Testing similarity in longitudinal networks: The Individual Network Invariance Test

The comparison of idiographic network structures to determine the presence of heterogeneity is a challenging endeavor in many applied settings. Previously, researchers eyeballed idiographic networks, computed correlations, and used techniques that make use of the multilevel structure of the data (e.g., group iterative multiple model estimation and multilevel vector autoregressive) to investigate individual differences. However, these methods do not allow for testing the (in)equality of idiographic network structures directly. In this article, we propose the Individual Network Invariance Test (INIT), which we implemented in the R package INIT. INIT extends common model comparison practices in structural equation modeling to idiographic network structures to test for (in)equality between idiographic networks. In a simulation study, we evaluated the performance of INIT on both saturated and pruned idiographic network structures by inspecting the rejection rate of the χ² difference test and model selection criteria, such as the Akaike information criterion (AIC) and Bayesian information criterion (BIC). Results show INIT performs adequately when t = 100 per individual. When applying INIT on saturated networks, the AIC performed best as a model selection criterion, while the BIC showed better results when applying INIT on pruned networks. In an empirical example, we highlight the possibilities of this new technique, illustrating how INIT provides researchers with a means of testing for (in)equality between idiographic network structures and within idiographic network structures over time. To conclude, recommendations for empirical researchers are provided. (PsycInfo Database Record (c) 2025 APA, all rights reserved).