simulate.tergm {tergm}

Draw from the distribution of a Temporal Exponential Family Random Graph Model

Description

simulate is used to draw from temporal exponential family random network models in their natural parameterizations. See tergm for more information on these models.

Usage

## S3 method for class 'tergm'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  coef = coefficients(object),
  constraints = object$constraints,
  monitor = object$targets,
  time.slices = 1,
  time.start = NULL,
  time.burnin = 0,
  time.interval = 1,
  control = control.simulate.tergm(),
  output = c("networkDynamic", "stats", "changes", "final", "ergm_state"),
  nw.start = NULL,
  stats = FALSE,
  verbose = FALSE,
  ...
)

## S3 method for class 'network'
simulate_formula(
  object,
  nsim = 1,
  seed = NULL,
  coef = NULL,
  constraints = ~.,
  monitor = NULL,
  time.slices = 1,
  time.start = NULL,
  time.burnin = 0,
  time.interval = 1,
  time.offset = 1,
  control = control.simulate.formula.tergm(),
  output = c("networkDynamic", "stats", "changes", "final", "ergm_state"),
  stats = FALSE,
  verbose = FALSE,
  ...,
  basis = ergm.getnetwork(object),
  dynamic = FALSE
)

## S3 method for class 'networkDynamic'
simulate_formula(
  object,
  nsim = 1,
  seed = NULL,
  coef = attr(basis, "coef"),
  constraints = ~.,
  monitor = NULL,
  time.slices = 1,
  time.start = NULL,
  time.burnin = 0,
  time.interval = 1,
  time.offset = 1,
  control = control.simulate.formula.tergm(),
  output = c("networkDynamic", "stats", "changes", "final", "ergm_state"),
  stats = FALSE,
  verbose = FALSE,
  ...,
  basis = eval_lhs.formula(object),
  dynamic = FALSE
)

Arguments

object

for simulate.tergm, an object of type tergm giving a model fit; for simulate_formula.network and simulate_formula.networkDynamic, a formula specifying the model

simulate_formula.network understands the lasttoggle "API".

nsim

Number of replications (separate chains of networks) of the process to run and return. The networkDynamic method only supports nsim=1.

seed

Seed value (integer) for the random number generator. See set.seed.

coef

Parameters for the model.

constraints

A formula specifying one or more constraints on the support of the distribution of the networks being modeled. Multiple constraints may be given, separated by “+” and “-” operators. See ergmConstraint for the detailed explanation of their semantics and also for an indexed list of the constraints visible to the ergm package.

The default is to have no constraints except those provided through the ergmlhs API.

Together with the model terms in the formula and the reference measure, the constraints define the distribution of networks being modeled.

It is also possible to specify a proposal function directly either by passing a string with the function's name (in which case, arguments to the proposal should be specified through the MCMC.prop.args argument to the relevant control function, or by giving it on the LHS of the hints formula to MCMC.prop argument to the control function. This will override the one chosen automatically.

Note that not all possible combinations of constraints and reference measures are supported. However, for relatively simple constraints (i.e., those that simply permit or forbid specific dyads or sets of dyads from changing), arbitrary combinations should be possible.

monitor

A one-sided formula specifying one or more terms whose value is to be monitored. If monitor is specified as a character (one of "formation", "dissolution", and "all") then the function .extract.fd.formulae is used to determine the corresponding formula; the user should be aware of its behavior and limitations.

time.slices

Number of time slices (or statistics) to return from each replication of the dynamic process. See below for return types. Defaults to 1, which, if time.burnin==0 and time.interval==1 (the defaults), advances the process one time step.

time.start

An optional argument specifying the time point at which the simulation is to start. See Details for further information.

time.burnin

Number of time steps to discard before starting to collect network statistics.

time.interval

Number of time steps between successive recordings of network statistics.

control

A list of control parameters for algorithm tuning. Constructed using control.simulate.tergm or control.simulate.formula.tergm. For backwards compatibility, control lists from control.simulate.stergm and control.simulate.network are allowed in calls to simulate.tergm; they are mapped to control.simulate.tergm by assigning:

