Skip to main content
SpringerLink
Log in

Analysis of Covariance Structures

  • Chapter
Advances in Educational and Psychological Testing: Theory and Applications

Part of the book series: Evaluation in Education and Human Services Series ((EEHS,volume 28))

  • 342 Accesses

Abstract

Research in the social and behavioral sciences often involves the formulation of theories that explain or predict phenomona of interest. These theories are operationalized in terms of models that specify relationships among the observed and hypothesized variables or constructs. Once a model is constructed, empirical evidence regarding the validity of the theory can be obtained by testing hypotheses based on the model. The validity of the theory is supported (but never proved) by the extent to which the hypotheses are confirmed. Similarly, the validity of psychological measures is assessed by constructing and testing hypotheses regarding relationships among variables and the underlying constructs.

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

Access this chapter

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anderson, T. W., & Rubin, H. (1956). Statistical inference in factor analysis. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability 5:111–150.

    Google Scholar 

  • Algina, J. (1980). A note on identification in the oblique and orthogonal factor analysis model. Psychometrika 45:393–396.

    Article  Google Scholar 

  • Bentler, P.M. (1976). Multistructure statistical model applied to factor analysis. Multivariate Behavioral Research 11:3–26.

    Article  Google Scholar 

  • Bentler, P.M. (1980). Multivariate analysis with latent variables: Causal modeling. Annual Review of Psychology 31:419–456.

    Article  Google Scholar 

  • Bentler, P.M. (1983). Some contributions to efficient statistics in structural models: Specification and estimation of moment structures. Psychometrika 48:493–517.

    Article  Google Scholar 

  • Bentler, P.M. (1984). Theory and implemention of EQS: A structural equation program. Los Angeles: BMDP Statistical Software.

    Google Scholar 

  • Bentler, P. M., & Bonnett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin 88:588–606.

    Article  Google Scholar 

  • Bentler, P.M., & Lee, S. Y. (1975). Some extensions of matrix calculus. General Systems 20:145–150.

    Google Scholar 

  • Bentler, P.M., & Speckart, C. (1979). An evaluation of models for attitude-behavior relations. Psychological Review 86:452–464.

    Article  Google Scholar 

  • Bock, R.D., & Bargmann, R.E. (1966). Analysis of covariance structures. Psychometrika 31:507–534.

    Article  Google Scholar 

  • Browne, M.W. (1982). Covariance structures. In D.M. Hawkins (ed.), Topics in applied multivariate analysis. Cambridge: Cambridge University Press.

    Google Scholar 

  • Corballis, M. C. (1973). A factor model for analyzing change. British Journal of Mathematical and Statistical Psychology 26:90–97.

    Article  Google Scholar 

  • Corballis, M.C., & Traub, R.E. (1970). Longitudinal factor analysis. Psychometrika 35:79–98.

    Article  Google Scholar 

  • Cudeck, R., & Browne, M. (1983). Cross-validation of covariance structures. Multivariate Behavioral Research 18:147–167.

    Article  Google Scholar 

  • Fishbein, M., & Ajzen, I. (1975). Belief, attitude, intention, and behavior: An introduction to theory and research. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Jennrich, R.I., & Robinson, S.M. (1969). A Newton-Raphson algorithm for maximum likelihood factor analysis. Psychometrika 34:111–124.

    Article  Google Scholar 

  • Jöreskog, K. G. (1966). Testing a simple structure hypothesis. Psychometrika 31:165–178.

    Article  Google Scholar 

  • Jöreskog, K. G. (1967). Some contributions to maximum likelihood factor analysis. Psychometrika 32:443–482.

    Article  Google Scholar 

  • Jöreskog, K. G. (1969). A general approach to confirmatory factor analysis. Psychometrika 34:183–201.

    Article  Google Scholar 

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

    Google Scholar 

  • Jöreskog, K. G. (1973). A general method for estimating a linear structural equation system. In A. S. Goldberger & O. D. Duncan (eds.), Structural equation models in the social sciences. New York: Seminar Press.

