IRT-based internal measures of differential functioning of items and tests

摘要

Internal measures of differential functioning of itemsand tests (DFIT) based on item response theory (IRT) areproposed. Within the DFIT context, the new differentialtest functioning (DTF) index leads to two new measuresof differential item functioning (DIF) with the followingproperties: (1) The compensatory DIF (CDIF) indexes forall items in a test sum to the DTF index for that test and,unlike current DIF procedures, the CDIF index for an itemdoes not assume that the other items in the test are unbiased; (2) the noncompensatory DIF (NCDIF) index, whichassumes that the other items in the test are unbiased, iscomparable to some of the IRT-based DIP indexes; and(3) CDIF and NCDIF, as well as DTF, are equally valid forpolytomous and multidimensional IRT models. Montecarlo study results, comparing these indexes with Lord’sX² test, the signed area measure, and the unsigned areameasure, demonstrate that the DFIT framework is accuratein assessing DTF, CDIF, and NCDIF. Index Terms:area measures of DIF, compensatory DIF, differentialfunctioning of items and tests (DFIT), differential itemfunctioning, differential test functioning, Lord’s X²;noncompensatory DIF, nonuniform DIF, uniform DIF.