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The Derivation of Some Tests for the Rasch Model from the Multinomial Distribution

Published online by Cambridge University Press:  01 January 2025

Cees A. W. Glas
Cees A. W. Glas*
Affiliation:
National Institute for Educational Measurement (CITO), Arnhem, The Netherlands
*
Requests for reprints should be sent to Cees A. W. Glas, Cito, PO Box 1034, 6801 MG Arnhem, THE NETHERLANDS.
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Abstract

The present paper is concerned with testing the fit of the Rasch model. It is shown that this can be achieved by constructing functions of the data, on which model tests can be based that have power against specific model violations. It is shown that the asymptotic distribution of these tests can be derived by using the theoretical framework of testing model fit in general multinomial and product-multinomial models. The model tests are presented in two versions: one that can be used in the context of marginal maximum likelihood estimation and one that can be applied in the context of conditional maximum likelihood estimation.

Keywords

Item response theoryRasch modelmodel test
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 4 , December 1988 , pp. 525 - 546
Copyright
Copyright © 1988 The Psychometric Society

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Footnotes

I am indebted to Norman Verhelst and Niels Veldhuijzen for their helpful comments.

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