The Effects of Parceling on Testing Group Differences in Second-Order CFA Models: A Comparison between Multi-Group CFA and MIMIC Models

Using multi-group confirmatory factor analysis (MCFA) and multiple-indicator-multiple-cause (MIMIC) to investigate group difference in the context of the second-order factor model with either the unparceled or parceled data had never been thoroughly examined. The present study investigated (1) the difference of MCFA and MIMIC in terms of Type I error rate and power when testing the mean difference of the higher-order latent factor (delta kappa) in a second-order confirmatory factor analysis (CFA) model; and (2) the impact of data parceling on the test of (delta kappa) between groups by using the two approaches. The methods were introduced, including the design of the models, the design of Monte Carlo simulation, the calculation of empirical Type I Error and empirical power, the two parceling strategies, and the adjustment of the random error variance.The results suggested that MCFA should be favored when the compared groups were when the different group sizes were paired with the different generalized variances, and MIMIC should be favored when the groups were balanced (i.e., have equal group sizes) in social science and education disciplines. This study also provided the evidence that parceling could improve the power for both MCFA and MIMIC when the factor loadings were low without bringing bias into the solution when the first-order factors were collapsed. However, parceling strategies might not be necessary when the factor loadings were high. The results also indicated that the two approaches were equally favored when domain representative parceling strategy was applied.