Comparing Networks of Different Sizes: An Extension of the HERGM

• Activity Number: 263
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Anna Mohr* and Catherine Calder and Christopher Browning
• Companies: The Ohio State University and The Ohio State University and The Ohio State University
• Keywords: Bayesian modeling ; Network analysis ; Social sciences

Abstract

Networks have become ubiquitous as a tool for analysis in many areas of applied research - one area in need of further statistical development is network comparison. Often the networks under consideration consist of differing numbers of nodes, and the comparison of statistics or other measures of interest across these networks is not straightforward. We demonstrate via simulation why direct comparison is often inappropriate. We argue that a more appropriate method of comparison would both adjust for network size as well as incorporate network dependence structure. Pulling from the vast literature on network modeling, we turn to the Hierarchical ERGM (Schweinberger & Handcock 2015), which consists of two dependence regimes: strong local dependence within network subgraphs (neighborhoods) and a weaker global dependence structure. We extend the HERGM to accommodate multiple networks by suggesting a relationship between network size and the size of the strong-dependence-neighborhoods within that network. We briefly outline the theory and demonstrate how this network comparison method allows for the detection of significant differences across a set of networks.