Modeling Item-Level and Step-Level Invariance Effects in Polytomous Items Using the Partial Credit Model

Karina A. Gattamorta, Randall D. Penfield, Nicholas D. Myers

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Measurement invariance is a common consideration in the evaluation of the validity and fairness of test scores when the tested population contains distinct groups of examinees, such as examinees receiving different forms of a translated test. Measurement invariance in polytomous items has traditionally been evaluated at the item-level, corresponding to what is broadly referred to as differential item functioning. However, recent advances in the study of measurement invariance in polytomous items has documented the value in examining invariance at the level of each step of the polytomous item, referred to as differential step functioning. To date, little documentation exists of methodology that can simultaneously evaluate both item-level and step-level invariance effects using a common parametric model. In this article, we describe how to use the partial credit model to simultaneously evaluate item-level and step-level invariance effects. A simulation study as well as a large empirical example are presented to demonstrate the use of this methodology applied to a large-scale administration of a translated test.

Original languageEnglish (US)
Pages (from-to)252-272
Number of pages21
JournalInternational Journal of Testing
Issue number3
StatePublished - Jul 2012


  • DIF
  • DSF
  • invariance
  • polytomous items
  • translated tests

ASJC Scopus subject areas

  • Education
  • Modeling and Simulation
  • Social Psychology


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