, Volume 78, Issue 3, pp 417–440 | Cite as

Assessing Item Fit for Unidimensional Item Response Theory Models Using Residuals from Estimated Item Response Functions

  • Shelby J. Haberman
  • Sandip SinharayEmail author
  • Kyong Hee Chon


Residual analysis (e.g. Hambleton & Swaminathan, Item response theory: principles and applications, Kluwer Academic, Boston, 1985; Hambleton, Swaminathan, & Rogers, Fundamentals of item response theory, Sage, Newbury Park, 1991) is a popular method to assess fit of item response theory (IRT) models. We suggest a form of residual analysis that may be applied to assess item fit for unidimensional IRT models. The residual analysis consists of a comparison of the maximum-likelihood estimate of the item characteristic curve with an alternative ratio estimate of the item characteristic curve. The large sample distribution of the residual is proved to be standardized normal when the IRT model fits the data. We compare the performance of our suggested residual to the standardized residual of Hambleton et al. (Fundamentals of item response theory, Sage, Newbury Park, 1991) in a detailed simulation study. We then calculate our suggested residuals using data from an operational test. The residuals appear to be useful in assessing the item fit for unidimensional IRT models.

Key words

2-parameter-logistic model generalized partial credit model item characteristic curve IRT model fit 


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Copyright information

© The Psychometric Society 2012

Authors and Affiliations

  • Shelby J. Haberman
    • 1
  • Sandip Sinharay
    • 3
    Email author
  • Kyong Hee Chon
    • 2
  1. 1.Research & DevelopmentEducational Testing ServicePrincetonUSA
  2. 2.Educational Administration, Leadership, and ResearchWestern Kentucky UniversityBowling GreenUSA
  3. 3.CTB/McGraw-HillMontereyUSA

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