Skip to main content
SpringerLink
Log in
Book cover

Handbook of Multivariate Experimental Psychology pp 207–230Cite as

Analysis of Covariance Structures

  • Chapter

Part of the book series: Perspectives on Individual Differences ((PIDF))

Abstract

Analysis of covariance structures is the common term for a number of techniques for analyzing multivariate data in order to detect and assess latent (unobserved) sources of variation and covariation in the observed measurements. The techniques of covariance structure analysis are general and flexible in that they can handle many types of covariance structures useful especially in the behavioral and social sciences. Although these techniques can be used for exploratory analysis, they have been most successfully applied to confirmatory analysis where the type of covariance structure is specified in advance. A covariance structure of a specified kind may arise because of a specified substantive theory or hypothesis, a given classificatory design for the measures, known experimental conditions, or because of results from previous studies based on extensive data. Sometimes the observed variables are ordered through time, as in longitudinal studies, or according to linear or circular patterns, as in Guttman’s (1954) simplex and circumplex models, or according to a given causal scheme, as in path analysis.

The contents of this chapter were first presented in lectures held at the Eighth Nordic Conference on Mathematical Statistics, held in Mariehamn, Finland, in May 1980. The chapter in its present form is reproduced, with modifications, from the Scandinavian Journal of Statistics, 1981, 8, 65–92.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Aitken, A. C. On least squares and the linear combination of observations. Proceedings of the Royal Society of Edinburgh, 1934–35, 55, 42–48.

    Google Scholar 

  • Anderson, T. W. Statistical inference for covariance matrices with linear structure. In P. R. Krishnaiah (Ed.), Multivariate analysis II. New York: Academic Press, 1969, pp. 55–66.

    Google Scholar 

  • Anderson, T. W. Estimation of covariance matrices which are linear combinations or whose inverses are linear combinations of given matrices. In R. C. Bose et al. (Eds.), Essays in probability and statistics. Chapel Hill: University of North Carolina Press, 1970, pp. 1–24.

    Google Scholar 

  • Bentler, P. M., and Weeks, D. G. Multivariate analysis with latent variables. In P. R. Krishnaiah and L. Kanal (Eds.), Handbook of statistics. Vol. 2. Amsterdam: North-Holland, 1985.

    Google Scholar 

  • Bock R. D. Components of variance analysis as a structural and discriminai analysis for phychological tests. British Journal of Statistical Psychology, 1960, 13, 151–163.

    Article  Google Scholar 

  • Bock, R. D., and Bargmann, R. E. Analysis of covariance structures. Psychometrika, 1966, 31, 507–534.

    Article  PubMed  Google Scholar 

  • Browne, M. W. Analysis of covariance structures. Paper presented at the annual conference of the South African Statistical Association, 1970.

    Google Scholar 

  • Browne, M. W. Generalized least squares estimators in the analysis of covariance structures. South African Statistical Journal, 1974, 8, 1–24.

    Google Scholar 

  • Browne, M. W. The analysis of patterned correlation matrices by generalized least squares. British Journal of Mathematical and Statistical Psychology, 1977, 30, 113–124.

    Article  Google Scholar 

  • Fletcher, R., and Powell, M. J. D. A rapidly convergent descent method for minimization. The Computer Journal, 1963, 6, 163–168.

    Google Scholar 

  • Gruvmus, G., and Jöreskog, K. G. A computer program for minimizing a function of several variables. Research Bulletin 70–14. Educational Testing Service, Princeton, N.J., 1970.

    Google Scholar 

  • Guttman, L. A. New approach to factor analysis: The radex. In P. F. Lazarsfeld (Ed.), Mathematical thinking in the social sciences. New York: Columbia University Press, 1954, pp. 258–348.

    Google Scholar 

  • Hauser, R. M., and Goldberger, A. S. The treatment of unobservable variables in path analysis. In H. L. Costner (Ed.), Sociological methodology 1971. San Francisco: Jossey–Bass, 1971, pp. 81–117.

    Google Scholar 

  • Humphreys, L. G. The fleeting nature of college academic success. Journal of Educational Psychology, 1968, 59, 375–380.

    Article  PubMed  Google Scholar 

  • Jöreskog, K. G. A general method for analysis of covariance structures. Biometrika, 1970a, 57, 239–251.

    Google Scholar 

  • Jöreskog, K. G. Estimation and testing of simplex models. British Journal of Mathematical and Statistical Psychology, 1970b, 23, 121–145.

    Article  Google Scholar 

  • Jöreskog, K. G. Simultaneous factor analysis in several populations. Psychometrika, 1971, 36, 409–426.

    Article  Google Scholar 

  • Jöreskog, K. G. Analysis of covariance structures. In P. R. Krishnaiah (Ed.), Multivariate analysis, III. New York: Academic Press, 1973a, pp. 263–285.

    Google Scholar 

  • Jösekog, K. G. A general method for estimating a linear structural equation system. In A. S. Goldberger and O. D. Duncan (Eds.), Structural equation models in the social sciences. New York: Seminar Press, 1973b, pp. 85–112.

    Google Scholar 

  • Jöreskog, K. G. Analyzing psychological data by structural analysis of covariance matrices. In R. C. Atkinson, D. H. Krantz, R. D. Luce, and P. Suppes (Eds.), Contemporary developments in mathematical psychology, II. San Francisco: Freeman, 1974, pp. 1–56.

    Google Scholar 

  • Jöreskog, K. G. Structural equation models in the social sciences: Specification, estimation and testing. In P. R. Krishnaiah (Ed.), Applications of statistics. Amsterdam: North-Holland, 1977, pp. 265–286.

    Google Scholar 

  • Jöreskog, K. G. Structural analysis of covariance and correlation matrices. Psychometrika, 1978, 43, 443–477.

