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.

abstract: A simulation study was conducted to explore the influence of partial loading invariance and partial intercept invariance on the latent mean comparison of the second-order factor within a higher-order confirmatory factor analysis (CFA) model. Noninvariant loadings or intercepts were generated to be at one of the two levels or both levels for a second-order CFA model. The numbers and directions of differences in noninvariant loadings or intercepts were also manipulated, along with total sample size and effect size of the second-order factor mean difference. Data were analyzed using correct and incorrect specifications of noninvariant loadings and intercepts. Results summarized across the 5,000 replications in each condition included Type I error rates and powers for the chi-square difference test and the Wald test of the second-order factor mean difference, estimation bias and efficiency for this latent mean difference, and means of the standardized root mean square residual (SRMR) and the root mean square error of approximation (RMSEA). When the model was correctly specified, no obvious estimation bias was observed; when the model was misspecified by constraining noninvariant loadings or intercepts to be equal, the latent mean difference was overestimated if the direction of the difference in loadings or intercepts of was consistent with the direction of the latent mean difference, and vice versa. Increasing the number of noninvariant loadings or intercepts resulted in larger estimation bias if these noninvariant loadings or intercepts were constrained to be equal. Power to detect the latent mean difference was influenced by estimation bias and the estimated variance of the difference in the second-order factor mean, in addition to sample size and effect size. Constraining more parameters to be equal between groups—even when unequal in the population—led to a decrease in the variance of the estimated latent mean difference, which increased power somewhat. Finally, RMSEA was very sensitive for detecting misspecification due to improper equality constraints in all conditions in the current scenario, including the nonzero latent mean difference, but SRMR did not increase as expected when noninvariant parameters were constrained. / Dissertation/Thesis / Masters Thesis Educational Psychology 2016