Modification indices for the 2-PL and the nominal response model

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Abstract

In this paper it is shown that various violations of the two parameter logistic (2PL) model can be evaluated using the Lagrange multiplier test (J. Aitchison and S. Silvey, 1958) or the equivalent difference score test. The tests focus on violation of local stochastic independence and insufficient capture of the form of the item characteristic curves. Primarily, the tests are item-oriented diagnostic tools, but taken together, they also serve the purpose of evaluation of global model fit. A useful feature of Lagrange multiplier statistics is that they are evaluated using maximum likelihood estimates of the null model only; that is, the parameters of alternative models need not be estimated. As numerical examples, an application on real data and some power studies are presented.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Faculty Educational Science and Technology
Number of pages97
Publication statusPublished - 1998

Publication series

NameOMD-research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.98-04

Keywords

  • Item Response Theory
  • Test Items
  • Goodness of Fit
  • METIS-136538
  • IR-103762
  • Maximum Likelihood Statistics
  • Foreign Countries

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    Glas, C. A. W. (1998). Modification indices for the 2-PL and the nominal response model. (OMD-research report; No. 98-04). Enschede: University of Twente, Faculty Educational Science and Technology.