Tractable and Consistent Random Graph Models
Stanford University - Department of Economics
Matthew O. Jackson
Stanford University - Department of Economics; Santa Fe Institute; Canadian Institute for Advanced Research (CIFAR)
September 21, 2012
We define a general class of network formation models, Statistical Exponential Random Graph Models (SERGMs), that nest standard exponential random graph models (ERGMs) as a special case. We analyze conditions for practical and consistent estimation of the associated network formation parameters, addressing two open issues in the estimation of exponential random graph models. First, there are no previous general results on whether estimates of such a model's parameters based a single network are consistent (i.e., become accurate as the number of nodes grows). Second, a recent literature has shown that standard techniques of estimating ERGMs have exponentially slow mixing times for many specifications in which case the software used for estimating these models will be unreliable. SERGMs reformulate network formation as a distribution over the space of sufficient statistics instead of the space of networks, greatly reducing the size of the space of estimation and making estimation practical and easy. We identify general classes of models for which maximum likelihood estimates are consistent and asymptotically normally distributed. We also develop a related, but distinct, class of models that we call subgraph generation models (SUGMs) that are useful for modeling sparse networks and whose parameter estimates are also consistent and asymptotically normally distributed. We show how choice-based (strategic) network formation models can be written as SERGMs and SUGMs, and illustrate the application of our models and techniques with network data from villages in Karnataka, India.
Number of Pages in PDF File: 72
Keywords: Random Networks, Random Graphs, Exponential Random Graph Models, Exponential Family, Social Networks, Network Formation, Consistency
JEL Classification: D85, C51, C01, Z13working papers series
Date posted: October 25, 2012 ; Last revised: September 11, 2013
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