Measurement invariance (MI) is an important assumption underlying meaningful comparisons of observed scores across groups. However, when data are unbalanced (e.g., groups vary considerably in sample size), the statistical power of commonly used fit indices and test statistics for testing MI can be severely compromised. Although several resampling methods have been proposed to address this issue, they are often computationally intensive and their relative performance has not been systematically evaluated. In addition, these studies have primarily focused on the role of measurement invariance in supporting cross-group mean comparisons, with less attention to its implications for subsequent structural analyses within groups. This raises a broader question of how measurement invariance constraints may benefit downstream inference beyond cross-group comparisons.

Therefore, in this talk, I will first present two recent projects that address the challenges of evaluating measurement invariance under unbalanced data conditions, focusing on full and partial invariance testing. Specifically, I will present simulation evidence supporting the use of multivariate Wald tests for evaluating full invariance assumptions and regularization estimators for identifying partial invariance models in unbalanced data.

After that, I will extend this framework to a third project showing that correctly specified invariance constraints can be leveraged to improve subsequent analyses. In brief, our results indicate that, in addition to supporting valid cross-group comparisons, measurement invariance constraints can increase statistical power and reduce the negative effects of missing data on structural parameter estimation within smaller groups. Together, these findings provide insights into both the evaluation of measurement invariance and the potential benefits of leveraging invariance constraints in unbalanced data settings.

About Po-Yi Chen

My methodological work focuses on measurement invariance (MI) testing and challenges arising from suboptimal data conditions in structural equation modeling (SEM). A major line of my research examines how to properly examine MI in the presence of unbalanced and missing data. Much of this work evaluates the impact of such data conditions on traditional MI testing procedures and identifies more robust alternative approaches. More recently, this research has extended to examining how to leverage established cross-group invariance constraints to improve and stabilize structural parameter estimation within smaller-sample groups under unbalanced data conditions.