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Loglinear Rasch Model Tests

Published online by Cambridge University Press:  01 January 2025

Hendrikus Kelderman
Hendrikus Kelderman*
Affiliation:
Twente University of Technology, Enschede, The Netherlands
*
Requests for reprints should be sent to Hendrikus Kelderman, Toegepaste Onderwijskunde, Technische Hogeschool Twente, Postbus 217, 7500 AE Enschede, The Netherlands.
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Abstract

Existing statistical tests for the fit of the Rasch model have been criticized, because they are only sensitive to specific violations of its assumptions. Contingency table methods using loglinear models have been used to test various psychometric models. In this paper, the assumptions of the Rasch model are discussed and the Rasch model is reformulated as a quasi-independence model. The model is a quasi-loglinear model for the incomplete subgroup × score × item 1 × item 2 × ... × item k contingency table. Using ordinary contingency table methods the Rasch model can be tested generally or against less restrictive quasi-loglinear models to investigate specific violations of its assumptions.

Keywords

latent-trait theoryRasch modelquasi-loglinear modelquasi independenceincomplete contingency tablechi-square tests
Type
Article
Information
Psychometrika , Volume 49 , Issue 2 , June 1984 , pp. 223 - 245
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

The author thanks Gideon J. Mellenbergh, Pieter Vijn, Wim J. van der Linden, Ivo W. Molenaar, and Sebie J. Oosterloo for comments and Carolien Schamhardt and Anita Burchartz for typing the manuscript.

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