Multilevel Network Analysis Using ERGM and Its Extension

Abstract

Exponentials random graph models (ERGMs) model network structure as endogenous based on the assumption that network ties are conditionally dependent, i.e. the existence of a network tie depends on the existence of other network ties conditioning on the rest of the network. In multilevel network contexts, ERGMs offer a statistical framework that captures complicated multilevel structure through some simple structural signatures or network configurations based on these tie dependence assumptions, i.e. network ties are interdependent not only within levels but also across levels. The interpretations of ERGM parameters make hypothesis testing about multilevel network structure possible. In this chapter, we first review the multilevel network data structure and multilevel ERGM specifications. Then we will apply these models to a dataset collected among 265 farmers and their communication network in a rural community in Ethiopia, thus providing an interesting description of this farming community. The modelling example highlights the features of these models and their theoretical importance, i.e. within-level network structures are interdependent with network structures of other levels; and within level nodal attributes can affect multilevel network structures. For example, we extend the model specifications with two new configurations, the ``Alternating'' forms of cross-level three-paths and Four-cycles, and discus their possible interpretations.