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Graphical Regression Models for Polytomous Variables

Published online by Cambridge University Press:  01 January 2025

Carolyn J. Anderson  and
Ulf Böckenholt
Carolyn J. Anderson*
Affiliation:
University of Illinois at Urbana-Champaign
Ulf Böckenholt
Affiliation:
University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Carolyn Anderson, Department of Educational Psychology, 1310 South Sixth Street, 230 Education Building, MC-708, Champaign, IL, 61820. E-Mail: [email protected]
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Abstract

When modeling the relationship between two nominal categorical variables, it is often desirable to include covariates to understand how individuals differ in their response behavior. Typically, however, not all the relevant covariates are available, with the result that the measured variables cannot fully account for the associations between the nominal variables. Under the assumption that the observed and unobserved variables follow a homogeneous conditional Gaussian distribution, this paper proposes RC(M) regression models to decompose the residual associations between the polytomous variables. Based on Goodman's (1979, 1985)RC(M) association model, a distinctive feature of RC(M) regression models is that they facilitate the joint estimation of effects due to manifest and omitted (continuous) variables without requiring numerical integration. The RC(M) regression models are illustrated using data from the High School and Beyond study (Tatsuoka & Lohnes, 1988).

Keywords

conditional independencelatent continuous variablesRC(M) association modelgraphical modelsmarginal maximum likelihood estimation
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 4 , December 2000 , pp. 497 - 509
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

This article was accepted for publication, when Willem J. Heiser was the Editor of Psychometrika. This research was supported by grants from the National Science Foundation (#SBR96-17510 and #SBR94-09531) and the Bureau of Educational Research at the University of Illinois. We thank Jee-Seon Kim for comments and computational assistance.

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