Section IV Future

Modeling Social Networks: Next Steps

Pip Pattison and Tom Snijders

In this final chapter, we review the progress made in modeling social networks using exponential random graph models (ERGMs) and identify some important questions that remain to be addressed, along with possible ways of approaching them. We also consider the development of ERGMs in the context of broader modeling developments for social networks.

Distinctive Features of ERGMs

As the preceding chapters demonstrate, ERGMs offer four features that are likely to be attractive to social scientists who are interested in deepening our understanding of social networks and the social processes associated with them.

First, and perhaps most important, ERGMs conceptualize social networks as the outcome of social processes that are dynamic, interactive, and local. They are therefore well aligned with many contemporary theoretical views about the evolution of social networks (e.g., Emirbayer, 1997), even though there are a variety of distinct views about the precise social mechanisms involved (e.g., Jackson, 2008; Pattison, Robins, & Kashima, 2008; Rivera, Soderstrom, & Uzzi, 2010; Snijders, 2006). ERGMs give expression to propositions about the outcomes of the dynamic, interactive, local processes that drive network formation and allow us to quantify and assess the observable regularities in social network structure implied by these propositions. Moreover, these assessments are set within a clear statistical framework. Even though there may not necessarily be a fine-grained match between hypothesized theoretical mechanisms and the form of an ERGM, or the means to explore model assumptions in detail (as we discuss later in the chapter), ERGMs nonetheless provide a valuable new capacity to demonstrate potential links between hypothesized network processes and observable network regularities. In brief, they provide social scientists with access to a statistical approach for exploring regularities in social networks and describing these regularities with greater precision.

The second major feature of ERGMs relative to alternative approaches for modeling social networks is a new capacity for models to reproduce many important observed network characteristics, including global network features that are not parameterized as effects in the model. This advantage has now been demonstrated on a number of occasions and provides some confidence that the approach that ERGMs afford to the specification of local dependencies is an effective one (Hunter & Hand- cock, 2006; Robins et al., 2007; Robins, Pattison, & Wang, 2009; Sni- jders et al., 2006). This is a particularly noteworthy feature of this class of models, and it supports the assumption of endogeneity in tie formation processes. Indeed, it is often impressive that models can reproduce a variety of characteristics of observed features of a network with a relatively small number of explicitly parameterized network effects in the model; Goodreau (2007), for example, provides an excellent illustration. The nature and extent of local clustering among nodes, the general distribution of node-to-node connectivity, and variations in local connectivity of each network node, are among the aspects of network structure that can often be satisfactorily reproduced (Hunter, 2007; Hunter & Handcock, 2006; Snijders et al., 2006).

Third, ERGMs can be applied in flexible ways to many different types of network or relational data. They have been developed for directed and nondirected networks and for bipartite and multirelational networks (Robins, Pattison, & Wang, 2009; Wang, Sharpe, Robins, & Pattison, 2009; see also Chapters 6, 10, 16, 20, and 21). In each case, a flexible approach can be adopted to building plausible model specification that rely on natural underlying graph-theoretical local dependencies, as explained further later in this chapter. More generally, ERGMs can be developed for relational observations among multiple types of nodes and multiple types of ties. It is straightforward to add a variety of node-level and dyadic covariates, including spatial and other relational covariates (e.g., Daraganova et al., 2012; Robins, Elliott, & Pattison, 2001; see Chapter 8). Furthermore, the general framework used to construct models for relational data can also be used to construct models for node-level characteristics in mutual dependence with network ties (Robins, Pattison, & Elliott, 2001). Chapters 9 and 18 illustrate application of this general approach to these various types of relational data.

Fourth, because ERGMs can be understood as the outcome of dynamic, interactive, local processes that drive network formation, it is possible to assess these processes more directly when longitudinal observations are available. As Chapters 11 and 19 illustrate, these ERGM-like models provide a more direct approach to understanding tie formation processes and are a valuable complement to the less direct approach for crosssectional data. This approach is the tie-oriented analogue of the actor- oriented models for longitudinal network data of Snijders (2001) and Snijders, van de Bunt, and Steglich (2010). Through the increased application of models to longitudinal observations, we stand to learn a great deal about the applicability and robustness of the stronger assumptions we make in cross-sectional applications.

Of course, it would be wrong to give the impression that we have reached the point where ERGM model fitting and model comparison are straightforward. Rather, it is not always easy to choose and fit an appropriate set of competing model specifications given some relevant data, nor can we necessarily make straightforward choices in selecting a preferred model. A number of important modeling challenges remain, and we consider several of these in this chapter. We first address the important topic of model specification, and then more general issues of model evaluation and comparison.

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