Exploratory Graph Analysis Trees - A Network-based Approach to Investigate Measurement Invariance with Numerous Covariates

When comparing latent means across groups, measurement invariance (MI) needs to be established to ensure that the test results are valid and meaningful conclusions can be drawn. Common tests of MI are not suitable for many groups and cannot be used during the development of measurement models. In addition, popular network-based alternatives to latent variable modeling lack established methods for MI testing. Therefore, we propose Exploratory Graph Analysis Trees (EGA trees) that apply the idea of model-based recursive partitioning to correlation matrices and combine it with EGA - which can be used instead of exploratory factor analysis. In a simulation study, we test the approach regarding its ability to detect configural or metric non-invariance in common factor models given numerous covariates and illustrate its usefulness in conditions with severe violations of configural invaraince based on diverging numbers of factors. The results demonstrate that EGA trees can be a valuable tool for the exploration of MI when constructing scales and working on measurement models. We provide R functions within the R package EFAtree to easily implement EGA trees.