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Exponential-Family Random Graph Models for Valued Networks

Abstract

Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through choice of model terms (sufficient statistics). However, those ERGMs modeling the more complex features have, to date, been limited to binary data: presence or absence of ties. Thus, analysis of valued networks, such as those where counts, measurements, or ranks are observed, has necessitated dichotomizing them, losing information. In this work, we generalize ERGMs to valued networks. Using the concept of reference measures, we describe a rigorous yet intuitive framework that retains many of the inferential and interpretability properties of the binary case, and discuss additional issues and caveats that emerge. Focusing on modeling counts, we introduce terms that generalize and model common social network features for count data, while avoiding degeneracy. We apply these methods on a commonly analyzed dataset whose values are counts of interactions.

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