  Statistical models for networks with complex dependencies pose particular
challenges for model selection and evaluation. In particular, many
well-established 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 where a model performs poorly,
and by quantitatively comparing predictive performance across competing models.
The proposed method is applied to model selection problem of two well-known
data sets, and the results are compared to those obtained via nominal AIC and
BIC scores.
