Local Structure Graph Models

• Activity Number: 670
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Emily Casleton*+ and Mark Kaiser and Dan Nordman
• Companies: Iowa State University and Iowa State University and Iowa State University
• Keywords: Network Analysis ; Spatial dependence ; Conditional model specification ; Graph

Abstract

Network or random graph analysis has been applied to problems in a variety of fields, such as biology, statistical physics, and social science, due to a network's ability to represent complex patterns of connections and dependencies. The Local Structure Graph Model (LGSM), a new model for representing and analyzing networks, is proposed. Each possible edge in the graph is denoted by a binary random variable, and the LSGM specifies a local conditional distribution for each graph edge. This modeling approach, along with a Markov dependence assumption, induces a global or joint distribution on the entire graph while permitting explicit and interpretable control of local dependence in the graph through neighborhood structures and centered parameterizations of the natural parameter function. The LSGM approach leads to a consistent interpretation of parameters across varying amounts of statistical dependence, which is especially important when incorporating node or edge attributes and aides in identifying areas of the parameter space where the model becomes degenerate. Features of the model will be demonstrated through simulation and compared with existing models for network analysis.