Skip to main content
Log in

A three-stage estimation procedure for structural equation models with polytomous variables

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

This paper is concerned with the analysis of structural equation models with polytomous variables. A computationally efficient three-stage estimator of the thresholds and the covariance structure parameters, based on partition maximum likelihood and generalized least squares estimation, is proposed. An example is presented to illustrate the method.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bentler, P. M., & Dijkstra, T. (1985). Efficient estimation via linearization in structural models. In P. R. Krishnaiah (Ed.),Multivariate analysis VI (pp. 9–42). Amsterdam: North-Holland.

    Google Scholar 

  • Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. (1980).Discrete Multivariate Analysis (6th ed.). Boston: MIT Press.

    Google Scholar 

  • Bock, R. D., & Lieberman, M. (1970). Fitting a response model forn dichotomously scored items.Psychometrika, 35, 179–197.

    Google Scholar 

  • Christoffersson, A. (1975). Factor analysis of dichotomized variables.Psychometrika, 40, 5–32.

    Google Scholar 

  • Ferguson, T. S. (1958). A method of generating best asymptotically normal estimates with applications to the estimation of bacterial densities.Annals of Mathematical Statistics, 29, 1046–1062.

    Google Scholar 

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

    Google Scholar 

  • Lee, S. Y., & Poon, W. Y. (1987). Two-step estimation of multivariate polychoric correlation.Communication in Statistics: Theory and Methods, 16, 307–320.

    Google Scholar 

  • Lee, S. Y., Poon, W. Y., & Bentler, P. M. (1990). Full maximum likelihood analysis of structural equation models with polytomous variables.Statistics and Probability Letters, 9, 91–97.

    Google Scholar 

  • Mislevy, R. J. (1986). Recent developments in factor analysis of categorical variables.Journal of Educational Statistics, 11, 3–31.

    Google Scholar 

  • Muthén, B. (1978). Contribution to factor analysis of dichotomous variables.Psychometrika, 43, 551–560.

    Google Scholar 

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

    Google Scholar 

  • Newcomb, M. D., & Bentler, P. M. (1988).Consequences of adolescent drug use: Impact on the lives of young adults. Newbury Park, CA: Sage.

    Google Scholar 

  • Parke, W. P. (1986). Pseudo maximum likelihood estimation: The asymptotic distribution.The Annals of Statistics, 14, 355–357.

    Google Scholar 

  • Poon, W. Y., & Lee, S. Y. (1987). Maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients.Psychometrika, 52, 409–430.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was supported in part by a research grant DA01070 from the U.S. Public Health Service. The production assistance of Julie Speckart is gratefully acknowledged.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, SY., Poon, WY. & Bentler, P.M. A three-stage estimation procedure for structural equation models with polytomous variables. Psychometrika 55, 45–51 (1990). https://doi.org/10.1007/BF02294742

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02294742

Key words

Navigation