ergm: simulate.ergm – R documentation

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simulate.ergm

Draw from the distribution of an Exponential Family Random Graph Model

Description

simulate is used to draw from exponential family random network models. See ergm for more information on these models.

The method for ergm objects inherits the model, the coefficients, the response attribute, the reference, the constraints, and most simulation parameters from the model fit, unless overridden by passing them explicitly. Unless overridden, the simulation is initialized with a random draw from the fitted model, saved by ergm().

Usage

## S3 method for class 'formula_lhs_network'
simulate(object, nsim = 1, seed = NULL, ...)

simulate_formula(object, ..., basis = eval_lhs.formula(object))

## S3 method for class 'network'
simulate_formula(
  object,
  nsim = 1,
  seed = NULL,
  coef,
  response = NULL,
  reference = ~Bernoulli,
  constraints = ~.,
  monitor = NULL,
  statsonly = FALSE,
  esteq = FALSE,
  output = c("network", "stats", "edgelist", "pending_update_network"),
  simplify = TRUE,
  sequential = TRUE,
  control = control.simulate.formula(),
  verbose = FALSE,
  ...,
  basis = eval_lhs.formula(object),
  do.sim = TRUE
)

## S3 method for class 'formula_lhs_pending_update_network'
simulate(object, nsim = 1, seed = NULL, ...)

## S3 method for class 'pending_update_network'
simulate_formula(
  object,
  nsim = 1,
  seed = NULL,
  coef,
  response = NULL,
  reference = ~Bernoulli,
  constraints = ~.,
  monitor = NULL,
  statsonly = FALSE,
  esteq = FALSE,
  output = c("network", "stats", "edgelist", "pending_update_network"),
  simplify = TRUE,
  sequential = TRUE,
  control = control.simulate.formula(),
  verbose = FALSE,
  ...,
  basis = eval_lhs.formula(object),
  do.sim = TRUE
)

## S3 method for class 'ergm_model'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  coef,
  response = NULL,
  reference = ~Bernoulli,
  constraints = ~.,
  monitor = NULL,
  basis = NULL,
  esteq = FALSE,
  output = c("network", "stats", "edgelist", "pending_update_network"),
  simplify = TRUE,
  sequential = TRUE,
  control = control.simulate.formula(),
  verbose = FALSE,
  ...
)

## S3 method for class 'ergm'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  coef = object$coef,
  response = object$response,
  reference = object$reference,
  constraints = object$constraints,
  monitor = NULL,
  basis = object$newnetwork,
  statsonly = FALSE,
  esteq = FALSE,
  output = c("network", "stats", "edgelist", "pending_update_network"),
  simplify = TRUE,
  sequential = TRUE,
  control = control.simulate.ergm(),
  verbose = FALSE,
  ...
)

Arguments

`object`	Either a `formula` or an `ergm` object. The `formula` should be of the form `y ~ <model terms>`, where `y` is a network object or a matrix that can be coerced to a `network` object. For the details on the possible `<model terms>`, see `ergm-terms`. To create a `network` object in , use the `network()` function, then add nodal attributes to it using the `%v%` operator if necessary.
`nsim`	Number of networks to be randomly drawn from the given distribution on the set of all networks, returned by the Metropolis-Hastings algorithm.
`seed`	Seed value (integer) for the random number generator. See `set.seed`.
`...`	Further arguments passed to or used by methods.
`basis`	a value (usually a `network`) to override the LHS of the formula.
`coef`	Vector of parameter values for the model from which the sample is to be drawn. If `object` is of class `ergm`, the default value is the vector of estimated coefficients.
`response`	Name of the edge attribute whose value is to be modeled in the valued ERGM framework. Defaults to `NULL` for simple presence or absence, modeled via a binary ERGM.
`reference`	A one-sided formula specifying the reference measure (h(y)) to be used. See help for ERGM reference measures implemented in the ergm package.
`constraints`	A one-sided formula specifying one or more constraints on the support of the distribution of the networks being simulated. See the documentation for a similar argument for `ergm` and see list of implemented constraints for more information. For `simulate.formula`, defaults to no constraints. For `simulate.ergm`, defaults to using the same constraints as those with which `object` was fitted.
`monitor`	A one-sided formula specifying one or more terms whose value is to be monitored. These terms are appeneded to the model, along with a coefficient of 0, so their statistics are returned. An `ergm_model` objectcan be passed as well.
`statsonly`	Logical: If TRUE, return only the network statistics, not the network(s) themselves. Deprecated in favor of `output=`.
`esteq`	Logical: If TRUE, compute the sample estimating equations of an ERGM: if the model is non-curved, all non-offset statistics are returned either way, but if the model is curved, the score estimating function values (3.1) by Hunter and Handcock (2006) are returned instead.
`output`	Normally character, one of `"network"` (default), `"stats"`, `"edgelist"`, or `"pending_update_network"` to determine the output format. Partial matching is performed. Alternatively, a function with prototype `function(pending_update_network, chain, iter, ...)` that is called for each returned network, and its return value, rather than the network itself, is stored. This can be used to, for example, store the simulated networks to disk without storing them in memory or compute network statistics not implemented using the ERGM API, without having to store the networks themselves.
`simplify`	Logical: If `TRUE` the output is "simplified": sampled networks are returned in a single list, statistics from multiple parallel chains are stacked, etc.. This makes it consistent with behavior prior to `ergm` 3.10.
`sequential`	Logical: If FALSE, each of the `nsim` simulated Markov chains begins at the initial network. If TRUE, the end of one simulation is used as the start of the next. Irrelevant when `nsim=1`.
`control`	A list of control parameters for algorithm tuning. Constructed using `control.simulate.ergm` or `control.simulate.formula`, which have different defaults.
`verbose`	Logical: If TRUE, extra information is printed as the Markov chain progresses.
`do.sim`	Logical: If `FALSE`, do not proceed to the simulation but rather return a list of arguments that would have been passed to `simulate.ergm_model()`. This can be useful if, for example, one wants to run several simulations with varying coefficients and did not want to reinitialize the model and the proposal ever time.

