Hostname: page-component-74656f9884-c52kr Total loading time: 0 Render date: 2026-11-08T20:38:42.701Z Has data issue: false hasContentIssue false
  • English
  • Français

A General Model for Two-Level Data with Responses Missing at Random

Published online by Cambridge University Press:  01 January 2025

Roderick P. McDonald
Roderick P. McDonald*
Affiliation:
University of Illinois
*
Requests for reprints should be sent to Roderick P. McDonald, Department of Psychology, University of Illinois, 603 E. Daniel Street, Champaign, IL 61820.
Get access Rights & Permissions [Opens in a new window]

Abstract

A general model for two-level multivariate data, with responses possibly missing at random, is described. The model combines regressions on fixed explanatory variables with structured residual covariance matrices. The likelihood function is reduced to a form enabling computational methods for estimating the model to be devised.

Keywords

multilevel datamissing datalinear structural relationscovariance structures

Information

Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 4 , December 1993 , pp. 575 - 585
Copyright
Copyright © 1993 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.)

Article purchase

Temporarily unavailable

Footnotes

This work was partly supported by a grant from the Economic and Social Research Council (UK) for the author's Visiting Fellowship to the Multilevel Project at the Institute of Education London University. Thanks are also due to Harvey Goldstein for his advice and encouragement, and to John Robinson and Malcolm Hudson for their comments on the manuscript.

References

Aitkin, M., & Longford, N. (1986). Statistical modelling issues in school effectiveness studies (with discussion). Journal of the Royal Statistical Society, Series A, 149, 1–43.CrossRefGoogle Scholar
de Leeuw, J., & Kreft, I. (1986). Random coefficient models for multilevel analysis. Journal of Educational Statistics, 11, 57–85.CrossRefGoogle Scholar
Dempster, A. P., Rubin, D. B., & Tsutakawa, R. K. (1981). Estimation in covariance component models. Journal of the American Statistical Association, 76, 341–353.CrossRefGoogle Scholar
Goldstein, H. (1986). Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika, 73, 43–56.CrossRefGoogle Scholar
Goldstein, H. (1987). Multilevel models in educational and social research, London: Griffin.Google Scholar
Goldstein, H., & McDonald, R. P. (1988). A general model for the analysis of multilevel data. Psychometrika, 53, 455–467.CrossRefGoogle Scholar
Hannan, M. T. (1971). Aggregation and disaggregation in sociology, Lexington, MA: Heath-Lexington.Google Scholar
Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association, 72, 320–340.CrossRefGoogle Scholar
Jöreskog, K. G., & Sörbom, D. (1979). Advances in factor analysis and structural equation models, Cambridge, MA: Abt. Books.Google Scholar
Lee, S.-Y. (1990). Multilevel analysis of structural equation models. Biometrika, 77, 763–772.CrossRefGoogle Scholar
Longford, N. (1987). A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects. Biometrika, 74, 817–827.CrossRefGoogle Scholar
Mason, W. M., Wong, G. Y., & Entwistle, B. (1984). The multilevel linear model: A better way to do contextual analysis. In Schuessler, K. F. (Eds.), Sociological Methodology (pp. 72–103). London: Jossey-Bass.Google Scholar
McArdle, J. J., & McDonald, R. P. (1984). Some algebraic properties of the reticular action model for moment structures. British Journal of Mathematical and Statistical Psychology, 37, 234–251.CrossRefGoogle ScholarPubMed
McDonald, R. P., Parker, P. M., & Ishizuka, T. (1993). A scale-invariant treatment for recursive path models. Psychometrika, 58, 431–443.CrossRefGoogle Scholar
McDonald, R. P., & Goldstein, H. (1989). Balanced versus unbalanced designs for linear structural relations in two-level data. British Journal of Mathematical and Statistical Psychology, 42, 215–232.CrossRefGoogle Scholar
Muthén, B. O. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54, 557–585.CrossRefGoogle Scholar
Pothoff, R. F., & Roy, S. N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika, 51, 313–326.CrossRefGoogle Scholar
Robinson, W. S. (1950). Ecological correlation and the behavior of individuals. American Sociology Review, 15, 351–357.CrossRefGoogle Scholar
Tate, R. L., & Wongbundhit, Y. (1983). Random versus nonrandom coefficient models for multilevel analysis. Journal of Educational Statistics, 8, 103–120.CrossRefGoogle Scholar