Further Investigation of the Performance of S - X2: An Item Fit Index for Use With Dichotomous Item Response Theory Models

Abstract

This study presents new findings on the utility of S - X² as an item fit index for dichotomous item response theory models. Results are based on a simulation study in which item responses were generated and calibrated for 100 tests under each of 27 conditions. The item fit indices S - X² and Q₁ - X² were calculated for each item. ROC curves were constructed based on the hit and false alarm rates of the two indices. Examination of these curves indicated that in general, the performance of S - X² improved with test length and sample size. The performance of S - X² was superior to that of Q₁ - X² under most but not all conditions. Results from this study imply that S - X² may be a useful tool in detecting the misfit of one item contained in an otherwise well-fitted test, lending additional support to the utility of the index for use with dichotomous item response theory models. Index Terms: item response theory, S - X², Q₁ - X, model = data fit, item fit index.