András Vörös
Department of Social Statistics, University of Manchester
SOST71032 Social Network AnalysisEvidence for communication with assessors
Introduction to Exponential Random Graph Models (ERGMs)
Goodness of Fit
Does our (converged) model provide a good representation of the observed
network?
But: Structurally isomorph networks have the same probability → no R2
(cf. are ERGMs good for tie prediction?)
Our definition of “model fit”:
how similar are simulated networks to the observed in different (not explicitly modeled)
structural characteristics (e.g. shortest paths, number of components, etc.)
How to perform such assessments of model fit?
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Goodness of Fit (GoF) for ERGMs
How to perform GoF tests?
The MCMC algorithm at the core of ERGM estimation:
3
Goodness of Fit (GoF) for ERGMs
Define parameters Assess convergence
Simulate many networks
Adjust parameters
How to perform GoF tests?
The MCMC algorithm at the core of ERGM estimation:
4
Goodness of Fit (GoF) for ERGMs
Define parameters Assess convergence
Simulate many networks
Adjust parameters
How to perform GoF tests?
The MCMC algorithm at the core of ERGM estimation:
5
Goodness of Fit (GoF) for ERGMs
Define parameters Assess convergence
Simulate many networks
Adjust parameters
How to perform GoF tests?
The MCMC algorithm at the core of ERGM estimation:
6
Goodness of Fit (GoF) for ERGMs
Define parameters Assess convergence
Simulate many networks
Adjust parameters
fit on unmodelled network
characteristics
How to perform GoF tests?
The MCMC algorithm at the core of ERGM estimation:
We can use the simulation part of the algorithm to test fit on any network statistic
7
Goodness of Fit (GoF) for ERGMs
Define parameters Assess convergence
Simulate many networks
Adjust parameters
fit on unmodelled network
characteristics
Multiple GoF tests may be performed
For example:
in-/out-degree distribution
triad census
shortest path lengths
number of components
etc.
Two things to keep in mind:
only statistics not explicitly modeled make sense!
only test GoF for converged models!
8
Goodness of Fit (GoF) for ERGMs
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Goodness of Fit (GoF) for ERGMs
Model 1 Model 2
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Goodness of Fit (GoF) for ERGMs
Model 1 Model 2
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Goodness of Fit (GoF) for ERGMs
Model 1 This is not GoF! It’s Model 2
convergence checking!
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Please continue with the next topic.
Handcock, M. S., Hunter, D. R., Butts, C. T., Goodreau, S. M., & Morris, M. (2008). statnet: Software tools
for the representation, visualization, analysis and simulation of network data. Journal of Statistical Software,
24(1), 1548.
Snijders, T. A., Pattison, P. E., Robins, G. L., & Handcock, M. S. (2006). New specifications for exponential
random graph models. Sociological Methodology, 36(1), 99-153.
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References