    Article  Google Scholar 

  • Jöreskog, K. G. Statistical estimation of structural models in longitudinal-developmental investigations. In J. R. Nesselroade and P. B. Baltes (Eds.), Longitudinal research in the study of behavior and development. New York: Academic Press, 1979, pp. 303–352.

    Google Scholar 

  • Jöreskog, K. G., and Goldberger, A. S. Factor analysis by generalized least squares. Psychometrika, 1972, 37, 243–260.

    Article  Google Scholar 

  • Jöreskog, K. G., and Goldberger, A. S. Estimation of a model with multiple indicators and multiple causes of a single latent variable. Journal of the American Statistical Association, 1975, 10, 631–639.

    Article  Google Scholar 

  • Jöreskog, K. G., and Sörbom, D. Statistical models and methods for analysis of longitudinal data. In D. J. Aigner and A. S. Goldberger (Eds.), Latent variables in socio-economic models. Amsterdam: North-Holland, 1977, pp. 235–285.

    Google Scholar 

  • Jöreskog, K. G., and Sörbom, D. Simultaneous analysis of longitudinal data from several cohorts. Research Report 80–5. Department of Statistics, University of Uppsala, 1980.

    Google Scholar 

  • Jöreskog, K. G., and Sörbom, D. LISREL—Analysis of linear structural relationships by the method of maximum likelihood. Mooresville, Ind.: Scientific Software, Inc., 1986.

    Google Scholar 

  • Lee, S. Y. The Gauss–Newton algorithm for the weighted least squares factor analysis. The Statistician, 1979, 27, 103–114.

    Article  Google Scholar 

  • Lee, S. Y., and Jennrich, R. I. A study of algorithms for covariance structure analysis with specific comparisons using factor analysis. Psychometrika, 1979, 44, 99–113.

    Article  Google Scholar 

  • Lord, F. M. A significance test for the hypothesis that two variables measure the same trait except for errors of measurement. Psychometrika, 1957, 22, 207–220.

    Article  Google Scholar 

  • Lord, F. M., and Novick, M. E. Statistical theories of mental test scores. Reading, Mass.: Addison–Wesley, 1968.

    Google Scholar 

  • McDonald, R. P. Testing pattern hypotheses for covariance matrices. Psychometrika, 1974, 39, 189–201.

    Article  Google Scholar 

  • McDonald, R. P. Testing pattern hypotheses for correlation matrices. Psychometrika, 1975, 40, 253–255.

    Article  Google Scholar 

  • McDonald, R. P. A simple comprehensive model for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 1978, 31, 59–72.

    Article  Google Scholar 

  • McGraw, B., and Jöreskog, K. G. Factorial invariance of ability measures in groups differing in intelligence and socioeconomic status. British Journal of Mathematical and Statistical Psychology, 1971, 24, 154–168.

    Article  Google Scholar 

  • Rao, C. R. Linear statistical inference and its applications ( 2nd ed. ). New York: Wiley, 1973.

    Book  Google Scholar 

  • Sörbom, D. A general method for studying differences in factor means and factor structures between groups. British Journal of Mathematical and Statistical Psychology, 1974, 27, 229–239.

    Article  Google Scholar 

  • Sörbom, D. Detection of correlated errors in longitudinal data. British Journal of Mathematical and Statistical Psychology, 1975, 28, 138–151.

    Article  Google Scholar 

  • Sörbom, D. A statistical model for the measurement of change in true scores. In D. N. M. de Gruijter and L. J. T. van der Kamp (Eds.), Advances in psychological and educational measurement. New York: Wiley, pp. 159-169.

    Google Scholar 

  • Sörbom, D. An alternative to the methodology for analysis of covariance. Psychometrika, 1978, 43, 381–396.

    Article  Google Scholar 

  • Sörbom, D. Structural equation models with structured means. In K. G. Jöreskog and H. Wold (Eds.), Systems under indirect observation: Causality, structure, prediction. Amsterdam: North-Holland, 1981.

    Google Scholar 

  • Werts, C. E., and Linn, R. L. Path analysis: Psychological examples. Psychological Bulletin, 1970, 67, 193–212.

    Article  Google Scholar 

  • Werts, C. E., Linn, R. L., and Jöreskog, K. G. Reliability of college grades from longitudinal data. Educational and Psychological Measurement, 1978, 38, 89–95.

    Article  Google Scholar 

  • Wheaton, B., Muthén, B., Alwin, D., and Summers, G. Assessing reliability and stability in panel models. In D. R. Heise (Ed.), Sociological methodology 1977. San Francisco: Jossey—Bass, 1977, pp. 84–136.

    Google Scholar 

  • Wiley, D. E., Schmidt, W. H., and Bramble, W. J. Studies of a class of covariance structure models. Journal of the American Statistical Association, 1973, 68, 317–323.

    Article  Google Scholar 

  • Wright, S. The method of path coefficients. The Annals of Mathematical Statistics, 1934, 5, 161–215.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Uppsala, S-751 20, Uppsala, Sweden

    Karl G. Jöreskog

Authors
  1. Karl G. Jöreskog
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Pennsylvania State University, University Park, Pennsylvania, USA

    John R. Nesselroade

  2. University of Hawaii at Manoa, 96844, Honolulu, Hawaii, USA

    Raymond B. Cattell

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Plenum Press, New York

About this chapter

Cite this chapter

Jöreskog, K.G. (1988). Analysis of Covariance Structures. In: Nesselroade, J.R., Cattell, R.B. (eds) Handbook of Multivariate Experimental Psychology. Perspectives on Individual Differences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0893-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0893-5_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8232-7

  • Online ISBN: 978-1-4613-0893-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation