Stochastic Weighted Graphs: Flexible Model Specification and Simulation

33 Pages Posted: 15 Jun 2016

See all articles by James Wilson

James Wilson

University of San Francisco

Matthew Denny

Pennsylvania State University

Shankar Bhamidi

University of North Carolina (UNC) at Charlotte

Skyler J. Cranmer

Ohio State University (OSU) - Department of Political Science

Bruce A. Desmarais

Pennsylvania State University

Date Written: March 30, 2016

Abstract

In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The generalized exponential random graph model (GERGM) is a recently proposed method used to simulate and model the edges of a weighted graph. The GERGM specifies a joint distribution for an exponential family of graphs with continuous-valued edge weights. However, current estimation algorithms for the GERGM only allow inference on a restricted family of model specifications. To address this issue, we develop a Metropolis -- Hastings method that can be used to estimate any GERGM specification, thereby significantly extending the family of weighted graphs that can be modeled with the GERGM. We show that new flexible model specifications are capable of avoiding likelihood degeneracy and efficiently capturing network structure in applications where such models were not previously available. We demonstrate the utility of this new class of GERGMs through application to two real network data sets, and we further assess the effectiveness of our proposed methodology by simulating non-degenerate model specifications from the well-studied two-stars model. A working R version of the GERGM code is available in the supplement and will be incorporated in the gergm CRAN package.

Keywords: Exponential Random Graph, Generalized Exponential Random Graph, Markov Chain Monte Carlo, Metropolis-Hastings

JEL Classification: C15, C61, C63

Suggested Citation

Wilson, James and Denny, Matthew and Bhamidi, Shankar and Cranmer, Skyler J. and Desmarais, Bruce A., Stochastic Weighted Graphs: Flexible Model Specification and Simulation (March 30, 2016). Political Networks Workshops & Conference 2016. Available at SSRN: https://ssrn.com/abstract=2795219 or http://dx.doi.org/10.2139/ssrn.2795219

James Wilson (Contact Author)

University of San Francisco ( email )

2130 Fulton Street
San Francisco, CA 94117
United States

Matthew Denny

Pennsylvania State University ( email )

Shankar Bhamidi

University of North Carolina (UNC) at Charlotte ( email )

9201 University City Boulevard
Charlotte, NC 28223
United States

Skyler J. Cranmer

Ohio State University (OSU) - Department of Political Science ( email )

Columbus, OH 43210
United States

Bruce A. Desmarais

Pennsylvania State University ( email )

University Park, State College, PA 16801
United States

HOME PAGE: http://sites.psu.edu/desmaraisgroup

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