Robins

Information about Robins

Published on September 25, 2007

Author: Dabby

Source: authorstream.com

Content

A two minute introduction to:Exponential random graph (p*)models for social networks SNAC Workshop, Illinois, November 2005 Garry Robins, University of Melbourne, Australia:  A two minute introduction to: Exponential random graph (p*)models for social networks SNAC Workshop, Illinois, November 2005 Garry Robins, University of Melbourne, Australia Collaborators: Pip Pattison, Tom Snijders, Mark Handcock, Stanley Wasserman (among others) Statistical modeling of endogenous network processes:  Statistical modeling of endogenous network processes Guiding principles: Network ties are the outcome of (unobserved) social processes that tend to be local and interactive There are both regularities and irregularities in these local interactive processes We hence construct statistical models in which: local interactivity is permitted and assumptions about form of 'local interactions' are explicit regularities are represented by model parameters and estimated from data consequences of local regularities for global network properties can be understood and can also provide an exacting approach to model evaluation Network topologies: what are the forms of local interactivity?:  Network topologies: what are the forms of local interactivity? Two tie variables are neighbours if: they share an actor Markov model (Frank andamp; Strauss, 1986) they share connections realisation-dependent model with two existing ties (Pattison andamp; Robins, 2002; (completing a social circuit) Snijders, Pattison, Robins andamp; Handcock, 2005) There are other possibilities, but these two get us a long way Exponential random graph models:  Exponential random graph models P(X = x) = (1/c) exp{Q QzQ(x)} normalizing quantity parameter network statistic the summation is over all neighbourhoods Q Estimation of parameters: Markov Chain Monte Carlo Maximum Likelihood Models with nodal attributes are also possible: social selection; social influence Neighbourhoods depend on proximity assumptions :  Neighbourhoods depend on proximity assumptions Assumptions: two ties are neighbours: if they share an actor Markov if they complete a 4-cycle realisation-dependent* Configurations for neighbourhoods edge 2-star 3-star 4-star …triangle + ... 4-cycle 2-triangle and others New specifications(Snijders, Pattison, Robins & Handcock, 2005):  New specifications (Snijders, Pattison, Robins andamp; Handcock, 2005) k nodes 2-independent 3-independent … k-independent … 2-path 2-path 2-path k nodes triangle 2-triangle 3-triangle … k-triangle … Slide7:  Some current issues Work in progress: Further work on model specification: directed networks; multiple networks; bipartite graphs Incorporation of actor attributes Efficiency of estimation Longer term goals: Extend modeling to large-scale social systems, including cross-level interactions Model estimation from sample data Extend capacity to model network evolution, including new specifications Co-evolution of psychological states and network structures

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