Detection of differential item functioning using Lagrange multiplier tests

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In this paper it is shown that differential item functioning can be evaluated using the Lagrange multiplier test or C. R. Rao's efficient score test. The test is presented in the framework of a number of item response theory (IRT) models such as the Rasch model, the one-parameter logistic model, the two-parameter logistic model, the generalized partial credit model, and the nominal response model. However, the paradigm for detection of differential item functioning presented here applies to other IRT models. The proposed method is based on a test statistic with a known asymptotic distribution. Two examples are given, one using simulated data and one using real data from 1,000 boys and 1,000 girls taking a Dutch secondary examination.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversiteit Twente, Faculteit Toegepaste Onderwijskunde
Number of pages40
Publication statusPublished - 1996

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology


  • Simulation
  • Scores
  • Item Response Theory
  • Secondary Education
  • IR-103764
  • Test Items
  • Item Bias
  • Foreign Countries
  • METIS-136523
  • Secondary School Students

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    Glas, C. A. W. (1996). Detection of differential item functioning using Lagrange multiplier tests. (OMD research report; No. 96-02). Enschede: Universiteit Twente, Faculteit Toegepaste Onderwijskunde.