Separable Temporal Exponential Family Random Graph Models
Description
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).
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 
Arguments
nw 
A

formation, dissolution 
Onesided 
constraints 
A onesided 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 postformation and the postdissolution 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. 
estimate 
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. 
times 
For CMLE and CMPLE estimation, times or indexes at which
the networks whose transition is to be modeled are
observed. Default to 
offset.coef.form 
Numeric vector to specify offset formation parameters. 
offset.coef.diss 
Numeric vector to specify offset dissolution parameters. 
targets 
Onesided 
target.stats 
A vector specifying the values of the 
eval.loglik 
Whether or not to calculate the loglikelihood of
a CMLE STERGM fit. See 
control 
A list of control parameters for algorithm
tuning. Constructed using 
verbose 
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 lowerlevel functions. 
Details
Model Terms
See ergm
and ergmterms
for details. At
this time, only linear ERGM terms are allowed.
For a brief demonstration, please see the tergm package vignette:
browseVignettes(package='tergm')
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
Value
stergm
returns an object of class stergm
that is a list
consisting of the following elements:
formation, dissolution
Formation and dissolution formulas, respectively.
targets
The targets formula.
target.stats
The target statistics.
estimate
The type of estimate.
opt.history
A matrix containing the full trace of the EGMME optimization process: coefficients tried and target statistics simulated.
sample
An
mcmc
object containing target statistics sampled at the estimate.covar
The full estimated variancecovariance 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.)
formation.fit, dissolution.fit
For CMLE and CMPLE,
ergm
objects from fitting formation and dissolution, respectively. For EGMME, stripped downergm
like lists.network
For
estimate=="EGMME"
, the original network; forestimate=="CMLE"
orestimate=="CMPLE"
, anetwork.list
(a discrete series of networks) to which the model was fit.control
The control parameters used to fit the model.
See the method print.stergm
for details on how
an stergm
object is printed. Note that the
method summary.stergm
returns a summary of the
relevant parts of the stergm
object in concise summary
format.
References
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(201201). http://stat.psu.edu/research/technicalreportfiles/2012technicalreports/modelingofdynamicnetworksbasedonegocentricdatawithdurationalinformation
See Also
ergm, network, %v%, %n%, ergmterms
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37  # 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)

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