A Monte Carlo investigation of several person and item fit statistics for item response models. Applied Psychological Measurement

This study investigated the behavior of several per-son and item fit statistics commonly used to test and obtain fit to the one-parameter item response model. Using simulated data for 500 persons and 15 items, the sensitivity of the total-t, mean-square residual, and between-t fit statistics to guessing, heterogeneity in discrimination parameters, and multidimensionality was examined. Additionally, 25 misfitting persons and a misfitting item were generated to test the power of the three fit statistics to detect deviations in a subset of observations. Neither the total-t nor the mean-square residual were able to detect deviation from any of the models fitted. Use of these statistics appears to be un-warranted. The between-t was a useful indicator of guessing and heterogeneity in discrimination parame