, Volume 64, Issue 3, pp 273–294

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

  • Cees A. W. Glas

DOI: 10.1007/BF02294296

Cite this article as:
Glas, C.A.W. Psychometrika (1999) 64: 273. doi:10.1007/BF02294296


In this paper, it is shown that various violations of the 2-PL model and the nominal response model can be evaluated using the Lagrange multiplier test or the equivalent efficient score test. The tests presented here 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 to real data and some power studies are presented.

Key words

efficient score test generalized partial credit model item response theory model fit modification indices 2-parameter logistic model nominal response model Lagrange multiplier test 

Copyright information

© The Psychometric Society 1999

Authors and Affiliations

  • Cees A. W. Glas
    • 1
  1. 1.Department of educational measurement and data analysisUniversity of TwenteThe Netherlands

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