Selection of Exponential-Family Random Graph Models via Held-Out Predictive Evaluation (HOPE)

Abstract

Statistical models for networks with complex dependencies pose particular challenges for model selection and evaluation. In particular, many wellestablished statistical tools for selecting between models assume conditional independence of observations and/or conventional asymptotics, and their theoretical foundations are not always applicable in a network modeling context. While simulation-based approaches to model adequacy assessment are now widely used, there remains a need for procedures that quantify a model's performance in a manner suitable for selecting among competing models. Here, we propose to address this issue by developing a predictive evaluation strategy for exponential family random graph models that is analogous to cross-validation. Our approach builds on the held-out predictive evaluation (HOPE) scheme introduced by Wang et al. (2016) to assess imputation performance. We systematically hold out parts of the observed network to: evaluate how well the model is able to predict the held-out data; identify where the model performs poorly based on which data are held-out, indicating e.g. potential weaknesses; and calculate general summaries of predictive performance that can be used for model selection. As such, HOPE can assist researchers in improving models by indicating

A Stein Goodness of fit Test for Exponential Random Graph Models

“…To assess the performance of the test, we replicate the synthetic benchmark-type settings from [Lusher et al, 2013;Rolls et al, 2015;Yang et al, 2018]. We then apply our tests to three real data networks: Lazega's lawyer network [Lazega, 2001] and a friendship network [Steglich et al, 2006] which are both studied in [Yin et al, 2019], as well as a co-sponsorship network from [Fowler, 2006a,b].…”