Exponential Random Graph Models for Multi-level networks 2 : Case studies

Exponential random graph models (ERGMs) treat the network structure as endogenous and a topic of research interest (Frank and Strauss; Wasserman and Pattison, 1996; Snijders et al., 2006; Robins et al., 2007). The overall network structure is seen as a collective result of various local network processes. The local network processes are represented by graph configurations within which all presented ties are assumed to be conditionally dependent reflecting hypotheses that empirical network ties do not form by random, but that they self organize into various patterns reflecting underlying social processes. For multilevel networks where ties of different types or nature are defined on nodes within and across levels, ERGMs are capable of capturing the interdependencies among the micro-, macro- and meso-level networks, and provide richer and more detailed descriptions of the multilevel network structure. Depending on the context and the research question, the definition of the levels in a multilevel network can be determined by either the different nature of the nodes or the classifications of nodes by their attributes. We propose ERGMs for multilevel network structure, and illustrate the properties of the models using simulations. The models are then applied to a couple of empirical data sets to illustrate firstly, how multilevel ERGMs may be used to test network heterogeneity in a gender and friendship network context; secondly the importance of the multilevel effects in both goodness of fit and model selection using the collaboration network among French cancer research elites (Lazega, et al., 2006, 2008). We see the models and examples presented as the first steps in a full elaboration of an ERGM approach to multilevel network analysis