Impact of error structure misspecification when testing measurement invariance and latent-factor mean difference using MIMIC and multiple-group confirmatory factor analysis

When multiple groups are compared, the error variance-covariance structure is not always invariant between groups. In this study we investigated the impacts of misspecified error structures on testing measurement invariance and the latent-factor mean difference between groups. A Monte Carlo study was conducted to examine how measurement invariance and latent mean difference tests were affected when heterogeneous error structures were misspecified as being invariant across groups. Multiple-group confirmatory factor analysis (MGCFA) and the multiple-indicator multiple-causes model (MIMIC) were employed in the present study. The rejection rates of both metric and strict invariance in measurement invariance testing, as well as the estimation accuracy and statistical inference of the factor mean difference, were investigated under error structure misspecification. In addition, sensitivity of the model fit indices to error structure misspecification was examined. Overall, misspecification of the error structure affected testing for metric but not scalar invariance. Metric invariance was often rejected, especially when error covariance in one group was ignored. In contrast, MGCFA and MIMIC performed comparatively well at detecting latent-factor mean differences between groups, with acceptable power and well-controlled Type I errors. The practical implications of these findings are discussed, as well as recommendations.