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Structural Equation Models with Continuous and Polytomous Variables

Published online by Cambridge University Press:  01 January 2025

Sik-Yum Lee ,
Wai-Yin Poon  and
P. M. Bentler
Sik-Yum Lee*
Affiliation:
The Chinese University of Hong Kong
Wai-Yin Poon
Affiliation:
The Chinese University of Hong Kong
P. M. Bentler
Affiliation:
University of California, Los Angeles
*
Request for reprints should be sent to Sik-Yum Lee, Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., HONG KONG.
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Abstract

A two-stage procedure is developed for analyzing structural equation models with continuous and polytomous variables. At the first stage, the maximum likelihood estimates of the thresholds, polychoric covariances and variances, and polyserial covariances are simultaneously obtained with the help of an appropriate transformation that significantly simplifies the computation. An asymptotic covariance matrix of the estimates is also computed. At the second stage, the parameters in the structural covariance model are obtained via the generalized least squares approach. Basic statistical properties of the estimates are derived and some illustrative examples and a small simulation study are reported.

Keywords

structural equation modelspolychoric correlationspolyserial correlationsmaximum likelihoodgeneralized least squaresasymptotic properties
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 1 , March 1992 , pp. 89 - 105
Copyright
Copyright © 1992 The Psychometric Society

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Footnotes

This research was supported in part by a research grant DA01070 from the U. S. Public Health Service. We are indebted to several referees and the editor for very valuable comments and suggestions for improvement of this paper. The computing assistance of King-Hong Leung and Man-Lai Tang is also gratefully acknowledged.

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