DIF Testing for Ordinal Items With Poly-SIBTEST, the Mantel and GMH Tests, and IRT-LR-DIF When the Latent Distribution Is Nonnormal for Both Groups

摘要

Differential item functioning (DIF) occurs when an item on a test, questionnaire, or interview has different measurement properties for one group of people versus another. One way to test items with ordinal response scales for DIF is likelihood ratio (LR) testing using item response theory (IRT), or IRT-LR-DIF. Despite the various advantages of IRT-LR-DIF, one disadvantage is that the latent variable is usually assumed to be normally distributed. If this normality assumption is violated, nonparametric alternatives such as the Mantel test, generalized Mantel-Haenszel (GMH) test, and poly-SIBTEST may be preferable. Simulations were carried out to compare IRT-LR-DIF to poly-SIBTEST and the GMH and Mantel tests when the latent density is nonnormal for both groups but presumed normal for IRT-LR-DIF. Results indicated that latent nonnormality detrimentally affected all three procedures, but IRT-LR-DIF was surprisingly more robust to latent nonnormality than all of the nonparametric approaches.