Testing Measurement Invariance: A Comparison of Multiple-Group Categorical CFA and IRT

This study investigated two major approaches in testing measurement invariance for ordinal measures: multiple-group categorical confirmatory factor analysis (MCCFA) and item response theory (IRT). Unlike the ordinary linear factor analysis, MCCFA can appropriately model the ordered-categorical measures with a threshold structure. A simulation study under various conditions was conducted for the comparison of MCCFA and IRT with respect to the power to detect the lack of invariance across groups. Both MCCFA and IRT showed reasonable power to identify the noninvariant item when differential item functioning (DIF) was large. The false positive rates were relatively high in both methods, however. The adjustment of critical values improved the performance of MCCFA by reducing false positive rates substantially and yet yielding adequate power. Alternative model fit indexes of MCCFA were also examined and they were found to be reliable to detect DIF, in general.