Psychometrika

, Volume 49, Issue 1, pp 115–132 | Cite as

A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators

  • Bengt Muthén
Article

Abstract

A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in addition to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed variable types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator modeling examples are given. One is a simultaneous analysis of two groups with a structural equation model underlying skewed Likert variables. The second is a longitudinal model with a structural model for multivariate probit regressions.

Key words

polychoric correlations probit regressions generalized least-squares weight matrix 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference notes

  1. Gruveaus, G. T., & Jöreskog, K. G. (1970). A computer program for minimizing a function of several variables. Research Bulletin 70-14. Princeton, N.J.: Educational Testing Service.Google Scholar
  2. Jöreskog, K. G., & Sörbom, D. (1981). LISREL V. Analysis of linear structural relationships by maximum likelihood and least squares methods. Research Report 81-8, Department of Statistics, University of Uppsala.Google Scholar

References

  1. Browne, M. W. (1974). Generalized least squares estimates in the analysis of covariance structures.South African Statistical Journal, 8, 1–24. (Reprinted in D. J. Aigner, & A. S. Goldberger (Eds.), (1977),Latent variables in socio-economic models. Amsterdam: North-Holland.)Google Scholar
  2. Cox, D. R. (1970).The analysis of binary data. London: Methuen.Google Scholar
  3. Henderson, A. S., Byrne, D. G., & Duncan-Jones, P. (1981).Neurosis and the social environment. Sidney: Academic Press.Google Scholar
  4. Jöreskog, K. G. (1973). 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, 85–112.Google Scholar
  5. Jöreskog, K. G. (1977). Structural equation models in the social sciences: Specification, estimation and testing. In P. R. Krishnaiah (Ed.),Applications of statistics. Amsterdam: North-Holland.Google Scholar
  6. Muthén, B. (1978). Contributions to factor analysis of dichotomous variables.Psychometrika, 43, 551–560.Google Scholar
  7. Muthén, B. (1979). A structural probit model with latent variables.Journal of the American Statistical Association, 74, 807–811.Google Scholar
  8. Muthén, B. (1983). Latent variable structural equation modeling with categorical data.Journal of Econometrics, 22, 43–65.Google Scholar
  9. Muthén, B., & Christoffersson, A. (1981). Simultaneous factor analysis of dichotomous variables in several groups.Psychometrika, 46, 407–419.Google Scholar
  10. Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient.Psychometrika, 44, 443–460. (a)Google Scholar
  11. Olsson, U. (1979). On the robustness of factor analysis against crude classification of the observations.Multivariate Behavioral Research, 14, 485–500. (b)Google Scholar
  12. Olsson, U., Drasgow, F., & Dorans, N. J. (1982). The polyserial correlation coefficient.Psychometrika, 47, 337–347.Google Scholar
  13. Sörbom, D. (1982). Structural equation models with structured means. In K. G. Jöreskog & H. Wold (Eds.),Systems under indirect observation: Causality, structure, prediction. Amsterdam: North-Holland Publishing Company.Google Scholar

Copyright information

© The Psychometric Society 1984

Authors and Affiliations

  • Bengt Muthén
    • 1
  1. 1.Graduate School of EducationUniversity of CaliforniaLos Angeles

Personalised recommendations