Estimates statistical network models using the exponential random graph modeling (ERGM) framework with extensions for dynamic/temporal models (STERGM).
netest(
nw,
formation,
target.stats,
coef.diss,
constraints,
coef.form = NULL,
edapprox = TRUE,
set.control.ergm = control.ergm(),
set.control.stergm = control.stergm(),
set.control.tergm = control.tergm(),
verbose = FALSE,
nested.edapprox = TRUE,
...
)A fitted network model object of class netest.
An object of class network.
Right-hand sided STERGM formation formula in the form
~edges + ..., where ... are additional network
statistics.
Vector of target statistics for the formation model, with one number for each network statistic in the model.
An object of class disscoef output from the
dissolution_coefs function.
Right-hand sided formula specifying constraints for the
modeled network, in the form ~..., where ... are
constraint terms. By default, no constraints are set.
Vector of coefficients for the offset terms in the formation formula.
If TRUE, use the indirect edges dissolution
approximation method for the dynamic model fit, otherwise use the
more time-intensive full STERGM estimation (see details).
Control arguments passed to ergm (see
details).
Deprecated control argument of class
control.stergm; use set.control.tergm instead.
Control arguments passed to tergm
(see details).
If TRUE, print model fitting progress to console.
Logical. If edapprox = TRUE the dissolution
model is an initial segment of the formation model (see details).
Additional arguments passed to other functions.
The edges dissolution approximation method is described in Carnegie et al. This approximation requires that the dissolution coefficients are known, that the formation model is being fit to cross-sectional data conditional on those dissolution coefficients, and that the terms in the dissolution model are a subset of those in the formation model. Under certain additional conditions, the formation coefficients of a STERGM model are approximately equal to the coefficients of that same model fit to the observed cross-sectional data as an ERGM, minus the corresponding coefficients in the dissolution model. The approximation thus estimates this ERGM (which is typically much faster than estimating a STERGM) and subtracts the dissolution coefficients.
The conditions under which this approximation best hold are when there are
few relational changes from one time step to another; i.e. when either
average relational durations are long, or density is low, or both.
Conveniently, these are the same conditions under which STERGM estimation is
slowest. Note that the same approximation is also used to obtain starting
values for the STERGM estimate when the latter is being conducted. The
estimation does not allow for calculation of standard errors, p-values, or
likelihood for the formation model; thus, this approach is of most use when
the main goal of estimation is to drive dynamic network simulations rather
than to conduct inference on the formation model. The user is strongly
encouraged to examine the behavior of the resulting simulations to confirm
that the approximation is adequate for their purposes. For an example, see
the vignette for the package tergm.
It has recently been found that subtracting a modified version of the
dissolution coefficients from the formation coefficients provides a more
principled approximation, and this is now the form of the approximation
applied by netest. The modified values subtracted from the formation
coefficients are equivalent to the (crude) dissolution coefficients with
their target durations increased by 1. The nested.edapprox argument
toggles whether to implement this modified version by appending the
dissolution terms to the formation model and appending the relevant values to
the vector of formation model coefficients (value = FALSE), whereas
the standard version subtracts the relevant values from the initial formation
model coefficients (value = TRUE).
The ergm and tergm functions allow control settings for the
model fitting process. When fitting a STERGM directly (setting
edapprox to FALSE), control parameters may be passed to the
tergm function with the set.control.tergm argument in
netest. The controls should be input through the
control.tergm() function, with the available parameters listed in the
control.tergm help page in the tergm package.
When fitting a STERGM indirectly (setting edapprox to TRUE),
control settings may be passed to the ergm function using
set.control.ergm in netest. The controls should be input
through the control.ergm() function, with the available parameters
listed in the control.ergm help page in the
ergm package. An example is below.
netest is a wrapper function for the ergm and stergm
functions that estimate static and dynamic network models, respectively.
Network model estimation is the first step in simulating a stochastic network
epidemic model in EpiModel. The output from netest is a
necessary input for running the epidemic simulations in netsim.
With a fitted network model, one should always first proceed to model
diagnostics, available through the netdx function, to check
model fit. A detailed description of fitting these models, along with
examples, may be found in the
Basic Network Models tutorials.
Krivitsky PN, Handcock MS. "A separable model for dynamic networks." JRSS(B). 2014; 76.1:29-46.
Carnegie NB, Krivitsky PN, Hunter DR, Goodreau SM. An approximation method for improving dynamic network model fitting. Journal of Computational and Graphical Statistics. 2014; 24(2): 502-519.
Jenness SM, Goodreau SM and Morris M. EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks. Journal of Statistical Software. 2018; 84(8): 1-47.
Use netdx to diagnose the fitted network model, and
netsim to simulate epidemic spread over a simulated
dynamic network consistent with the model fit.
# Initialize a network of 100 nodes
nw <- network_initialize(n = 100)
# Set formation formula
formation <- ~edges + concurrent
# Set target statistics for formation
target.stats <- c(50, 25)
# Obtain the offset coefficients
coef.diss <- dissolution_coefs(dissolution = ~offset(edges), duration = 10)
# Estimate the STERGM using the edges dissolution approximation
est <- netest(nw, formation, target.stats, coef.diss,
set.control.ergm = control.ergm(MCMC.burnin = 1e5,
MCMC.interval = 1000))
est
# To estimate the STERGM directly, use edapprox = FALSE
# est2 <- netest(nw, formation, target.stats, coef.diss, edapprox = FALSE)
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