Statistica Sinica 8(1998), 647-667

DETECTION OF DIFFERENTIAL ITEM FUNCTIONING

USING LAGRANGE MULTIPLIER TESTS

C. A. W. Glas

University of Twente, Enschede, the Netherlands

Abstract: In the present paper it is shown that differential item functioning can be evaluated using the Lagrange multiplier test or Rao's efficient score te st. The test is presented in the framework of a number of IRT models such as the Ra sch model, the OPLM, the 2-parameter logistic model, the generalized partial cr edit model and the nominal response model. However, the paradigm for detection o f differential item functioning presented here also applies to other IRT mode ls. Two examples are given, one using simulated data and one using real data.

Key words and phrases: DIF, generalized partial credit model, item response theory, Lagrange multiplier test, model fit, nominal response model, OPLM, Rao' s efficient score test, Rasch model, two-parameter logistic model.