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 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
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.