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Outliers and Influential Observations in Exponential Random Graph Models.

Johan Koskinen1,2,3, Peng Wang4, Garry Robins5

  • 1The Mitchell Centre for Social Network Analysis and the Department of Social Statistics, School of Social Sciences, University of Manchester, Manchester,  M139PL, UK. johan.koskinen@manchester.ac.uk.

Psychometrika
|September 20, 2018
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Summary
This summary is machine-generated.

This study introduces new methods for detecting influential nodes in social network models. These methods help identify actors whose network behavior deviates significantly from the norm.

Keywords:
case deletionexponential random graph modelsleveragemissing data principleoutliersstatistical analysis of social networks

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Area of Science:

  • Social Network Analysis
  • Statistical Modeling
  • Network Science

Background:

  • Exponential family random graph (ERG) models are widely used for social network analysis.
  • Identifying influential nodes and outliers is crucial for understanding network structure and dynamics.
  • Existing methods for outlier detection in ERG models can be computationally intensive.

Purpose of the Study:

  • To develop and validate novel measures for detecting influential nodes in ERG models.
  • To propose computationally efficient methods that do not require model refitting.
  • To provide tools for routine application within ERGM fitting procedures.

Main Methods:

  • Focus on node-level influence within ERG models.
  • Utilize case-deletion strategies (unobserved tie-variables or induced subgraphs).
  • Employ information theory and parameter estimation differences for influence quantification.
  • Develop MCMC p-values for assessing node extremity.

Main Results:

  • Several influence measures are proposed, with two identified for routine application.
  • The proposed measures effectively identify nodes with distinctive network structural roles.
  • Application to real-world datasets demonstrates the utility of the influence measures.

Conclusions:

  • The developed influence measures offer a computationally feasible approach to identifying distinctive actors in social networks.
  • These methods enhance the interpretability of ERG models by highlighting nodes that deviate from structural norms.
  • The findings contribute to a deeper understanding of network structure and individual actor influence.