Loglinear multidimensional IRT models for polytomously scired Items

Henk Kelderman

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A loglinear item response theory (IRT) model is proposed that relates polytomously scored item responses to a multidimensional latent space. Each item may have a different response function where each item response may be explained by one or more latent traits. Item response functions may follow a partial credit model (D. Andrich, 1978; and G. N. Masters, 1982), a multidimensional Rasch model (G. Rasch, 1961; and E. B. Andersen, 1973, 1983), or other forms of response functions to be defined by the user. Conditional maximum likelihood estimates are derived, and the models may be tested generally or against alternative loglinear models. The latter tests are sensitive to deviations from local independence subgroup invariance or assumptions about the form of the operating characteristic curves. The model was illustrated through application to data from a test to identify learning problems in Dutch children from 4 to 6.5 years of age. Fifteen items were administered to 66 children aged 4 to 5 years, 132 children aged 5 to 5.5 years, and 65 children aged 5.5 to 6 years. Three appendices illustrate the dichotomous Rasch model, the partial credit model, and Rasch's multidimensional model.
Original languageUndefined
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente, Faculty Educational Science and Technology
Number of pages39
Publication statusPublished - 1988

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology


  • Latent Trait Theory
  • Test Items
  • Equations (Mathematics)
  • Learning Problems
  • Early Childhood Education
  • Young Children
  • Mathematical Models
  • Maximum Likelihood Statistics
  • Goodness of Fit
  • Multidimensional Scaling
  • Foreign Countries
  • Estimation (Mathematics)
  • IR-104182
  • Scoring

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