Bias-corrected root mean square deviation estimators

The root mean square deviation (RMSD) is a widely used item fit statistic in item response models. However, the sample RMSD is known to exhibit positive bias in small samples. To address this, seven alternative bias-corrected RMSD estimators are proposed and evaluated in a simulation study involving items with uniform differential item functioning (DIF). The results demonstrate that the proposed estimators effectively reduce the bias of the original RMSD statistic. Their performance is compared, and the most favorable estimators are highlighted for empirical research. Finally, the application of the various RMSD statistics is illustrated using PISA 2006 reading data.