Title: A Bootstrap Method for Goodness of Fit and Model Selection with a Single Observed Network,
Abstract: Network models are applied in numerous domains where data can be represented
as a system of interactions among pairs of actors. While both statistical and
mechanistic network models are increasingly capable of capturing various
dependencies amongst these actors, these dependencies imply the lack of
independence. This poses statistical challenges for analyzing such data,
especially when there is only a single observed network, and often leads to
intractable likelihoods regardless of the modeling paradigm, which limit 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
finer and higher dimensional comparisons than simply 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 procedure produces a flexible resampling distribution
that can be based on any statistics of one's choosing and can be employed
regardless of choice of model.