Introduction to
Stochastic Actor-oriented Models
Goodness of FitAssessment Brief
András Vörös
Department of Social Statistics, University of Manchester
SOST71032 Social Network Analysis
* Thanks to Christoph Stadtfeld for many nice figures and examples.
Simulated networks in SAOMs
SAOM parameters are estimated by simulating
networks
starting from the network observed at t1
trying to reach a network similar to the one observed at t2
thus, the simulated chains of tie changes represent likely paths
how the network could have evolved between t1 and t2
The estimation optimizes fit on the target statistics of
the effects included in the model
But are the simulated networks realistic in their other
characteristics?
these are not explicitly modeled
we are often interested in macro features
e.g. degree distribution, distances, clustering
Estimation through simulation
Estimation through simulation
What is “good”?
Fit on the target statistics used for the
estimation is not goodness of fit yet…
The observed network at t2 has 99 ties of which 72 are
reciprocated; there are 164 transitive triplets, …
The (method of moments) estimation in RSiena aims at
simulating networks which have similar statistics
But this does not necessarily mean that the networks
are realistic in other (macro) characteristics
e.g. degree distribution, distances, components
The two observed networks
A good simulation from an outdegreereciprocity model
With triadic effects (transitivity, 3-cycle)
With gender and ethnic homophily
Assessing goodness of fit in RSiena – the
sienaGOF function
We used visual inspection to determine whether fit was
good
The goodness of fit function in RSiena (sienaGOF)
calculates statistics for specific (macro-)characteristics
of the simulated networks and compares them to the
same features of the observed network
degree distribution
geodesic distances
triad census
distribution of components
…
sienaGOF takes all simulated networks into account (cf.
we looked at only one earlier)
Goodness of fit on indegree distribution
Goodness of fit on outdegree distribution
Goodness of fit on distance distribution
Goodness of fit on triad census
Goodness of fit on number of components
Summary
Simulations are very important in SAOMs as the
estimation of parameters builds on the simulated
networks
By design, the (method of moments) estimation in
RSiena simulates networks which have a good “fit” in
terms of the explicitly modeled target statistics
But this is most often not enough to judge how
realistic our model is
The simulated networks can also be used to assess the
goodness of fit of the model on any specific network
statistic
We are often interested in macro-level features of nets.
Please continue with the next topic.