Brief summary:
The author compared the measurement invariance in MCCFA and 2PL IRT model respectively. The two models have a direct connection in slope parameter and location parameter. The study manipulated the small and large DIF (only one DIF item in total six items) in dichotomous and polytomous cases. The method for identifying DIF item is likelihood ratio chi-square difference test with backward procedure. The author only demonstrated such a simple condition to show that IRT model is somewhat more powerful than MCCFA under different sample size conditions. Finally, other model fit indexes were also examined compared with LR ratio test. 「In order to」 decrease the false positive (FP) in MCCFA, Oort correction method was used, especially for MCCFA. Like an ad hoc method.
Questions:
1. The author argued the backward procedure is common used among researchers and reasonable. But I can't find out its more convincing advantages over forward procedure.
2. It provided us the results and more robust modified method to get better results. Such as adjust the critical value method to control Type I error. I still have no idea what makes IRT model more appropriate than MCCFA model in first study. What I saw is the ad hoc adjustment indexes for 「unexpected」 results in MCCFA and we got better results then. What have we learned?
3. Only one DIF item in six items. The condition is quite simple. When sample size is small, it is reasonable to see the bad results in DIF study. More large size, more better. So, is anything special?
Further ideas:
1. Can guessing parameter embedded in MCCFA in addition to threshold parameter?
2. Once more DIF items exist, anchor item methods will play an important role in this study. We may be able to predict the same results from this study if good anchor items are selected.