Assessing Item-Level Fit for Higher Order Item Response Theory Models

Xue Zhang, Chun Wang, Jian Tao

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Testing item-level fit is important in scale development to guide item revision/deletion. Many item-level fit indices have been proposed in literature, yet none of them were directly applicable to an important family of models, namely, the higher order item response theory (HO-IRT) models. In this study, chi-square-based fit indices (i.e., Yen’s Q1, McKinley and Mill’s G2, Orlando and Thissen’s S-X2, and S-G2) were extended to HO-IRT models. Their performances are evaluated via simulation studies in terms of false positive rates and correct detection rates. The manipulated factors include test structure (i.e., test length and number of dimensions), sample size, level of correlations among dimensions, and the proportion of misfitting items. For misfitting items, the sources of misfit, including the misfitting item response functions, and misspecifying factor structures were also manipulated. The results from simulation studies demonstrate that the S-G2 is promising for higher order items.

Original languageEnglish (US)
Pages (from-to)644-659
Number of pages16
JournalApplied Psychological Measurement
Issue number8
StatePublished - Nov 1 2018

Bibliographical note

Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the National Natural Science and Social Science Foundations of China (Grant 11571069) and Institute of Education Sciences (IES) (Grant R305D160010).

Publisher Copyright:
© The Author(s) 2018.


  • S-G
  • S-X
  • correct detection rate
  • false positive rate
  • higher order IRT models
  • item fit


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