks, S. S. Moments and distributions of estimates of population parameters from fragmentary samples.Annals of Mathematical Statistics, 1932,3, 163–195.
Author information
Authors and Affiliations
Additional information
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.
Rights and permissions
About this article
Cite this article
Finkbeiner, C. Estimation for the multiple factor model when data are missing. Psychometrika 44, 409–420 (1979). https://doi.org/10.1007/BF02296204
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02296204