The S-χ2 item fit index is one of the few item fit indices that appears to maintain accurate Type I error rates. This study explored grouping examinees by the rest score or summed score, prior distributions for the item parameters, and the shape of the ability distribution. Type I error was slightly closer to the nominal level for the total-score S-χ2 for the longest tests, but power was higher for the rest-score S-χ2 in every condition where power was < 1. Prior distributions reduced the proportion of estimates with extreme standard errors but slightly inflated the Type I error rates in some conditions. When the ability distribution was not normally distributed, integrating over an empirically-estimated distribution yielded Type I error rates closer to the nominal value than integrating over a normal distribution.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
DeMars, C. E. & Sauder, D. (2019, April). Considerations in S-χ2: Rest score or summed score, priors, and violations of normality. Electronic poster presented at the annual meeting of the National Council on Measurement in Education, Toronto, Canada.