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A General Structural Equation Model with Dichotomous, Ordered Categorical, and Continuous Latent Variable Indicators

Published online by Cambridge University Press:  01 January 2025

Bengt Muthén
Bengt Muthén*
Affiliation:
Graduate School of Education, University of California, Los Angeles, California
*
Requests for reprints should be sent to Bengt Muthrn, Graduate School of Education, University of California, Los Angeles, California 90024.
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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.

Keywords

polychoric correlationsprobit regressionsgeneralized least-squaresweight matrix
Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 1 , March 1984 , pp. 115 - 132
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

This research was supported by Grant No. 81-IJ-CX-0015 from the National Institute of Justice, by Grant No. DA 01070 from the U.S. Public Health Service, and by Grant No. SES-8312583 from the National Science Foundation. I thank Julie Honig for drawing the figures.

References

Reference Notes

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A correction has been issued for this article:

Errata for the Volume 49 Index