Metric Invariance in Exploratory Graph Analysis via Permutation Testing

Establishing measurement invariance (MI) is vital to ensure applicability and comparability across groups (or time points) in psychological measurement. If MI is violated, differences between groups could be due to measurement rather than true differences between groups. Factor analytic methods are commonly used to test MI; however, many existing methods have reduced power to detect MI due to model misspecification (e.g., noninvariant referent indicators, reliance on data-driven methods). Literature reviews on MI studies have reported inaccurate or inadequately described models with modeling errors primarily predicted by software choice. Another reduction in power may be due to goodness of fit measures when group sample sizes vary. Network psychometrics methods to test MI are limited and primarily focus on partial correlation differences. In the present research, we propose a novel network psychometrics method to test MI within the Exploratory Graph Analysis framework. This method leverages so-called network loadings by calculating their differences between groups and uses permutation testing to stasitically compare these differences to the permutated null distribution. A simulation study was conducted using data structures common in psychological research (factor models) that included unequal group sample sizes. The proposed network psychometrics method demonstrated comparable ability to factor analytic methods in detecting MI, with some improvement in certain conditions such as lower noninvariance effect sizes in smaller or unequal sample sizes.