Asymptotic distribution of an IRT person fit index

Jan Kogut

Research output: Book/ReportReportOther research output

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Abstract

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
No.88-13

Keywords

  • IR-104177

Cite this

Kogut, J. (1988). Asymptotic distribution of an IRT person fit index. (OMD research report; No. 88-13). Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology.
Kogut, Jan. / Asymptotic distribution of an IRT person fit index. Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1988. 40 p. (OMD research report; 88-13).
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keywords = "IR-104177",
author = "Jan Kogut",
note = "Project Psychometric Aspects of Item Banking No. 38",
year = "1988",
language = "Undefined",
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publisher = "University of Twente, Faculty Educational Science and Technology",
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Kogut, J 1988, Asymptotic distribution of an IRT person fit index. OMD research report, no. 88-13, University of Twente, Faculty Educational Science and Technology, Enschede, the Netherlands.

Asymptotic distribution of an IRT person fit index. / Kogut, Jan.

Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1988. 40 p. (OMD research report; No. 88-13).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Asymptotic distribution of an IRT person fit index

AU - Kogut, Jan

N1 - Project Psychometric Aspects of Item Banking No. 38

PY - 1988

Y1 - 1988

N2 - 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.

AB - 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.

KW - IR-104177

M3 - Report

T3 - OMD research report

BT - Asymptotic distribution of an IRT person fit index

PB - University of Twente, Faculty Educational Science and Technology

CY - Enschede, the Netherlands

ER -

Kogut J. Asymptotic distribution of an IRT person fit index. Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology, 1988. 40 p. (OMD research report; 88-13).