Testing goodness of fit of a model for network data is a difficult problem that has received some attention recently from the statistical community. We will overview this problem from the point of view of contingency tables and exact testing, and illustrate it on a few examples.
The contingency table point of view follows late Stephen Fienberg’s vision, and the developments highlight his affinity for contingency table problems and reinterpreting models with a fresh look, which gave rise to a new approach for hypothesis testing of network models that are linear exponential families. The family of the so-called log-linear exponential random graph models turns out to be surprisingly broad and includes many popular models, such as degree-based, stochastic blockmodels, and combinations of these.
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