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A Goodness of Fit Test for the Rasch Model

Published online by Cambridge University Press:  01 January 2025

Erling B. Andersen
Erling B. Andersen*
Affiliation:
Copenhagen School of Economics Educational Testing Service*
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Abstract

The Rasch model is an item analysis model with logistic item characteristic curves of equal slope, i.e. with constant item discriminating powers. The proposed goodness of fit test is based on a comparison between difficulties estimated from different scoregroups and over-all estimates.

Based on the within scoregroup estimates and the over-all estimates of item difficulties a conditional likelihood ratio is formed. It is shown that—2 times the logarithm of this ratio is x2-distributed when the Rasch model is true.

The power of the proposed goodness of fit test is discussed for alternative models with logistic item characteristic curves, but unequal discriminating items from a scholastic aptitude test.

Type
Original Paper
Information
Psychometrika , Volume 38 , Issue 1 , March 1973 , pp. 123 - 140
Copyright
Copyright © 1973 The Psychometric Society

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Footnotes

*

Now at: Royal Veterinary and Agricultural University.

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