A Bootstrap Method for Goodness of Fit and Model Selection with a Single Observed Network.

Network models are applied in numerous domains where data arise from systems of interactions among pairs of actors. Both statistical and mechanistic network models are increasingly capable of capturing various dependencies among these actors. Yet, these dependencies pose statistical challenges for analyzing such data, especially when the data set comprises only a single observation of one network, often leading to intractable likelihoods regardless of the modeling paradigm and limiting the application of existing statistical methods for networks. We explore a subsampling bootstrap procedure to serve as the basis for goodness of fit and model selection with a single observed network that circumvents the intractability of such likelihoods. Our approach is based on flexible resampling distributions formed from the single observed network, allowing for more nuanced and higher dimensional comparisons than point estimates of quantities of interest. We include worked examples for model selection, with simulation, and assessment of goodness of fit, with duplication-divergence model fits for yeast (S.cerevisiae) protein-protein interaction data from the literature. The proposed approach produces a flexible resampling distribution that can be based on any network statistics of one's choosing and can be employed for both statistical and mechanistic network models.