Alternatives to Weighted Item Fit Statistics for Establishing Measurement Invariance in Many Groups

Evaluating scale comparability in international large-scale assessments depends on measurement invariance (MI). The root mean square deviation (RMSD) is a standard method for establishing MI in several programs, such as the Programme for International Student Assessment and the Programme for the International Assessment of Adult Competencies. Previous research showed that the RMSD was unable to detect departures from MI when the latent trait distribution was far from item difficulty. In this study, we developed three alternative approaches to the original RMSD: equal, item information, and b-norm weighted RMSDs. Specifically, we considered the item-centered normalized weight distributions to compute the item characteristic curve difference in the RMSD procedure more efficiently. We further compared all methods’ performance via a simulation study and the item information and b-norm weighted RMSDs showed the most promising results. An empirical example is demonstrated, and implications for researchers are discussed.