Main idea:
This study introduced multiple-group categorical confirmatory factor analysis (MCCFA) and item response theory (IRT) used to test measurement invariance. Because classic CFA which assumes that observed variables are continuous and normally distributed is not an optimal analysis for ordered-categorical data , the MCCFA was used to compare to the differential item functioning (DIF) analysis under IRT. MCCFA can appropriately model the ordered-categorical measures with a threshold structure which is comparable to difficulty parameters in IRT. The IRT LR test was used in detecting measurement bias. The performance of chi-square goodness of fit, root mean square error of approximation (RMSEA), and weighted root mean square residual (WRMR) of the partially invariant model were examined in detecting DIF.
The 48 different scenarios were created for the comparison of MCCFA and IRT with respect to the power to detect the lack of invariance across groups. The Mplus 5.2 and the IRTLRDIF programs were used to estimate the parameter.
The result shows when the magnitude of DIF was large and the source of DIF was at least a threshold or more, the two tools demonstrated desirable power in detecting non-invariant items. When considering both TP and FP rates, IRT performed better than MCCFA. Both MCCFA and IRT methods worked better for the polytomous cases than the dichotomous data conditions.
Comments:
1 To compare the MCCFA with the differential item functioning (DIF) analysis under IRT is very new field to me. Though first contact MCCFA, I am attracted by this method for it is really useful especial for the liket scales. For usually when using CFA, we just consider the liket scales to be continuous. However it is not proper in practice.
2 The simulation only contains 6 items. The impact of different number of items on the result is not considered.
3 The third sentence of paragraph 1 on page 215, it seems like the variable Xij should be added on a star.