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 -