Random Graphs with Latent Spatial Structure

• Activity Number: 356
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Emily Casleton*+ and Mark Kaiser and Dan Nordman
• Companies: Iowa State University and Iowa State University and Iowa State University
• Keywords: network data ; Random Graph ; Spatial

Abstract

A variety of random graph generators and models have been developed. A number of these generators utilize physical locations of nodes to help determine the structure of a realized graph. These models incorporate geography that intuitively, but indirectly, affect the dependence structure. With respect to statistical modeling and analysis, Exponential Random Graph Models (ERGM) are the most popular. Through specification of a joint distribution, ERGMs induce a dependence structure. A limitation of ERGMs is that, although they allow for dependence, they fail to model or explain it directly. The method proposed here combines the concepts of geography and an explicit specification of a dependence structure. Geographic information is incorporated through a latent spatial structure which determines Markov neighborhoods for edges that dictate conditional dependencies. A binary Markov random field is then applied to the resulting configuration of edges. Under appropriate model restrictions, a joint distribution results from the conditional specification. This allows for explicit modeling and interpretation of the conditional dependence and independence between edges.