We thank Emmanuel Lazega for permission to use data collected by him. A portion of this paper was written in part while the first author was an honorary senior fellow at the University of Melbourne.
NEW SPECIFICATIONS FOR EXPONENTIAL RANDOM GRAPH MODELS
Article first published online: 9 NOV 2006
Volume 36, Issue 1, pages 99–153, December 2006
How to Cite
Snijders, T. A. B., Pattison, P. E., Robins, G. L. and Handcock, M. S. (2006), NEW SPECIFICATIONS FOR EXPONENTIAL RANDOM GRAPH MODELS. Sociological Methodology, 36: 99–153. doi: 10.1111/j.1467-9531.2006.00176.x
- Issue published online: 17 NOV 2006
- Article first published online: 9 NOV 2006
The most promising class of statistical models for expressing structural properties of social networks observed at one moment in time is the class of exponential random graph models (ERGMs), also known as p* models. The strong point of these models is that they can represent a variety of structural tendencies, such as transitivity, that define complicated dependence patterns not easily modeled by more basic probability models. Recently, Markov chain Monte Carlo (MCMC) algorithms have been developed that produce approximate maximum likelihood estimators. Applying these models in their traditional specification to observed network data often has led to problems, however, which can be traced back to the fact that important parts of the parameter space correspond to nearly degenerate distributions, which may lead to convergence problems of estimation algorithms, and a poor fit to empirical data.
This paper proposes new specifications of exponential random graph models. These specifications represent structural properties such as transitivity and heterogeneity of degrees by more complicated graph statistics than the traditional star and triangle counts. Three kinds of statistics are proposed: geometrically weighted degree distributions, alternating k-triangles, and alternating independent two-paths. Examples are presented both of modeling graphs and digraphs, in which the new specifications lead to much better results than the earlier existing specifications of the ERGM. It is concluded that the new specifications increase the range and applicability of the ERGM as a tool for the statistical analysis of social networks.