Separable Temporal Exponential Family Random Graph Models
stergm is used for finding Separable Temporal ERGMs'
(STERGMs) Conditional MLE (CMLE) (Krivitsky and Handcock, 2010) and
Equilibrium Generalized Method of Moments Estimator (EGMME) (Krivitsky, 2009).
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A one-sided formula specifying one or more constraints
on the support of the distribution of the networks being modeled,
using syntax similar to the
It is also possible to specify a proposal function directly
by passing a string with the function's name. In that case,
arguments to the proposal should be specified through the
The default is
See the ERGM constraints documentation for
the constraints implemented in the
For STERGMs in particular, the constraints apply to the post-formation and the post-dissolution network, rather than the final network. This means, for example, that if the degree of all vertices is constrained to be less than or equal to three, and a vertex begins a time step with three edges, then, even if one of its edges is dissolved during its time step, it won't be able to form another edge until the next time step. This behavior may change in the future.
Note that not all possible combinations of constraints are supported.
One of "EGMME" for Equilibrium Generalized Method of Moments Estimation, based on a single network with some temporal information and making an assumption that it is a product of a STERGM process running to its stationary (equilibrium) distribution; "CMLE" for Conditional Maximum Likelihood Estimation, modeling a transition between two networks, or "CMPLE" for Conditional Maximum PseudoLikelihood Estimation, using MPLE instead of MLE. CMPLE is extremely inaccurate at this time.
For CMLE and CMPLE estimation, times or indexes at which
the networks whose transition is to be modeled are
observed. Default to
Numeric vector to specify offset formation parameters.
Numeric vector to specify offset dissolution parameters.
A vector specifying the values of the
Whether or not to calculate the log-likelihood of
a CMLE STERGM fit. See
A list of control parameters for algorithm
tuning. Constructed using
logical or integer; if TRUE or positive, the program will print out progress information. Higher values result in more output.
Additional arguments, to be passed to lower-level functions.
ergm-terms for details. At
this time, only linear ERGM terms are allowed.
For a brief demonstration, please see the tergm package vignette:
A more detailed tutorial is avalible on the statnet wiki: http://statnet.csde.washington.edu/workshops/SUNBELT/current/tergm/tergm_tutorial.pdf
For more usage examples, see the wiki page at https://statnet.csde.washington.edu/trac/wiki/tergmUsage
stergm returns an object of class
stergm that is a list
consisting of the following elements:
Formation and dissolution formulas, respectively.
The targets formula.
The target statistics.
The type of estimate.
A matrix containing the full trace of the EGMME optimization process: coefficients tried and target statistics simulated.
mcmcobject containing target statistics sampled at the estimate.
The full estimated variance-covariance matrix of the parameter estimates for EGMME. (Note that although the CMLE formation parameter estimates are independent of the dissolution parameter estimates due to the separability assumption, this is not necessarily the case for EGMME.)
For CMLE and CMPLE,
ergmobjects from fitting formation and dissolution, respectively. For EGMME, stripped down
estimate=="EGMME", the original network; for
network.list(a discrete series of networks) to which the model was fit.
The control parameters used to fit the model.
See the method
print.stergm for details on how
stergm object is printed. Note that the
summary.stergm returns a summary of the
relevant parts of the
stergm object in concise summary
Krivitsky PN, Handcock MS (2010). A Separable Model for Dynamic Networks. http://arxiv.org/abs/1011.1937
Krivitsky, P.N. (2012). Modeling of Dynamic Networks based on Egocentric Data with Durational Information. Pennsylvania State University Department of Statistics Technical Report, 2012(2012-01). http://stat.psu.edu/research/technical-report-files/2012-technical-reports/modeling-of-dynamic-networks-based-on-egocentric-data-with-durational-information
ergm, network, %v%, %n%,
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# EGMME Example par(ask=FALSE) n<-30 g0<-network.initialize(n,dir=FALSE) # edges, degree(1), mean.age target.stats<-c( n*1/2, n*0.6, 20) dynfit<-stergm(g0,formation = ~edges+degree(1), dissolution = ~edges, targets = ~edges+degree(1)+mean.age, target.stats=target.stats, estimate="EGMME", control=control.stergm(SA.plot.progress=TRUE)) par(ask=TRUE) mcmc.diagnostics(dynfit) summary(dynfit) # CMLE Example data(samplk) # Fit a transition from Time 1 to Time 2 samplk12 <- stergm(list(samplk1, samplk2), formation=~edges+mutual+transitiveties+cyclicalties, dissolution=~edges+mutual+transitiveties+cyclicalties, estimate="CMLE") mcmc.diagnostics(samplk12) summary(samplk12) # Fit a transition from Time 1 to Time 2 and from Time 2 to Time 3 jointly samplk123 <- stergm(list(samplk1, samplk2, samplk3), formation=~edges+mutual+transitiveties+cyclicalties, dissolution=~edges+mutual+transitiveties+cyclicalties, estimate="CMLE") mcmc.diagnostics(samplk123) summary(samplk123)