Geometric View of Goodness-of-Fit Tests for Network Models

We study networks from a point of view of exponential random graph models. This flexible and versatile statistical family comes equipped with tools to perform inferential statistics, however the standard toolbox assumes large sample sizes and the use of asymptotic theory. In networks, this assumption is not met, as we only observe a sample of size 1. Moreover, due to their complex nature, model specification is challenging, and many networks exhibit poor model fit.

This motivates the study of exact goodness of fit tests. We explore the inner workings of linear exponential families which allows us to develop a geometric interpretation of exact goodness of fit tests. Specifically, we develop a new framework for carrying out goodness-of-fit tests for linear network models. The proposed methodology can be used for any linear discrete model with finite support, as long as the sufficient statistic is not one-dimensional. We discuss the specifics of the exact conditional test: choice of a test statistic and sampling methods for obtaining its empirical distribution. We showcase the performance of the test on two models: the latent-variable stochastic blockmodel, and the degeneracy-restricted beta model.

Event Topic

Nonlinear Algebra and Statistics (NLASTATS)