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Constructing the Exact Significance Level for a Person Fit Statistic

Published online by Cambridge University Press:  01 January 2025

Michelle Liou  and
Chih-Hsin Chang
Michelle Liou*
Affiliation:
Academia Sinica
Chih-Hsin Chang
Affiliation:
Academia Sinica
*
Requests for reprints should be sent to Michelle Liou, Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan, R.O.C.
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Abstract

This paper uses an extension of the network algorithm originally introduced by Mehta and Patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the Rasch model. By assuming that item difficulties are known, the algorithm is applicable to the statistical tests either given the maximum likelihood ability estimate or conditioned on the total score. A simulation study indicates that the network algorithm is an efficient tool for computing the significance level of a person fit statistic based on test lengths of 30 items or less.

Keywords

exact testsmaximum likelihoodperson fit statisticsthe network algorithmthe Rasch model
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 2 , June 1992 , pp. 169 - 181
Copyright
Copyright © 1992 The Psychometric Society

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References

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