S − χ 2 is a popular item fit index that is available in commercial software packages such as flexMIRT. However, no research has systematically examined the performance of S − χ 2 for detecting item misfit within the context of the multidimensional graded response model (MGRM). The primary goal of this study was to evaluate the performance of S − χ 2 under two practical misfit scenarios: first, all items are misfitting due to model misspecification, and second, a small subset of items violate the underlying assumptions of the MGRM. Simulation studies showed that caution should be exercised when reporting item fit results of polytomous items using S − χ 2 within the context of the MGRM, because of its inflated false positive rates (FPRs), especially with a small sample size and a long test. S − χ 2 performed well when detecting overall model misfit as well as item misfit for a small subset of items when the ordinality assumption was violated. However, under a number of conditions of model misspecification or items violating the homogeneous discrimination assumption, even though true positive rates (TPRs) of S − χ 2 were high when a small sample size was coupled with a long test, the inflated FPRs were generally directly related to increasing TPRs. There was also a suggestion that performance of S − χ 2 was affected by the magnitude of misfit within an item. There was no evidence that FPRs for fitting items were exacerbated by the presence of a small percentage of misfitting items among them.

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Performance of the S − χ 2 Statistic for the Multidimensional Graded Response Model