Internal measures of differential functioning of items
and tests (DFIT) 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 unbiased
; (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) CDIF 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
X² test, the signed area measure, and the unsigned area
measure, demonstrate that the DFIT framework is accurate
in assessing DTF, CDIF, and NCDIF. Index Terms:
area measures of DIF, compensatory DIF, differential
functioning of items and tests (DFIT), differential item
functioning, differential test functioning, Lord’s X²;
noncompensatory DIF, nonuniform DIF, uniform DIF.
Raju, Nambury S.; Van der Linden, Wim J.; Fleer, Paul F..
IRT-based internal measures of differential functioning of items and tests.
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