The distribution of person fit using true and estimated person parameters

A variety of methods have been developed to deter-mine the extent to which a person’s response vector fits an item response theory model. These person-fit meth-ods are statistical methods that allow researchers to identify nonfitting response vectors. The most promising. method has been the 1, statistic, which is a standardized person-fit index. Reise & Due (1991) concluded that un-der the null condition (i.e., when data were simulated to fit the model) 1, performed reasonably well. The present study extended the findings of past researchers (e.g., Drasgow, Levine, & McLaughlin, 1987; Molenaar & Hoijtink, 1990; Reise and Due). Results show that 11 may not perform as expected when estimated person pa-rameters (6) are used rather than true 0. This study also examined the influence of the pseudo-guessing param-eter, the method used to identify nonfitting response vectors, and the method used to estimate 0. When 0 was better estimated, 1, was more normally distributed, and, the false positive rate for a single cut score did not char-. acterize the distribution of lz. Changing the c parameter from.20 to 0.0 did not improve the normality of the 1. distribution. Index terms: appropriateness measure-ment, Bayesian estimation, item response theory, maxi-mum likelihood estimation, person fit. During the past 15 years, several methods have been proposed to investigate a person’s response pattern to a set of test items to determine whether ~ that person is being accurately measured in the con-text of item response theory (IRT) models (e.g., Levin