Multidimensional Item Response Theory Models with Collateral Information as Poisson Regression Models

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Multiple choice items on tests and Likert items on surveys are ubiquitous in educational, social and behavioral science research; however, methods for analyzing of such data can be problematic. Multidimensional item response theory models are proposed that yield structured Poisson regression models for the joint distribution of responses to items. The methodology presented here extends the approach described in Anderson, Verkuilen, and Peyton (2010) that used fully conditionally specified multinomial logistic regression models as item response functions. In this paper, covariates are added as predictors of the latent variables along with covariates as predictors of location parameters. Furthermore, the models presented here incorporate ordinal information of the response options thus allowing an empirical examination of assumptions regarding the ordering and the estimation of optimal scoring of the response options. To illustrate the methodology and flexibility of the models, data from a study on aggression in middle school (Espelage, Holt, and Henkel 2004) is analyzed. The models are fit to data using SAS.

Original languageEnglish (US)
Pages (from-to)276-303
Number of pages28
JournalJournal of Classification
Issue number2
StatePublished - Jul 2013


  • Constrained optimization
  • Covariates
  • Fully conditionally specified models
  • Log-multiplicative association models
  • Ordinal response scales
  • Polytomous items

ASJC Scopus subject areas

  • Library and Information Sciences
  • Mathematics (miscellaneous)
  • Psychology (miscellaneous)
  • Statistics, Probability and Uncertainty


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