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Simultaneous Analysis of Multivariate Polytomous Variates in Several Groups

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
*
Requests for reprints should be sent to Sik-Yum Lee, Department of Statistics, The Chinese University of Hong Kong, Shatin, N. T. HONG KONG, or to P. M. Bentler, Department of Psychology, University of California, Los Angeles, CA 90024-1563.
Requests for reprints should be sent to Sik-Yum Lee, Department of Statistics, The Chinese University of Hong Kong, Shatin, N. T. HONG KONG, or to P. M. Bentler, Department of Psychology, University of California, Los Angeles, CA 90024-1563.
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Abstract

The frequencies of m independent p-way contingency tables are analyzed by a model that assumes that the ordinal categorical data in each of m groups are generated from a latent continuous multivariate normal distribution. The parameters of these multivariate distributions and of the relations between the ordinal and latent variables are estimated by maximum likelihood. Goodness-of-fit statistics based on the likelihood ratio criterion and the Pearsonian chisquare are provided to test the hypothesis that the proposed model is correct, that is, it fits the observed sample data. Hypotheses on the invariance of means, variances, and polychoric correlations of the latent variables across populations are tested by Wald statistics. The method is illustrated on an example involving data on three five-point ordinal scales obtained from male and female samples.

Keywords

polychoric correlationcontingency tablelatent variableordinal variablecategorical data
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 1 , March 1989 , pp. 63 - 73
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

This research was supported in part by research grant DA01070 from the U.S. Public Health Service. The authors are indebted to anonymous reviewers for some very valuable suggestions. The assistance of J. Speckart in manuscript production is also gratefully acknowledged.

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