Ordinal linear CFA (i.e., CFA for continuous measured variables) disregards the discrete proper of the category data and treats dichotomous/ polytomous scores as continuous and normally distributed variables.
Category confirmatory factor analysis (CCFA) modeled the ordered-categorical measures with a threshold analysis. It was assumed that the latent response variates are continuous but the threshold(s) ‘cut’ them into discrete scores.
Questions:
1. The current research simulated that only one DIF item in 6 items. Suppose there are more DIF items in long test, what are the effectiveness of the MCCFA?
2. From the Table 1, the Oort adjustment decreased the Type I significantly . For example, for polytomous data when DIF existed in both parameters, the FP rate of the large-sample large-DIF condition decreased from 95% to 0%. Is the approach is so convincing and consistent as the authors claimed? Is it proper to use an adjustment to improve the performance of an approach?
3. The research used the mixed strategy in which the factor loading of an item are set to be equal across groups, the factor variance of the reference group is fixed to be 1, and all parameters in the focal group are free for estimation. What are the potential disadvantages of the constraint?
4. The research used all other items method for the LR test in IRT. It seemed to be problematic.
5. As we know, there are several different DIF techniques in IRT or Non-IRT framework. The researcher selected LR test because they think LR test is commonly used in IRT and CFA. However, according to the result of the study, the LR test in MCCFA using the backward procedure is lfikely to an invalid conclusion for measurement invariance when large DIF is present with large sample size. Whether we can use other techniques that suitable in testing factorial invariance in CFA or detecting DIF in IRT?
Future study:
1. I think future study may explore using purification procedure , DIF-free-then-DIF strategy to incorporate MCCFA. For example, if I use the first constrain strategy for identification where one item as assigned as a reference variable. Can I use the purification procedure, DIF-free-then-DIF to find the clean item as the reference variable? If yes, what are the effectiveness?
2. To manipulate the DIF percent and test length in future study.
3. Using other DIF technique (e.g.,MIMIC) and evalute the performance.
4. To manipulate other factors affecting the measurement invariance (e.g., unique factor variance parameters, DIF source in thresholds) in future study.