Faculty of Medicine, Dentistry and Health Sciences School of Behavioural Science

Research: Garry Robins

My research focusses on the analysis of social networks, and in particular the development of exponential random graph models for social networks (p* models). General descriptions of social network analysis can be found on the INSNA website.

Early papers describing exponential random graph models are Frank & Strauss (1986), Wasserman & Pattison (1996), Pattison & Wasserman (1999) and Robins, Pattison & Wasserman (1999).  These models assume that a large-scale network emerges from combinations of local patterns of interaction among small overlapping subsets of people. Such patterns can often be interpreted as the result of a localized social process, a set of behaviours within each subset of individuals. 

Current collaborators on exponential random graph (p*) models include Professor Pip Pattison of the University of Melbourne, Professor Tom Snijders of the Universities of Oxford and Groningen, and Professor Mark Handcock of the University of Washington.

For details of general social networks research at the University of Melbourne, go to the Melnet website, which describes the activities of our social networks research group here at Melbourne. It includes details of publications, projects, software, courses, presentations and other material.

For a list of my publications, including some preprints, see my publications page.

For other details, see the following pages on:

recent research grants and contracts
recent conference presentations
current teaching


Why social networks?

Although the claim that social processes are interactive, dynamic, and socially-situated is neither new nor controversial, commentaries across social science disciplines continue to emphasise the need for a new understanding of social phenomena that takes these features seriously.  By dynamic and interactive, we mean that the actions of one individual may both depend on and, in turn, influence the actions of others.  By socially-situated, we mean that actions depend on a multi-layered complex of social entities that includes social relations, group affiliations, social settings and spatial neighbourhoods.  These aspects of social “location” both constrain and provide opportunities for possible future actions.  Further, an action by one individual may change the context for other individuals in neighbouring locations, so that a dynamic, interactive characterisation of social processes necessarily implicates an understanding of social location. The task of building models for such complex processes is difficult, both theoretically and technically, and few approaches have captured simultaneously their dynamic, interactive, and location-dependent qualities. 

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Why model social networks?

A fuller recognition of the interdependent nature of social processes brings with it a quantitative imperative: relatively precise characterisations of local interactive processes are required in order to understand their implications at an aggregate or global system level (eg group, community).   Small local changes can have dramatic global effects.

The guiding principle of our approach: Network ties/social action are the outcome of unobserved local interactive processes. There are both regularities and irregularities in these local interactive processes.

With exponential random graph models, we can construct a stochastic model formulation in which:

Interest in social network applications is growing fast, bringing a demand for new network modelling techniques.Our commitment is to methodological development but with a clear linkage to empirical data and to meaningful applications.  Methodological advances also entail theoretical development. We are engaged in the linkages between local social processes and system-wide outcomes. A greater theoretical understanding of these linkages is an important step.


Selection of current research projects
 


Exponential random graph models
(Collaborators: Professor Tom Snijders, University of Groningen; Professor Pip Pattison, University of Melbourne; Professors Mark Handcock and Martina Morris, University of Washington; Dr Steve Goodreau, University of Washington; Dr Dave Hunter, Penn State University; Mr Peng Wang, University of Melbourne)
Previously, the most popular form of these models has been the Markov random graphs of Frank and Strauss (1986).  In recent years, however, problems with degeneracy in these models have become more apparent (see the ergm reference list for relevant articles). Snijders, Pattison, Robins & Handcock (2006) proposed three new statistics that can be included in exponential random graph models: alternating k-stars; alternating k-triangles, and alternating independent two-paths.

The following is taken from the abstract of Robins, Snijders, Wang, Handcock & Pattison (2007) - see my publications page.

"This article reviews new specifications for exponential random graph models ... and demonstrates their improvement over standard Markov random graphs in fitting models to empirical network data.  Not only do the new specifications show improvements in goodness of fit, they help address the problems of near-degeneracy that often afflict Markov random graph models, when coherent parameter estimates are simply not available. Degeneracy in Markov models may occur when graphs have high levels of transitivity, often the case for observed network data.  While the new specifications do not remove all issues of degeneracy, the inclusion of a new higher order transitivity statistic assists considerably. In estimating models for a large number of classical small-scale network data sets, the new specifications show a dramatically better performance than Markov graphs.  We also illustrate the use of the new specifications with a larger network, for which Markov graph models are degenerate, and show how actor attributes may be used to draw inferences about homophily or other social selection effects.  We compare Monte Carlo maximum likelihood estimates with less accurate pseudo-likelihood methods.  We review three current programs that can produce maximum likelihood estimates.  We conclude by discussing whether the older forms of p* models (i.e. Markov random graphs) may be superseded by the new specifications, and how additional elaborations may further improve model performance."

