Hostname: page-component-5f745c7db-j9pcf Total loading time: 0 Render date: 2025-01-06T22:53:47.670Z Has data issue: true hasContentIssue false
  • English
  • Français

An Alternative to the Methodology for Analysis of Covariance

Published online by Cambridge University Press:  01 January 2025

Dag Sörbom
Dag Sörbom*
Affiliation:
University of Uppsala
*
Requests for reprints should be sent to Dag Sörbom, Department of Statistics, University of Uppsala, P.O. Box 513, S-751 20 Uppsala, SWEDEN.
Get access Rights & Permissions [Opens in a new window]

Abstract

A general statistical model for simultaneous analysis of data from several groups is described. The model is primarily designed to be used for the analysis of covariance. The model can handle any number of covariates and criterion variables, and any number of treatment groups. Treatment effects may be assessed when the treatment groups are not randomized. In addition, the model allows for measurement errors in the criterion variables as well as in the covariates. A wide variety of hypotheses concerning the parameters of the model can be tested by means of a large sample likelihood ratio test. In particular, the usual assumptions of ANCOVA may be tested.

Keywords

confirmatory factor analysissimultaneous factor analysismeasurement errors
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 3 , September 1978 , pp. 381 - 396
Copyright
Copyright © 1978 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

Research reported in this paper has been partly supported by the Swedish Council for Social Science Research under project “Statistical methods for analysis of longitudinal data”, project director Karl G. Jöreskog, and partly by the Bank of Sweden Tercentenary Foundation under project “Structural Equation Models in the Social Sciences”, project director Karl G. Jöreskog.

References

Reference Notes

Bergman, L. R. Change as the dependent variable, 1972, Stockholm, Sweden: The University of Stockholm, Psychological Laboratories.Google Scholar
Cronbach, L. J., Rogosa, D., Price, G. & Floden, R. Analysis of covariance, temptress and deluder? Or angel of salvation?, 1976, Palo Alto: Stanford University, Stanford Evaluation Consortium.Google Scholar
Gruvaeus, G. T. & Jöreskog, K. G. A computer program for minimizing a function of several variables, 1970, Princeton, N.J.: Educational Testing Service.Google Scholar
Jöreskog, K. G. & Sörbom, D. Some regression estimates useful in the measurement of change, 1974, Uppsala, Sweden: University of Uppsala, Department of Statistics.Google Scholar
Keesling, J. W. & Wiley, D. E. Measurement error and the analysis of quasi-experimental data (Version III), 1975, Chicago: University of Chicago.Google Scholar
Olsson, S. An experimental study of the effects of training on test scores and factor structure, 1973, Uppsala, Sweden: University of Uppsala, Department of Education.Google Scholar
Porter, A. C. How errors of measurement affect ANOVA, regression analysis, ANCOV A and factor analysis. Paper presented at the AERA convention, New York, 1971.Google Scholar

References

Bock, R. D. Multivariate statistical methods in behavioral research, 1975, New York: McGraw-Hill.Google Scholar
Campbell, D. T. From description to experimentation: Interpreting trends as quasi-experiments. In Harris, Chester W. (Eds.), Problems in measuring change. Madison: The University of Wisconsin Press. 1963, 212–242.Google Scholar
Cochran, W. G. Errors of measurement in statistics. Technometrics, 1968, 10, 637–666.CrossRefGoogle Scholar
Elashoff, J. D. Analysis of covariance: A delicate instrument. American Educational Research Journal, 1969, 6, 383–402.CrossRefGoogle Scholar
Fletcher, R. & Powell, M. J. D. A rapidly convergent descent method for minimization. Computer Journal, 1963, 6, 163–168.CrossRefGoogle Scholar
Frederiksen, N. & Schrader, W. B. Adjustment to college., 1951, Princeton, New Jersey: Educational Testing Service.Google Scholar
Härnqvist, K. Manual for DBA, 1962, Stockholm: Skandinaviska Testförlaget.Google Scholar
Jöreskog, K. G. Simultaneous factor analysis in several populations. Psychometrika, 1971, 36, 409–426.CrossRefGoogle Scholar
Jöreskog, K. G. Statistical analysis of sets of congeneric tests. Psychometrika, 1971, 36, 109–133.CrossRefGoogle Scholar
Jöreskog, K. G. A general method for estimating a linear structural equation system. In Goldberger, A. S. & Duncan, O. D. (Eds.), Structural equation models in the social sciences. New York: Seminar Press. 1973, 85–112.Google Scholar
Jöreskog, K. G. & Sörbom, D. Statistical models and methods for test-retest situations. In de Gruijter, D. N. M., van der Kamp, L. J. Th. & Crombag, H. F. (Eds.), Advances in Psychological and Educational Measurement, 1976, London: Wiley.Google Scholar
Jöreskog, K. G. & Sörbom, D. LISREL III—Estimation of linear structural equation systems by maximum likelihood methods: A FORTRAN IV program, 1976, Chicago: International Educational Services.Google Scholar
Jöreskog, K. G. & Sörbom, D. Statistical models and methods for analysis of longitudinal data. In Aigner, D. J. & Goldberger, A. S. (Eds.), Latent variables in socioeconomic models, 1977, Amsterdam: North Holland Publishing Company.Google Scholar
Lawley, D. N. & Maxwell, A. E. Factor analysis as a statistical method., 2nd ed., London: Butterworth & Company, 1971.Google Scholar
Lord, F. M. Large sample covariance analysis when the control variable is fallible. Journal of the American Statistical Association, 1960, 55, 307–321.CrossRefGoogle Scholar
Lord, F. M. Elementary models for measuring change. In Harris, Chester W. (Eds.), Problems in measuring change. Madison: The University of Wisconsin Press. 1963, 21–38.Google Scholar
Lord, F. M. A paradox in the interpretation of group comparisons. Psychological Bulletin, 1967, 68, 304–305.CrossRefGoogle ScholarPubMed
Lord, F. M. & Novick, M. E. Statistical theories of mental test scores, 1968, Reading: Addison-Wesley Publishing Company.Google Scholar
Smith, H. F. Interpretation of adjusted treatment means and regressions in analysis of covariance. Biometrics, 1957, 13, 282–308.CrossRefGoogle Scholar
Sörbom, D. A general method for studying differences in factor means and factor structure between groups. British Journal of Mathematical and Statistical Psychology, 1974, 27, 229–239.CrossRefGoogle Scholar
Sörbom, D. Detection of correlated errors in longitudinal data. British Journal of Mathematical and Statistical Psychology, 1975, 28, 138–151.CrossRefGoogle Scholar