Assessing the Item Response Theory With Covariate (IRT-C) Procedure for Ascertaining Differential Item Functioning

Louis Tay, Jeroen K. Vermunt, Chun Wang

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We evaluate the item response theory with covariates (IRT-C) procedure for assessing differential item functioning (DIF) without preknowledge of anchor items (Tay, Newman, & Vermunt, 2011). This procedure begins with a fully constrained baseline model, and candidate items are tested for uniform and/or nonuniform DIF using the Wald statistic. Candidate items are selected in turn based on high unconditional bivariate residual (UBVR) values. This iterative process continues until no further DIF is detected or the Bayes information criterion (BIC) increases. We expanded on the procedure and examined the use of conditional bivariate residuals (CBVR) to flag for DIF; aside from the BIC, alternative stopping criteria were also considered. Simulation results showed that the IRT-C approach for assessing DIF performed well, with the use of CBVR yielding slightly better power and Type I error rates than UBVR. Additionally, using no information criterion yielded higher power than using the BIC, although Type I error rates were generally well controlled in both cases. Across the simulation conditions, the IRT-C procedure produced results similar to the Mantel-Haenszel and MIMIC procedures.

Original languageEnglish (US)
Pages (from-to)201-222
Number of pages22
JournalInternational Journal of Testing
Issue number3
StatePublished - Jul 2013


  • differential item functioning
  • item response theory
  • multiple covariates
  • simulation


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