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On Scaling Models Applied to Data from Several Groups

Published online by Cambridge University Press:  01 January 2025

Clifford C. Clogg  and
Leo A. Goodman
Clifford C. Clogg*
Affiliation:
Departments of Sociology and Statistics, The Pennsylvania State University
Leo A. Goodman
Affiliation:
Departments of Statistics and Sociology, University of Chicago
*
Requests for reprints should be sent to Clifford C. Clogg, Department of Statistics, The Pennsylvania State University, University Park, PA 16802.
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Abstract

Statistical methods are presented to facilitate a more complete analysis of results obtained when a scaling model is applied to data from two or more groups. These methods can be used to (a) compare the corresponding estimated latent distributions obtained using the scaling model applied to the different groups, (b) compare the corresponding estimated item reliabilities (or item response error rates) for the different groups, and (c) test whether the scaling model applied to the several groups can be replaced by a more parsimonious scaling model that includes various homogeneity constraints (i.e., constraints that describe which parameters in the model are the same for the several groups). Various kinds of scaling models are considered here in the multiple-group context.

Keywords

Scaling modelsGuttman's modelmultiple-group scaling modelslatent class modelsmultiple-group latent structure models
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 1 , March 1986 , pp. 123 - 135
Copyright
Copyright © 1986 The Psychometric Society

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Footnotes

Support for this research was provided in part by the National Science Foundation, to Clogg by Grant No. SES-7823759 and to Goodman by Grant No. SES-8303838. Clogg and Goodman were Fellows at the Center for Advanced Study in the Behavioral Sciences when part of the research was done, with financial support provided in part by National Science Foundation grant BNS-8011494 to the Center. The authors are indebted to Mark P. Becker and James W. Shockey for helpful comments.

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