### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede, the Netherlands |

Publisher | University of Twente, Faculty Educational Science and Technology |

Number of pages | 40 |

Publication status | Published - 1988 |

### Publication series

Name | OMD research report |
---|---|

Publisher | University of Twente, Faculty of Educational Science and Technology |

No. | 88-13 |

### Keywords

- IR-104177

### Cite this

*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.

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*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.

Research output: Book/Report › Report › Other 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 -