Testing Measurement Invariance: A Comparison of Multiple-Group Categorical CFA and IRT
Measurement invariance is a basic property that we develop test to meet such goal. More specifically, test itself measures the trait in the same way across all groups which belong to physical membership. On the other word, we hope that there is not any DIF item in the test. A series of simulations were conducted to compare multiple-group categorical confirmatory factor analysis (MCCFA) and item response theory (IRT) on assessing measurement invariance. An adjustment of critical values was adopted in MCCFA for the situation of type I error would be inflated with DIF increasing. Results shown that the performance on IRT approach is better than MCCFA on comparing index of type I and power, in generally. However, MCCFA with Oort’s adjustment, it could effectively improve the type I error and obtain adequate power. Finally, a model fit of MCCFA was examined.
Sharing, Question and Future study:
1) It’s easy to understand that the meaning of DIF in dichotomous item. When a dichotomous item with DIF, we know that different membership like gender or race, they would have different performance even they actually have equal ability. However, it’s hard for me to getting the point of DIF in polytomous item due to over two categories for items. I know this is not an issue or responsibility to be explained on the present paper. Just want to know anyone can explain DIF in polytomous items.
2) I’m agree with Xuelan’s suggestion, we can do a future study by adopting DIF-free-then-DIF strategy into the present paper but I’m not sure whether the strategy can be used in MCCFA approach.