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 and introducing biases. In this work, we generalize ERGMs to valued networks. Focusing on modeling counts, we formulate an ERGM for networks whose ties are counts and discuss issues that arise when moving beyond the binary case. We introduce model terms that generalize and model common social network features for such data and apply these methods to a network dataset whose values are counts of interactions.
Highlights
Networks are used to represent and analyze phenomena ranging from sexual partnerships (Morris and Kretzschmar, 1997), to advice giving in an office (Lazega and Pattison, 1999), to friendship relations (Goodreau, Kitts and Morris, 2008; Newcomb, 1961), to international relations (Ward and Hoff, 2007), to scientific collaboration, and many other domains (Goldenberg et al, 2009)
We formulate an Exponential-family random graph models (ERGMs) for networks whose ties are counts and discuss issues that arise when moving beyond the binary case
In sexual partnership networks, some ties are short-term while others are longterm or marital; friendships and acquaintance have degrees of strength, as do international relations; and while a particular individual seeking advice might seek it from some coworkers but not others, he or she will likely do it in some specific order and weight advice of some more than others
Summary
Networks are used to represent and analyze phenomena ranging from sexual partnerships (Morris and Kretzschmar, 1997), to advice giving in an office (Lazega and Pattison, 1999), to friendship relations (Goodreau, Kitts and Morris, 2008; Newcomb, 1961), to international relations (Ward and Hoff, 2007), to scientific collaboration, and many other domains (Goldenberg et al, 2009). Observing messages (Freeman and Freeman, 1980; Diesner and Carley, 2005), instances of personal interaction (Bernard, Killworth and Sailer, 1979–1980), or counting co-occurrences or common features of social actors (Zachary, 1977; Batagelj and Mrvar, 2006) produce relations in the form of counts Measurements, such as duration of interaction (Wyatt, Choudhury and Bilmes, 2009) or volume of trade (Westveld and Hoff, 2011) produce relations in the form of (effectively) continuous values. A major limitation of ERGMs to date has been that they have been applied almost exclusively to binary relations: a relationship between a given actor i and a given actor j is either present or absent This is a serious limitation: valued network data have to be dichotomized for ERGM analysis, an approach which loses information and may introduce biases.
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