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Outliers and Influential Observations in Exponential Random Graph Models

Published online by Cambridge University Press:  01 January 2025

Johan KoskinenOpen the ORCID record for Johan Koskinen[Opens in a new window],
Peng Wang,
Garry Robins and
Philippa Pattison
Johan Koskinen*
Affiliation:
University of ManchesterThe University of MelbourneUniversity of Linköping
Peng Wang
Affiliation:
Swinburne University of Technology
Garry Robins
Affiliation:
The University of Melbourne
Philippa Pattison
Affiliation:
The University of Sydney
*
Correspondence should be made to Johan Koskinen, The Mitchell Centre for Social Network Analysis and the Department of Social Statistics, School of Social Sciences, University of Manchester, Manchester M139PL, UK. Email: johan.koskinen@manchester.ac.uk
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Abstract

We discuss measuring and detecting influential observations and outliers in the context of exponential family random graph (ERG) models for social networks. We focus on the level of the nodes of the network and consider those nodes whose removal would result in changes to the model as extreme or “central” with respect to the structural features that “matter”. We construe removal in terms of two case-deletion strategies: the tie-variables of an actor are assumed to be unobserved, or the node is removed resulting in the induced subgraph. We define the difference in inferred model resulting from case deletion from the perspective of information theory and difference in estimates, in both the natural and mean-value parameterisation, representing varying degrees of approximation. We arrive at several measures of influence and propose the use of two that do not require refitting of the model and lend themselves to routine application in the ERGM fitting procedure. MCMC p values are obtained for testing how extreme each node is with respect to the network structure. The influence measures are applied to two well-known data sets to illustrate the information they provide. From a network perspective, the proposed statistics offer an indication of which actors are most distinctive in the network structure, in terms of not abiding by the structural norms present across other actors.

Keywords

statistical analysis of social networksexponential random graph modelsoutliersleveragemissing data principlecase deletion

Information

Type
Original Paper
Information
Psychometrika , Volume 83 , Issue 4 , December 2018, pp. 809 - 830
Copyright
Copyright © 2018 The Psychometric Society

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Footnotes

Johan Koskinen would like to acknowledge financial support from the Leverhulme Trust Grant RPG-2013-140 and SRG2012.

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