, Volume 38, Issue 1, pp 123–140 | Cite as

A goodness of fit test for the rasch model

  • Erling B. Andersen


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 isx 2-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.


Item Difficulty Item Parameter Conditional Likelihood Likelihood Equation Asymptotic Covariance Matrix 
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Copyright information

© Psychometric Society 1973

Authors and Affiliations

  • Erling B. Andersen
    • 1
    • 2
  1. 1.Copenhagen School of EconomicsDenmark
  2. 2.Educational Testing ServiceUSA

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