Asymptotic distribution of an IRT person fit index

Jan Kogut

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The distribution of a certain item response theory (IRT) based person fit index to identify systematic types of aberrance is discussed. For the Rasch model, it is proved that: (1) the joint distribution of subtest-residuals (the components of the index) is asymptotically multivariate normal; and (2) the distribution of the index is asymptotically chi-square. The parameters of these asymptotic distributions depend on whether ability of a person is known or estimated. Furthermore, the rate of convergence to the asymptotic distribution of the subtest-residuals is analyzed. In order to verify the results for short tests, a simulation study was conducted. The hypothetical test was composed of 40 items designed according to the Rasch model.
Original languageUndefined
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente, Faculty Educational Science and Technology
Number of pages40
Publication statusPublished - 1988

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology


  • IR-104177

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