Graphical regression models for polytomous variables

Carolyn J. Anderson, Ulf Böckenholt

Research output: Contribution to journalArticlepeer-review


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
Issue number4
StatePublished - Dec 2000


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

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • General Psychology
  • Psychology (miscellaneous)
  • Social Sciences (miscellaneous)


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