Statistical properties of estimators of the RMSD item fit statistic

In this article, statistical properties of the root mean square deviation (RMSD) item fit statistic in item response models are studied. It is shown that RMSD estimates will indicate even misfit for items whose parametric assumption of the item response function is correct (i.e., fitting items) if some item response functions in the test are misspecified. Moreover, it is demonstrated that the RMSD values of misfitting and fitting items depend on the proportion of misfitting items. We propose three alternative bias-corrected RMSD estimators that reduce the bias for fitting items. However, these alternative estimators provide slightly negatively biased estimates for misfitting items compared to the originally proposed RMSD statistic. In the numerical experiments, we study the case of a misspecified one-parameter logistic item response model and the behavior of the RMSD statistic if differential item functioning occurs.