REVIEW on Testing Measurement Invariance: A Comparison of Multiple-Group Categorical CFA and IRT
This paper motivated MCCFA to assess measurement invariance by argue that the ordinary CFA is not appropriate for categorical data. In order to evaluate its properties, dichotomous 2PL IRT model and grade response model were employed to do the comparison by using the Likelihood Ratio test and sticking to the backward procedure. After a simulation study, it was found that the IRT performs better than MCCFA in general, especially in the False Positive Rates. Since this article is not aim to do the comparison but proposed the MCCFA for assessing measurement invariance, some improvement techniques were examined to yield better performance. First, the author examined three other model fit index of MCCFA; second, the author conducted a supplemental analysis using adjusted critical value (Oort’s correction) and found that adjusted critical value can help to decrease the False Positive Rates.
This article is very well logical organized and clearly describe the theories and procedures. However, for the main purpose of this study is proposed MCCFA for assessing measurement invariance, this article is too stick to the comparison with IRT approach. As the author states that choosing the backward LR procedure is for comparable purpose, but it is not necessary. If there is another procedure to conduct MCCFA rather than backward procedure which can yield better performance, why not just show its power for the purpose? By doing so, the supplemental procedures (such as other model fit indices, Oort’s correction) can be omitted which increased the complexity of the application of MCCFA.
Meanwhile, the author proposed two aspects for future study: 1) Oort adjustment for IRT when using LR test. 2) MIMIC with different critical values for testing measurement invariance.