We are currently undertaking further work along the lines of these new specifications, including: elaborations for directed networks, for multiple networks, and for bipartite graphs; and further development of estimation software.

There are lots of details and papers, etc, on the Melnet website.




Missing data in networks
(Collaborators: Dr Johan Koskinen, Professor Pip Pattison, University of Melbourne.)
 

As exponential random graph models provide a principled statistical approach to model a social network, they can be adapted for parameter estimation in the presence of missing observations. Once parameters have been estimated, then – provided the amount of missing data is not too extreme – it is possible to make inferences about the missing observations. Koskinen et al (2007) identified five types of network missing data problems to which this general strategy may be extended in various ways, especially within a Bayesian framework:

  1. particular links in the social network are not known;
  2. pooling incomplete relational data information from different sources;
  3. covert actors (i.e. where the network relations of some actors are not known, although the presence of these actors is suspected);
  4. some actors may be operating with multiple aliases (network doppelgangers); identifying who those actors might be;
  5. network data where personal information about particular actors is not known.

To date, our work has concentrated on the first of these, parameter estimation and link prediction when a certain number of edges are missing.  Work in the other four areas is at early stages, although Koskinen et al (2007) provided some thoughts on possible ways forward.

This work has been funded by DSTO.




Estimation from sampled network data
(Collaborators: Professor Pip Pattison, Professor Tom Snijders, Dr Johan Koskinen, Mr Peng Wang)
We are developing methods to estimate exponential random graph models from network data collected through snowball samples.


pnet
 
(Collaborators: Professor Pip Pattison, Mr Peng Wang, Mr Lei Xing, University of Melbourne)


pnet is the publicly available software we have developed for estimation of exponential random graph models. See the Melnet website..

 

Environmental governance: the management of critical water resources

(In collaboration with CSIRO)



Masculine behaviours and social structures (including in elite sporting teams)

(Collaborators: Dr Dean Lusher, Melbourne University, Dr Peter Kremer, Deakin University)

Issues related to male attitudes towards women are important to the community as a whole, and have attracted recent negative attention to various football codes, including the Australian Football League.  Only a small minority of players may be implicated in extreme behaviours but a central issue is how the norms that permit such behaviours – even among only a few – are developed and maintained. Past research shows that norms are sustained within social groupings.  For sporting clubs, the team environment may foster a variety of strong informal norms affecting behaviours. This project, sponsored by the AFL, examines the range of attitudes towards women by AFL players, related to the social structures in the club, using the new specifications for exponential random graph models. 

Here is a copy of the Executive Summary of our report to the AFL. 

This research is part of a broader program, led by Dr Lusher, about attitudes toward gender and social networks. More generally this work extends into investigations of social networks, individual attitudes and cultural norms. See Dr Lusher's website for further details.


Local government and innovation

(Collaborators: Professor Mark Considine, Dr Jenny Lewis, Melbourne University)
We are fitting exponential random graph models to innovation networks in a number of Victorian local government councils.  For further details of the project, see Dr Lewis's webpage.




Network epidemiology
 (Principal collaborators: Mr Graeme Garner, Mr Sam Beckett, DAFF, Ms Jodie McVernon, University of Melbourne, Associate Professor Margaret Hellard, MacFarlane Burnet Centre, Professor Anthony Smith, Latrobe University, Professor Pip Pattison, University of Melbourne)

We are involved in several projects relating to the social contact structure relevant to the spread of influenza, and the spread of Hepatitus C and HIV through social networks.



Identity and organisational structure
 (Principal collaborators: Professor Alessandro Lomi, University of Lugano, Dr Dean Lusher, University of Melbourne)

Using statistical models for multiple social networks we explore the interplay between hierarchies, social networks and organizational identities within an international multiunit organization.

Updated 21 May 2009

 

 

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