The unique correspondence of the item response function and item category response functions in polytomously scored item response models

Hua Hua Chang, John Mazzeo

Research output: Contribution to journalArticle

Abstract

The item response function (IRF) for a polytomously scored item is defined as a weighted sum of the item category response functions (ICRF, the probability of getting a particular score for a randomly sampled examinee of ability θ). This paper establishes the correspondence between an IRF and a unique set of ICRFs for two of the most commonly used polytomous IRT models (the partial credit models and the graded response model). Specifically, a proof of the following assertion is provided for these models: If two items have the same IRF, then they must have the same number of categories; moreover, they must consist of the same ICRFs. As a corollary, for the Rasch dichotomous model, if two tests have the same test characteristic function (TCF), then they must have the same number of items. Moreover, for each item in one of the tests, an item in the other test with an identical IRF must exist. Theoretical as well as practical implications of these results are discussed.

Original languageEnglish (US)
Pages (from-to)391-404
Number of pages14
JournalPsychometrika
Volume59
Issue number3
DOIs
StatePublished - Sep 1 1994

Keywords

  • generalized partial credit model
  • graded response model
  • invariance
  • item response theory
  • ordered categories
  • partial credit model
  • polytomous item

ASJC Scopus subject areas

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

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