*Test Items IDENTIFIERS Aberrance; *Asymptotic Distributions; *Person Fit Measures; F.asch Model; Residuals (Statistics);

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. Four data tables and two graphs present the numerical data from the simulation. (Author/SLD) Reproductions supplied by EDRS are the best that can be made from the original document. ********************************************************A************** Asymptotic Distribution of a