As we know, there is two approach in testing measurement invariance: IRT approach and Structural Equation Model approach. IRT approach adopts the probability function to model the differential item functioning while SEM approach uses a direct path from a grouping variable as covariate to each observed variable. Under SEM, both of multiple group confirmatory factor analysis (CFA) and multiple-indicators multiple-causes (MIMIC) modeling are often employed for measurement invariance testing. The parameters of IRT approach (specifically, the two-parameter logistic model) and SEM approach could be easily converted.
The purpose of the present study aims to investigate the performance of MIMIC when the assumption of equivalence of factor loading and intercepts over groups was violated. The simulation study includes both continuous and categorical variables under various conditions. It was found that the MIMIC model is not sensitive to the noninvariance of factor loadings. In addition, all model fit indices (CFI, RMSEA, SRMR, and WRMR) were sensitive to large DIF which were caused by the presence of noninvariance in intercepts/thresholds while the CFI and SRMR were not sensitive to small DIF. Finally, the likelihood ratio test of MIMIC with Oort adjustment outperform the Bonferroni method in controlling Type I error rate and maintaining power.
Future study:
When there is more than one noninvariant variables, both of the models (the baseline model and the augmented model with one DIF variable) in LR test are incorrectly specified, which may lead to deflated power. Thus, iterative LR test could be considered.