The Performance of Some Observed
and Unobserved Conditional Invariance
Techniques for the Detection of Diﬀerential
Fund for Scientiﬁc Research (FWO), Flanders, Belgium
Address for Oﬀprints: Jerry Welkenhuysen-Gybels, Department of Sociology, K.U.Leuven,
Edward Van Evenstraat 2B, 3000-Leuven, Belgium. Tel. + 32 16 32.31.32, Fax. + 32 16
32.33.65, E-mail: email@example.com
Abstract. The current research investigates the performance of some conditional and
unconditional invariance measures of diﬀerential item functioning (DIF), namely: the log-
linear model, the logistic regression model, the signed and the unsigned area, the SOS1 and the
SOS3. A simulation study is used to evaluate their ability to detect uniform as well as non-
directional nonuniform DIF under several test conditions. The factors that were subject to
experimental manipulation in the simulation study are the size of the DIF, the ability distri-
bution of the focal and the reference group, the sample size, the proportion of DIF items and
the length of the test.
Key words: diﬀerential item functioning, log-linear model, logistic regression model, signed
area, unsigned area, SOS1, SOS3, uniform DIF, nondirectional DIF, nonuniform DIF.
Techniques for the detection of diﬀerential item functioning (DIF) are
commonly divised into two categories (Millsap and Meredith, 1992; Millsap
and Everson, 1993). Unobserved conditional invariance (UCI) techniques,
such as item response theory (IRT) models, use an unobserved latent variable
W as the matching criterion for the detection of DIF in an observable ran-
dom variable Y across two or more subpopulations deﬁned by V. The
unobserved conditional invariance for Y with respect to W and V is deﬁned
as holding if and only if
fðYjW ¼ w; V ¼ vÞ¼fðYjW ¼ wÞ: ð1Þ
Equation (1) implies that the item’s characteristic curve (ICC) is identical
across all subpopulations deﬁned by V. This deﬁnition of UCI (Millsap and
Quality & Quantity 38: 681–702, 2004.
Ó 2004 Kluwer Academic Publishers. Printed in the Netherlands.