Local Dependence in Random Graph Models: Characterization, Properties, and Statistical Inference

• Activity Number: 181
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Michael Schweinberger*+ and Mark S. Handcock
• Companies: Rice University and University of California, Los Angeles
• Keywords: social networks ; weak dependence ; local dependence ; M-dependence ; model degeneracy ; exponential families

Abstract

Dependent phenomena, such as relational, spatial, and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-de?ned sense are dependent. In contrast to spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighborhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential-family random graph models induce strong dependence and are not amenable to statistical inference. We take ?rst steps to characterize local dependence in random graph models, inspired by the notion of ?nite neighborhoods in spatial statistics and M-dependence in time series, and show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighborhood structure. In the absence of observed neighborhood structure, we take a Bayesian view and express the uncertainty a