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Modification Indices for the 2-PL and the Nominal Response Model

Published online by Cambridge University Press:  01 January 2025

Cees A. W. Glas
Cees A. W. Glas*
Affiliation:
Department of educational measurement and data analysis, University of Twente
*
Requests for reprints should be sent to Cees A. W. Glas, Department of Educational Measurement and Data Analysis, P.O. Box 217, 7500 AE Enschede, the Netherlands.
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Abstract

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.

Keywords

efficient score testgeneralized partial credit modelitem response theorymodel fitmodification indices2-parameter logistic modelnominal response modelLagrange multiplier test
Type
Original Paper
Information
Psychometrika , Volume 64 , Issue 3 , September 1999 , pp. 273 - 294
Copyright
Copyright © 1999 The Psychometric Society

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