Computing confidence intervals of item fit statistics in the family of Rasch models using the bootstrap method.

The item infit and outfit mean square errors (MSE) and their t-transformed statistics are widely used to screen poorly fitting items. The t-transformed statistics, however, do not follow the standard normal distribution so that hypothesis testing of item fit based on the conventional critical values is likely to be inaccurate (Wang and Chen, 2005). The MSE statistics are effect-size measures of misfit and have an expected value of unity when the data fit the model's expectation. Unfortunately, most computer programs for item response analysis do not report confidence intervals of the item infit and outfit MSE, mainly because their sampling distributions are analytically intractable. Hence, the user is left without interval estimates of the magnitudes of misfit. In this study, we developed a FORTRAN 90 computer program in conjunction with the commercial program WINSTEPS (Linacre, 2001) that yields confidence intervals of the item infit and outfit MSE using the bootstrap method. The utility of the program is demonstrated through three illustrations of simulated data sets.