For decades, there have been debates and discussion on measurement invariance. Mainstream discussions have been focused on MCCFA for many years. In recent years, IRT practitioners have joined the debate by introducing the idea of latent trait and its special relationship with raw item responses under various IRT model specifications. They particularly emphasized on the idea of differential item functioning. In this article, the author incorporates the ideas from both CFA and IRT to introduce category CFA (CCFA) which takes into account of thresholds between each response category to test measurement invariance of latent variables across subgroups of a population.
Further improvement based on the current study:
Besides the six-item test (where one item constrained to be biased and five invariant), some more test with more items (with different combination of the ratio of biased items and invariant items) should be considered. It helps inform about the effectiveness of the MCCFA.