Testing similarity in longitudinal networks: The Individual Network Invariance Test (INIT)

The comparison of idiographic network structures in order to determine the presence of heterogeneity is a challenging endeavor in many applied settings. Previously, researchers eyeballed idiographic networks, computed correlations between idiographic networks, as well as used techniques that make use of the multilevel structure of the data (e.g., GIMME and mlVAR) to investigate individual differences. However, these methods do not allow for testing the equality of idiographic network structures directly. In this paper, we propose the Individual Network Invariance Test (INIT). INIT extends common model comparison practices in Structural Equation Modeling (SEM) to idiographic network structures to test for (in)equality between idiographic network structures. 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 of model selection criteria such as the AIC and BIC. Results show INIT performs adequately when 100 or more data points are available per individual. When applying INIT on saturated networks, AIC performed best as a model selection criteria, while 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.