Existence of maximum likelihood estimates in exponential random graph models

04/10/2022

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by   Henry Bayly, et al.

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We present a streamlined proof of the foundational result in the theory of exponential random graph models (ERGMs) that the maximum likelihood estimate exists if and only if the target statistic lies in the relative interior of the convex hull of the set of realizable statistics. We also discuss how linear dependence or "approximate linear dependence" of network statistics may lead to degeneracy during model fitting.