Detection of differential item functioning using Lagrange multiplier tests

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 test. The test is presented in the framework of a number of IRT models such as the Rasch model, the OPLM, the 2-parameter logistic model, the generalized partial credit model and the nominal response model. However, the paradigm for detection of differential item functioning presented here also applies to other IRT models. Two examples are given, one using simulated data and one using real data.