The Impact of Partial Measurement Invariance on Between-group Comparisons of Second-Order Factor Means

A simulation study was conducted to explore the influence of partial measurement invariance on the second-order factor mean difference estimation. The types, positions, numbers, and directions of between-group differences for noninvariant parameters were manipulated, along with sample size and effect size of the latent mean difference. 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 noninvariant parameters was consistent with the direction of the latent mean difference, and vice versa. The numbers, types, and positions of noninvariant parameters also had an influence on the estimation bias. Power to detect the latent mean difference was influenced by the corresponding estimation bias and estimated variance, in addition to sample size and effect size.