Performance of the generalized S-X^sup 2^ item fit index for the graded response model

The utility of Orlando and Thissen's ( 2000 , 2003 ) S-X^sup 2^ fit index was extended to the model-fit analysis of the graded response model (GRM). The performance of a modified S-X^sup 2^ in assessing item-fit of the GRM was investigated in light of empirical Type I error rates and power with a simulation study having various conditions typically encountered in applied testing situations. The results show that the Type I error rates were controlled adequately around the nominal alpha by S-X^sup 2^. The power of the S-X^sup 2^ statistic was much lower when the source of misfit was multidimensionality than when it was due to discrepancy from the true GRM curves. Once the data size increased sufficiently, however, appropriate power was obtained regardless of the source of the item-misfit. In summary, the generalized S-X^sup 2^ appears to be a promising index for investigating item fit for polytomous items in educational and psychological assessments.