Graphical regression models for polytomous variables

Carolyn J. Anderson*, Ulf Böckenholt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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).

Original languageEnglish (US)
Pages (from-to)497-509
Number of pages13
JournalPsychometrika
Volume65
Issue number4
DOIs
StatePublished - Dec 2000

Funding

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. 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]

Keywords

  • Conditional independence
  • Graphical models
  • Latent continuous variables
  • Marginal maximum likelihood estimation
  • RC(M) association model

ASJC Scopus subject areas

  • General Psychology
  • Applied Mathematics

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