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • Jöreskog, K. G., & Lawley, D.N. (1968). New methods in maximum likelihood factor analysis. British Journal of Mathematical and Statistical Psychology 21:85–96.

    Article  Google Scholar 

  • Jöreskog, K.G., & Sörbom, D. (1975). Statistical models and methods for the analysis of longitudinal data (Research Report 75–65). Uppsala: University of Uppsala.

    Google Scholar 

  • Jöreskog, K. G. (1984). LISREL IV: Analysis of linear structural relationships by maximum likelihood, instrumental variables, and least squares methods. Mooresville, IN: Scientific Software.

    Google Scholar 

  • Lawley, D.N. (1958), Estimation in factor analysis under various initial assumptions. British Journal of Mathematical and Statistical Psychology 34:149–151.

    Google Scholar 

  • Lee, S.Y. (1980). Estimation of covariance structure models with parameters subject to functional restraints. Psychometrika 45:309–324.

    Article  Google Scholar 

  • Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Lunneborg, C. E., & Abbott, R.D. (1983). Elementary multivariate analysis for the behavioral sciences. New York: North Holland.

    Google Scholar 

  • McDonald, R. P. (1969). A generalized common factor analysis based on residual covariance matrices of prescribed structure. British Journal of Mathematical and Statistical Psychology 22:149–163.

    Article  Google Scholar 

  • McDonald, R. P. (1976). The McDonald-Swaminathan matrix calculus: Clarifications, extensions, and illustrations. General Systems 21:87–94.

    Google Scholar 

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

    Article  Google Scholar 

  • McDonald, R. P. (1980). A simple comprehensive model for the analysis of covariance structures: Some remarks on applications. British Journal of Mathematical and Statistical Psychology 33:161–183.

    Article  Google Scholar 

  • McDonald, R. P., & Swaminathan, H. (1972). Structural analysis of dispersion matrices. Unpublished manuscript, Ontario Institute for Studies in Education, University of Toronto.

    Google Scholar 

  • McDonald, R. P. (1973). A simple matrix calculus with applications to structural models for multivariate analysis. General Systems 18:37–54.

    Google Scholar 

  • Muthén, B. (1984). A general structural equation model with dichotomous, ordered, categorical, and continuous latent variable indicators. Psychometrika 49:115–132.

    Article  Google Scholar 

  • Muthén, B. Some uses of structural equation modelling in validity studies: Extending IRT to external variables using SIMS results (Research Report No. 268). Los Angeles: Center for the Study of Evaluation, University of California

    Google Scholar 

  • Swaminathan, H. (1984). Factor analysis of longitudinal data. In H. G. Law, C. W. Snyder, J. A. Hattie, & R. P. McDonald (eds.), Research methods for multimode analysis. New York: Praeger Publishers.

    Google Scholar 

  • Swaminathan, H. (1976). Matrix calculus for functions of partitioned matrices. General Systems 21:95–99.

    Google Scholar 

  • Swaminathan, H., & Algina, J. (1977). Scale-freeness in factor analysis. Psychometrika 43:581–584.

    Article  Google Scholar 

  • Wiley, D.E. (1973). The identification problem for structural equation models with unmeasured variables. In A.S. Goldberger & O. D. Duncan (eds.), Structural equation models in the social sciences. New York: Seminar Press, pp. 69–83.

    Google Scholar 

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

    Article  Google Scholar 

  • Wheaton, B., Muthén, B., Alwin, D.F., & Summers, G.F. (1977). Assessing reliability and stability in panel studies. In D. R. Heise (ed.), Sociological Methodology. San Francisco: Jossey Bass.

    Google Scholar 

Download references

Authors
  1. H. Swaminathan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ronald K. Hambleton Jac N. Zaal

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Swaminathan, H. (1991). Analysis of Covariance Structures. In: Hambleton, R.K., Zaal, J.N. (eds) Advances in Educational and Psychological Testing: Theory and Applications. Evaluation in Education and Human Services Series, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2195-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-2195-5_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7484-1

  • Online ISBN: 978-94-009-2195-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation