A Stein Goodness of fit Test for Exponential Random Graph Models
This addresses a specific statistical challenge for network analysts, representing an incremental improvement in ERGM testing methodology.
The authors tackled the problem of assessing goodness of fit for exponential random graph models (ERGMs) with a single network observation by proposing a nonparametric test based on kernel Stein discrepancy, showing theoretical properties and applications in simulations and real networks.
We propose and analyse a novel nonparametric goodness of fit testing procedure for exchangeable exponential random graph models (ERGMs) when a single network realisation is observed. The test determines how likely it is that the observation is generated from a target unnormalised ERGM density. Our test statistics are derived from a kernel Stein discrepancy, a divergence constructed via Steins method using functions in a reproducing kernel Hilbert space, combined with a discrete Stein operator for ERGMs. The test is a Monte Carlo test based on simulated networks from the target ERGM. We show theoretical properties for the testing procedure for a class of ERGMs. Simulation studies and real network applications are presented.