The distribution of person fit using true and estimated person parameters

Abstract

A variety of methods have been developed to determine the extent to which a person’s response vector fits an item response theory model. These person-fit methods are statistical methods that allow researchers to identify nonfitting response vectors. The most promising method has been the lz statistic, which is a standardized person-fit index. Reise & Due (1991) concluded that under the null condition (i.e., when data were simulated to fit the model) lz 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 lz may not perform as expected when estimated person parameters (θˆ) are used rather than true θ. This study also examined the influence of the pseudo-guessing parameter, the method used to identify nonfitting response vectors, and the method used to estimate θ. When θ was better estimated, lz, was more normally distributed, and the false positive rate for a single cut score did not characterize the distribution of lz. Changing the c parameter from .20 to 0.0 did not improve the normality of the lz. distribution. Index terms: appropriateness measurement, Bayesian estimation, item response theory, maximum likelihood estimation, person fit.