IRT-Based Internal Measures of Differential Functioning of Items and Tests

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Abstract
Internal measures of differential functioning of items and tests (DHFIT) based on item response theory (IRT) are proposed. Within the DFIT context, the new differential test functioning (DTF) index leads to two new measures of differential item functioning (DIF) with the following properties: (1) The compensatory DIF (CDIF) indexes for all items in a test sum to the DTF index for that test and, unlike current DIF procedures, the CDIF index for an item does not assume that the other items in the test are unbi ased ; (2) the noncompensatory DIF (NCDIF) index, which assumes that the other items in the test are unbiased, is comparable to some of the IRT-based DIP indexes; and (3) COIF and NCDIF, as well as DTF, are equally valid for polytomous and multidimensional IRT models. Monte carlo study results, comparing these indexes with Lord's χ2 test, the signed area measure, and the unsigned area measure, demonstrate that the DFIT framework is accu rate in assessing DTF, COIF, and NCDIF.