Details

A sample of networks is randomly drawn from the specified model. The model is specified by the first argument of the function. If the first argument is a formula then this defines the model. If the first argument is the output of a call to ergm then the model used for that call is the one fit – and unless coef is specified, the sample is from the MLE of the parameters. If neither of those are given as the first argument then a Bernoulli network is generated with the probability of ties defined by prob or coef.

Note that the first network is sampled after burnin steps, and any subsequent networks are sampled each interval steps after the first.

More information can be found by looking at the documentation of ergm.

Value

If output=="stats" an mcmc object containing the simulated network statistics. If control$parallel>0, an mcmc.list object. If simplify=TRUE (the default), these would then be "stacked" and converted to a standard matrix. A logical vector indicating whether or not the term had come from the monitor= formula is stored in attr()-style attribute "monitored".

Otherwise, a representation of the simulated network is returned, in the form specified by output. In addition to a network representation or a list thereof, they have the following attr-style attributes:

formula: The formula used to generate the sample.
stats: An mcmc or mcmc.list object as above.
control: Control parameters used to generate the sample.
constraints: Constraints used to generate the sample.
reference: The reference measure for the sample.
monitor: The monitoring formula.
response: The edge attribute used as a response.

The following are the permitted network formats:

"network": If nsim==1, an object of class network. If nsim>1, it returns an object of class network.list (a list of networks) with the above-listed additional attributes.
"edgelist": An edgelist representation of the network, or a list thereof, depending on nsim.
"pending_update_network": A semi-internal representation of a network consisting of a network object emptied of edges, with an attached edgelist matrix, or a list thereof, depending on nsim.

If simplify==FALSE, the networks are returned as a nested list, with outer list being the parallel chain (including 1 for no parallelism) and inner list being the samples within that chains (including 1, if one network per chain). If TRUE, they are concatenated, and if a total of one network had been simulated, the network itself will be returned.

Note

simulate.ergm_model() is a lower-level interface, providing a simulate() method for ergm_model class. The basis argument is required; monitor, if passed, must be an ergm_model as well; and constraints can be an ergm_proposal object instead.

Examples

#
# Let's draw from a Bernoulli model with 16 nodes
# and density 0.5 (i.e., coef = c(0,0))
#
g.sim <- simulate(network(16) ~ edges + mutual, coef=c(0, 0))
#
# What are the statistics like?
#
summary(g.sim ~ edges + mutual)
#
# Now simulate a network with higher mutuality
#
g.sim <- simulate(network(16) ~ edges + mutual, coef=c(0,2))
#
# How do the statistics look?
#
summary(g.sim ~ edges + mutual)
#
# Let's draw from a Bernoulli model with 16 nodes
# and tie probability 0.1
#
g.use <- network(16,density=0.1,directed=FALSE)
#
# Starting from this network let's draw 3 realizations
# of a edges and 2-star network
#
g.sim <- simulate(~edges+kstar(2), nsim=3, coef=c(-1.8,0.03),
               basis=g.use, control=control.simulate(
                 MCMC.burnin=1000,
                 MCMC.interval=100))
g.sim
summary(g.sim)
#
# attach the Florentine Marriage data
#
data(florentine)
#
# fit an edges and 2-star model using the ergm function
#
gest <- ergm(flomarriage ~ edges + kstar(2))
summary(gest)
#
# Draw from the fitted model (statistics only), and observe the number
# of triangles as well.
#
g.sim <- simulate(gest, nsim=10, 
            monitor=~triangles, output="stats",
            control=control.simulate.ergm(MCMC.burnin=1000, MCMC.interval=100))
g.sim

# Custom output: store the edgecount (computed in R), iteration index, and chain index.
output.f <- function(x, iter, chain, ...){
  list(nedges = network.edgecount(as.network(x)),
       chain = chain, iter = iter)
}
g.sim <- simulate(gest, nsim=3,
            output=output.f, simplify=FALSE,
            control=control.simulate.ergm(MCMC.burnin=1000, MCMC.interval=100))
unclass(g.sim)

ergm

Fit, Simulate and Diagnose Exponential-Family Models for Networks

v3.11.0

GPL-3 + file LICENSE

Authors

Mark S. Handcock [aut], David R. Hunter [aut], Carter T. Butts [aut], Steven M. Goodreau [aut], Pavel N. Krivitsky [aut, cre] (<https://orcid.org/0000-0002-9101-3362>), Martina Morris [aut], Li Wang [ctb], Kirk Li [ctb], Skye Bender-deMoll [ctb], Chad Klumb [ctb], Michał Bojanowski [ctb], Ben Bolker [ctb]

Initial release

2020-10-14