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

Published online by Cambridge University Press:  01 January 2025

Shelby J. Haberman ,
Sandip Sinharay  and
Kyong Hee Chon
Shelby J. Haberman
Affiliation:
Educational Testing Service
Sandip Sinharay*
Affiliation:
Educational Testing Service
Kyong Hee Chon
Affiliation:
Western Kentucky University
*
Requests for reprints should be sent to Sandip Sinharay, CTB/McGraw-Hill, Monterey, CA, USA. E-mail: sandip_sinharay@ctb.com
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Abstract

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.

Keywords

2-parameter-logistic modelgeneralized partial credit modelitem characteristic curveIRT model fit
Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 3 , July 2013 , pp. 417 - 440
Copyright
Copyright © 2012 The Psychometric Society

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Footnotes

Note: Any opinions expressed in this publication are those of the authors and not necessarily of Educational Testing Service. Sandip Sinharay conducted this study and wrote this report while on staff at Educational Testing Service. He is currently at CTB/McGraw-Hill.

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