The Invariance Partial Pruning Approach to The Network Comparison in Time-Series and Panel Data

Network models in time-series and panel data have been powerful tools to investigate the dynamical relations among variables. A common goal of empirical research is to compare the networks of different groups, such as treatment and control, to understand how the dynamical relations are shaped by grouping variables. However, existing methods for comparing n = 1 idiographic networks are restricted to global tests, which lack the capacity to 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 determine the exact locus of heterogeneity at the edge level with partial pruning. Through simulation studies, we discovered that network invariance test based on Akaike Information Criterion performed well. Bayesian Information Criterion performed similarly well but also showed insufficient power to detect smaller true differences at small sample sizes, and the Likelihood Ratio Test was prone to false discovery. Comparison with the fully constrained model revealed superior performance than comparison with the fully unconstrained model. Partial pruning successfully uncovered specific edge difference with high sensitivity and specificity. We conclude that IVPP is an essential supplement to the existing network methodology by allowing the comparison of networks from both time-series and panel data, and also allowing the test of specific edge difference. We implement the algorithm in the R-package IVPP.