10 - Exponential Random Graph Model Extensions: Models for Multiple Networks and Bipartite Networks

Summary

In previous chapters, we presented details of models for univariate one-mode network data. Exponential random graph models (ERGMs), however, can also be applied to other relational data types. In this chapter, we extend ERGM specifications to (1) multivariate analysis of two networks and (2) bipartite (or two-mode) networks. We discuss model specifications and possible parameter interpretations for both classes of models.

Multiple Networks

Social network analyses are not limited to one type of network, and it is often the case that more than one type of relational tie can be defined among a given set of nodes – for example, we can define both friendship and advice-giving ties among staff of an organization. When we have multiple network ties, we can then ask the research question about how different types of networks interact with each other, and how these interactions affect the structure of each network. For example, do friends seek advice from each other in the organization? We refer to the statistical analysis of multiple networks as “multivariate network analysis.”

Several techniques have been developed for the analysis of multiple networks, including blockmodels for multiple networks (White, Boorman, & Breiger, 1976), quadratic assignment procedures (Dekker, Krackhardt, & Snijders, 2007; Krackhardt, 1987), network algebraic models (Pattison, 1993), and ERGMs (Pattison & Wasserman, 1999). In this chapter, we focus on the simplest multivariate ERGM specifications for networks involving two types of ties defined on a common set of nodes.