András Vörös
Department of Social Statistics, University of Manchester
SOST71032 Social Network AnalysisASSESSMENT COVER SHEET
Introduction to Exponential Random Graph Models (ERGMs)
Mechanisms of tie formation
(Thanks to Bálint Néray and Zsófia Boda for a lot of materials on these slides!)
Dyadic:
reciprocity (Gouldner 1960; Blau 1964; Emerson 1976)
homophily (McPherson, Smith-Loving & Cook 2001)
…
Triadic:
balance (Heider 1958)
clustering (Davis 1969)
differential clustering of strong and weak ties (Granovetter 1973)
structural holes and brokerage (Burt 1992; Krackhardt 1999)
…
Degree-based / positional
popularity Matthew effect, i.e. “rich gets richer” (Merton 1968)
…
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Theories and mechanisms of network tie formation
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Theories and mechanisms of network tie formation
Lusher, Koskinen & Robins 2013, p. 24
From Lusher, Koskinen & Robins 2013:
1. Social networks are locally emergent
2. Network ties not only self-organize (dependence between ties), but they are
influenced by actor attributes and other exogenous factors
3. The patterns within networks can be seen as evidence for ongoing structural
processes
4. Multiple processes can operate simultaneously
5. Social networks are structured, yet stochastic
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ERGM ‘metatheory’ – general assumptions
From Lusher, Koskinen & Robins 2013:
1. Social networks are locally emergent
2. Network ties not only self-organize (dependence between ties), but they are
influenced by actor attributes and other exogenous factors
3. The patterns within networks can be seen as evidence for ongoing structural
processes
4. Multiple processes can operate simultaneously
5. Social networks are structured, yet stochastic
5
ERGM ‘metatheory’ – general assumptions
From Lusher, Koskinen & Robins 2013:
1. Social networks are locally emergent
2. Network ties not only self-organize (dependence between ties), but they are
influenced by actor attributes and other exogenous factors
3. The patterns within networks can be seen as evidence for ongoing structural
processes??????
4. Multiple processes can operate simultaneously
5. Social networks are structured, yet stochastic
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ERGM ‘metatheory’ – general assumptions
Most ERGMs are estimated on a single observation of a network
(see extensions though)
How can we talk about social processes generating the network?
The key is interdependence and self-organization
E.g. the last tie in a triangle had to be affected by the first two that was there
Of course, we cannot distinguish between processes that result in the same
outcome
selection-influence
multiple theories of clustering, etc.
We have to be careful not to over-interpret our models, but it is a generally
accepted way to talk about generating processes based on ERGM results
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Inference to social processes from cross-sectional data?
Even by analyzing cross-sectional data, we may find evidence for social
processes if they result in structural configurations which appear in the network
more frequently than expected by chance (Lusher, Koskinen & Robins 2013)
Caution! multiple processes leading to the same outcome
We cannot draw too specific conclusions about actual processes
Need longitudinal data to better grasp that
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Typically modeled network configurations
reciprocity transitive
closure in-degree out-degree homphily
Various processes are likely to operate at the same time
A number of configurations can be simultaneously tested in an ERGM to see
which processes influence the network structure
Configurations are often nested within one another
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Network configurations – combinations of processes
‘Purely structural’ effects, based on internal processes of the network
reciprocity (in directed networks)
in-degree-based effects – in-stars
out-degree-based effects – out-stars
two-paths: in-and out-degree – mixed stars or two-paths
2-stars, 3-stars… k-stars – represent the degree distribution
(k: the number of ties centered on the node)
‘alternating’ and ‘geometrically weighted’ star effects: more ties are assumed to matter less
in undirected networks: stars
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Network configurations – endogenous processes
‘Purely structural’ effects, based on internal processes of the network
Network closure effects: clustering and (in case of directed ties) transitivity
transitive triads and cyclic triads (in directed cases)
triads (in undirected cases)
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Network configurations – endogenous processes
multiple triangulation: triads occur together in clique-like structures
“not simply represent triangulation in the network but additionally is a measure of the extent to
which triangles themselves group together in larger higher order ‘clumps’ in the network”
(Robins et al. 2007)
alternating and geometrically weighted triangle effects
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Network configurations – endogenous processes
characteristics of nodes may be very important in tie formation
node attributes: exogenous independent variables (except: see extensions)
ties involve pairs of node: senders and receivers
sender effects: nodes with certain attributes send more ties
receiver effects: nodes with certain attributes receive more ties
homophily effects: same or similar nodes are more likely to be tied to each other
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Network configurations – node (actor) attributes
networks are often multiplex (multilayer, multivariate)
different networks can affect each other
(e.g. friendship and advice networks)
different network dimensions may be measured at the same time
dyadic covariates: effects of another social network considered to be fixed and
exogenous in the model
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Network configurations – dyadic covariates
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Please continue with the next topic