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Statistical Inference for Valued-Edge Networks: Generalized Exponential Random Graph Models

Bruce A. Desmarais, Skyler J. Cranmer

arXiv:1103.4615v1physics.data-anstat.ME

TL;DR

ERGMs are defined only for binary ties, while many networks have valued edges; continuous or infinite support also complicates ensuring a proper probability distribution. GERGMs specify dependence on a restricted network X, then transform X onto the support of Y, with network statistics representing dependence features. For the data, Wald statistic = 119.19 on 5 degrees of freedom was statistically significant at the 0.001 level, indicating GERGM fits better than a Cauchy GLM.

  • Problem

    ERGMs are defined only for binary ties, while many networks have valued edges; continuous or infinite support also complicates ensuring a proper probability distribution.

    Source: p. 1

  • Method

    GERGMs specify dependence on a restricted network X, then transform X onto the support of Y, with network statistics representing dependence features.

    Source: p. 1

  • Results

    For the data, Wald statistic = 119.19 on 5 degrees of freedom was statistically significant at the 0.001 level, indicating GERGM fits better than a Cauchy GLM.

    Source: p. 4

  • Takeaways & Limitations

    The model retains flexible network statistics while providing a proper probability distribution for networks with continuous edges.

    Source: p. 1

    The denominator integral is typically intractable, making estimation of θ and Λ nontrivial.

    Source: p. 2

Abstract

from arXiv · show

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a ubiquitous means of analysis. However, they are limited by an inability to model networks with valued edges. We solve this problem by introducing a class of generalized exponential random graph models capable of modeling networks whose edges are valued, thus greatly expanding the scope of networks applied researchers can subject to statistical analysis.

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