Antw: [Rasch] chi-square in rasch model

Moritz Heene heene at psy.lmu.de
Sat Aug 9 23:45:55 EST 2008


Dear Juanito,

Usually, this kind of chi-square statistic is a so-called global model test, comparing the difference between the observed and expected response pattern frequencies under the Rasch model. So this statistic should tell you whether the Rasch model was able to "predict" the observed pattern frequencies. However, with empirical data the problem arises that not all possible response patterns can be observed and the expected frequencies are therefore very low. Take for example a test consisting of 20 dichotomous items. Furthermore, let us assume your sample sample size is 100. Theoretically, we expect 2^100 = 1267650600228229401496703205376 different response patterns. But at best we can only observe 100. But a necessary requirement for the chi-square statistic is that the expected pattern frequencies are greater than one. So many patterns are not observed and the asymptotic requirements of the test statistic are not met. In this case the test statistic is no longer chi-square distributed and statistical inferences are invalid or at least unreliable.
But my guess is that Mike or somebody else could explain that better ;-)

Best,

Moritz.


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Dr. Moritz Heene
Ludwig Maximilian University Munich
Department Psychology
Methodology and Psychological Assessment
Leopoldstrasse 13
80802 Munich, Germany

Tel.: +49 89 / 2180 5192
Fax: +49 89 / 2180 3000

Web: http://www.psy.lmu.de/pm/Mitarbeiter/Moritz-Heene.html
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