With a threshold structure, MCCFA can be used to test measurement invariance of ordered-categorical measures. This paper introduced the framework of MCCFA, and then compared the performance of MCCFA and IRT in testing the measurement invariance.
Procedure:
Item: 6 * dichotomous/polytomous (5 points)
Sample size: 100/ 200/ 500/ 1000 (equal sample size)
DIF: item 5; a) factor loading, .2/ .4 decrease in focal group; b) threshold, .3/ .6 increase in focal group; c) change both factor loading and thresholds.
Common factor: a) reference group, mean 0.0, variance 1.0; b) focal group, mean 0.5, variance 1.3.
Data analysis: LR tests, backward procedure, baseline model with all factor loading set to be equal across groups, factor variance of the first group set at 1.
Criterion: true positive (power) and false positive (Type I error) were compared for the MCCFA and IRT approaches.
Results:
True/ False Positive: In general, IRT approach performed well under various conditions. Type I error inflated with MCCFA when sample size and degree of DIF increased. After using the Oort method to correct the chi-square critical value, performance of MCCFA improved substantially.
Model fit index: chi-square goodness-of-fit statistic, RMSEA, and WRMR are all appropriate indicators for MCCFA.
Question: MCCFA and IRT approaches are useful for what kind of practical conditions? What are the essential differences between these two approaches?
Further: more complicate conditions for DIF items, like change the number of items, percentage of DIF items.