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Outliers and Influential Observations in Exponential Random Graph Models

Author

Listed:
  • Johan Koskinen

    (University of Manchester
    The University of Melbourne
    University of Linköping)

  • Peng Wang

    (Swinburne University of Technology)

  • Garry Robins

    (The University of Melbourne)

  • Philippa Pattison

    (The University of Sydney)

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.

Suggested Citation

  • Johan Koskinen & Peng Wang & Garry Robins & Philippa Pattison, 2018. "Outliers and Influential Observations in Exponential Random Graph Models," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 809-830, December.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:4:d:10.1007_s11336-018-9635-8
    DOI: 10.1007/s11336-018-9635-8
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    References listed on IDEAS

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    1. Garry Robins & Philippa Pattison & Stanley Wasserman, 1999. "Logit models and logistic regressions for social networks: III. Valued relations," Psychometrika, Springer;The Psychometric Society, vol. 64(3), pages 371-394, September.
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    3. D. A. Williams, 1987. "Generalized Linear Model Diagnostics Using the Deviance and Single Case Deletions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(2), pages 181-191, June.
    4. Sonja Kuhnt, 2004. "Outlier Identification Procedures for Contingency Tables using Maximum Likelihood and L1 Estimates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 431-442, September.
    5. C J Rhodes & P Jones, 2009. "Inferring missing links in partially observed social networks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(10), pages 1373-1383, October.
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    Cited by:

    1. Verena Bauer & Karl Fürlinger & Göran Kauermann, 2019. "A note on parallel sampling in Markov graphs," Computational Statistics, Springer, vol. 34(3), pages 1087-1107, September.
    2. Johan Koskinen & Galina Daraganova, 2022. "Bayesian analysis of social influence," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1855-1881, October.

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