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Outliers and Influential Observations in Exponential Random Graph Models
Linköping University, Department of Management and Engineering, The Institute for Analytical Sociology, IAS. Linköping University, Faculty of Arts and Sciences. Univ Manchester, England; Univ Melbourne, Australia.
Swinburne Univ Technol, Australia.
Univ Melbourne, Australia.
Univ Sydney, Australia.
2018 (English)In: Psychometrika, ISSN 0033-3123, E-ISSN 1860-0980, Vol. 83, no 4, p. 809-830Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
SPRINGER , 2018. Vol. 83, no 4, p. 809-830
Keywords [en]
statistical analysis of social networks; exponential random graph models; outliers; leverage; missing data principle; case deletion
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-153155DOI: 10.1007/s11336-018-9635-8ISI: 000450043100002PubMedID: 30229530OAI: oai:DiVA.org:liu-153155DiVA, id: diva2:1267332
Note

Funding Agencies|Leverhulme Trust [RPG-2013-140, SRG2012]

Available from: 2018-12-01 Created: 2018-12-01 Last updated: 2018-12-01

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CiteExportLink to record
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  • apa
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