A Monte Carlo investigation of several person and item fit statistics for item response models

This study investigated the behavior of several personand item fit statistics commonly used to test andobtain 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, andbetween-t fit statistics to guessing, heterogeneity indiscrimination parameters, and multidimensionalitywas examined. Additionally, 25 misfitting persons anda misfitting item were generated to test the power ofthe three fit statistics to detect deviations in a subset ofobservations. Neither the total-t nor the mean-squareresidual were able to detect deviation from any of themodels fitted. Use of these statistics appears to be unwarranted.The between-t was a useful indicator ofguessing and heterogeneity in discrimination parameters,but was unable to detect multidimensionality.These results show that use of person and item fitstatistics to test and obtain overall fit to the one-parametermodel can lead to acceptance of the modeleven when it is grossly inappropriate. Assessments ofmodel fit based on this strategy are inadequate. Alternativemethods must be sought.