Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-07T18:54:32.371Z Has data issue: false hasContentIssue false
  • English
  • Français

The Estimation of Variance-Covariance and Correlation Matrices from Incomplete Data

Published online by Cambridge University Press:  01 January 2025

Neil H. Timm
Neil H. Timm*
Affiliation:
Carnegie Commission on the Future of Higher Education University of California, Berkeley
Get access Rights & Permissions [Opens in a new window]

Abstract

Employing simulated data, several methods for estimating correlation and variance-covariance matrices are studied for observations missing at random from data matrices. The effect of sample size, number of variables, percent of missing data and average intercorrelations of variables are examined for several proposed methods.

Type
Original Paper
Information
Psychometrika , Volume 35 , Issue 4 , December 1970 , pp. 417 - 437
Copyright
Copyright © 1970 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

The author is indebted to Professors Leonard A. Marascuilo, Gus W. Haggstrom, espsecially Henry F. Kaiser for their invaluable suggestions throughout this work. Appreciation is also extended to the Computer Center facility of the University of California at Berkeley for the use of computer time to complete the necessary computations.

References

Afifi, A. & Elashoff, R. M. Missing observations in multivariate statistics I. Review of the literature. Journal of the American Statistical Association, 1966, 61, 595–604Google 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, 10–29Google 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, 200–203CrossRefGoogle Scholar
Buck, S. F. A method of estimation of missing values in multivariate data suitable for use with an electronic computer. Journal of the Royal Statistical Society, Series B, 1960, 22, 302–307CrossRefGoogle Scholar
Christoffersson, A. A method for component analysis when the data are incomplete, 1965, Uppsala: University Institute of StatisticsGoogle Scholar
Coleman, J. S. Equality of Education Opportunity, 1966, Washington: United States Government Printing OfficeGoogle Scholar
Dear, R. E. “A principle-component missing data method for multiple regression models,” System Development Corporation, Technical report SP-86, 1959.Google Scholar
Dempster, A. P. Elements of Continuous Multivariate Analysis, 1969, Massachusetts: Addison and WesleyGoogle Scholar
Edgett, G. L. Multiple regression with missing observations among the independent variables. Journal of the American Statistical Association, 1956, 51, 122–131Google Scholar
Federspiel, C. F., Monroe, R. J., & Greenberg, B. G., “An investigation of some multiple regression methods for incomplete samples,” University of North Carolina, Institute of Statistics, Mineo Series, No. 236, August 1959.Google Scholar
Glasser, M. Linear regression analysis with missing observations among the independent variables. Journal of the American Statistical Association, 1964, 59, 834–844CrossRefGoogle Scholar
Haitovsky, Y. Missing data in regression analysis. Journal of the Royal Statistical Society, 1968, 30, 67–82Google Scholar
Hocking, R. R. & Smith, W. B. Estimation of parameters in the multivariate normal distribution with missing observations. Journal of the American Statistical Association, 1968, 63, 159–173CrossRefGoogle Scholar
Jackson, E. C. Missing values in linear multiple discriminant analysis. Biometrics, 1968, 24, 835–844Google Scholar
Jensen, A. 1969, Personal commumication.Google Scholar
Kaiser, H. F. A measure of the average intercorrelation. Educational and Psychological Measurement, 1968, 28, 245–247CrossRefGoogle Scholar
Kaiser, H. F. & Dickman, K. Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika, 1962, 27, 179–182CrossRefGoogle Scholar
Kendall, M. G. A Course in Multivariate Analysis, 1961, New York: HafnerGoogle Scholar
Lawley, D. N., & Maxwell, A. E. Factor Analysis as a Statistical Method, 1963, London: ButterworthsGoogle Scholar
Lord, Frederick M. Estimation of parameters from incomplete data. Journal of the American Statistical Association, 1955, 50, 870–876CrossRefGoogle Scholar
Lord, Frederick M. Equating test scores—a maximum likelihood solution. Psychometrika, 1955, 20, 193–200Google Scholar
Matthai, A. Estimation of parameters from incomplete data with application to design of sample surveys. Sankhya, 1951, 2, 145–152Google Scholar
Nicholson, G. E. Jr. Estimation of parameters from incomplete multivariate samples. Journal of the American Statistical Association, 1957, 52, 523–536CrossRefGoogle Scholar
Rao, C. R. Analysis of dispersion with incomplete observations on one of the characters. Journal of the Royal Statistical Society, 1956, 18, 259–264CrossRefGoogle Scholar
Timm, Neil H. “Estimating variance-covariance and correlation matrices from incomplete data,” (unpublished Doctoral Dissertation), Berkeley, California.Google Scholar
Trawinski, I. M. & Bargmann, R. Maximum likelihood estimation with incomplete multivariate data. Annals of Mathematical Statistics, 1964, 35, 647–657CrossRefGoogle Scholar
Tukey, J. W. Bias and confidence in not quite large samples. Annals of Mathematical Statistics, 1958, 29, 614–614Google Scholar
Walsh, J. E. Computer-feasible method for handling incomplete data in regression analysis. Journal of the Association for Computer Machinery, 1961, 18, 647–657Google Scholar
Wechsler, D. The Measurement and Appraisal of Adult Intelligence, Baltim, (4th edition), New York, 1958.Google Scholar
Wilks, S. S. Moments and distributions of estimates of population parameters from fragmentary samples. Annals of Mathematical Statistics, 1932, 3, 163–195CrossRefGoogle Scholar
Wold, H. Nonlinear estimation by iterative least squares procedures. In David, F. N. (Eds.), Festchrift Jerzy Neyman, 1966, New York: John Wiley and SonsGoogle Scholar
Wold, H. Estimation of principal components and related models. In Krishnaiah, P. R. (Eds.), Multivariate Analysis, 1966, New York: Academic PressGoogle Scholar