The invariance partial pruning approach to the network comparison in time-series and panel data

Network models in time-series and panel data are powerful tools to investigate the dynamical relations among variables. Empirical research often seeks to compare network structures across groups/individuals to understand how element-wise associations respond differently to treatments, providing a framework to explain individual heterogeneity in treatment response and the relative efficacy of different intervention approaches. However, existing methods for comparing n = 1 idiographic networks are restricted to global tests, which cannot identify the precise location of edge heterogeneity. Furthermore, there is a lack of easily applicable methods to compare networks from panel data where just a few time points are available per person. We therefore present the invariance partial pruning (IVPP) approach, which first evaluates heterogeneity globally with the network invariance test and then determines the exact locus of heterogeneity at the edge level with partial pruning. Through simulations, we discovered that the network invariance test based on Akaike Information Criterion and Bayesian Information Criterion performed well. However, at small sample sizes, Akaike Information Criterion showed inflated false positive rates and Bayesian Information Criterion showed insufficient power to detect smaller true differences. The likelihood ratio test was prone to false discovery. Comparison with the fully constrained model revealed superior performance to the fully unconstrained model. Partial pruning successfully uncovered specific edge differences with desirable sensitivity and specificity. We conclude that IVPP is an essential supplemental to existing network methodology, enabling the comparison of networks from both time-series and panel data and testing specific edge differences. We implement the algorithm in the R package IVPP. (PsycInfo Database Record (c) 2026 APA, all rights reserved).