• MCMC.prop.form to MCMC.prop,

• MCMC.prop.args.form to MCMC.prop.args,

• MCMC.prop.weights.form to MCMC.prop.weights.

output

A character vector specifying output type: one of "networkDynamic" (the default), "stats", "changes", "final", and "ergm_state", with partial matching allowed. See Value section for details.

nw.start

A specification for the starting network to be used by simulate.tergm, optional for EGMME fits, but required for CMLE and CMPLE fits:

a numeric index i

use ith time-point's network, where the first network in the series used to fit the model is defined to be at the first time point;

"first" or "last"

the first or last time point used in fitting the model; or

network

specify the network directly.

networkDynamics cannot be used as starting networks for simulate.tergm at this time. (They can be used as starting networks for simulate_formula.networkDynamic, of course.)

stats

Logical: Whether to return model statistics. This is not the recommended method: use monitor argument instead.

verbose

A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.

...

Further arguments passed to or used by methods.

time.offset

Argument specifying the offset between the point when the state of the network is sampled (time.start) and the the beginning of the spell that should be recorded for the newly simulated network state.

basis

For the network and networkDynamic methods, the network to start the simulation from. (If basis is missing, the default is the left hand side of the object argument.)

dynamic

Logical; if TRUE, dynamic simulation is performed in tergm; if FALSE (the default), ordinary ergm simulation is performed instead. Note that when dynamic=FALSE, default argument values for ergm's simulate methods are used.

Details

The dynamic process is run forward and the results are returned. For the method for networkDynamic, the simulation is resumed from the last generated time point of basis (or the left hand side of object if basis is missing), by default with the same model and parameters.

The starting network for the tergm object method (simulate.tergm) is determined by the nw.start argument.

• If time.start is specified, it is used as the initial time index of the simulation.

• If time.start is not specified (is NULL), then if the object carries a time stamp from which to start or resume the simulation, either in the form of a "time" network attribute (for the network method — see the lasttoggle "API") or in the form of an net.obs.period network attribute (for the networkDynamic method), this attribute will be used. (If specified, time.start will override it with a warning.)

• Othewise, the simulation starts at 0.

Value

Depends on the output argument:

"stats"

If stats == FALSE, an mcmc matrix with monitored statistics, and if stats == TRUE, a list containing elements stats for statistics specified in the monitor argument, and stats.gen for the model statistics. If stats == FALSE and no monitored statistics are specified, an empty list is returned, with a warning. When nsim>1, an mcmc.list (or list of them) of the statistics is returned instead.

"networkDynamic"

A networkDynamic object representing the simulated process, with ties present in the initial network having onset -Inf and ties present at the end of the simulation having terminus +Inf. The method for networkDynamic returns the initial networkDynamic with simulated changes applied to it. The net.obs.period network attribute is updated (or added if not existing) to reflect the time period that was simulated. If the network does not have any persistent.ids defined for vertices, a vertex.pid will be attached in a vertex attribute named 'tergm_pid' to facilitate 'bookkeeping' between the networkDynamic argument and the simulated network time step. Additionally, attributes (attr, not network attributes) are attached as follows:

formula, monitor:

Model and monitoring formulas used in the simulation, respectively.

stats, stats.gen:

Network statistics as above.

coef:

Coefficients used in the simulation.

changes:

A four-column matrix summarizing the changes in the "changes" output. (This may be removed in the future.)

When nsim>1, a network.list of these networkDynamics is returned.

"changes"

An integer matrix with four columns (time, tail, head, and to), giving the time-stamped changes relative to the current network. to is 1 if a tie was formed and 0 if a tie was dissolved. The convention for time is that it gives the time point during which the change is effective. For example, a row c(5,2,3,1) indicates that between time 4 and 5, a tie from node 2 to node 3 was formed, so that it was absent at time point 4 and present at time point 5; while a row c(5,2,3,0) indicates that in that time, that tie was dissolved, so that it is was present at time point 4 and absent at time point 5. Additionally, the same attributes (attr, not network attributes) as with output=="networkDynamic" are attached. When nsim>1, a list of these change matrices is returned.

"final"

A network object representing the last network in the series generated. lasttoggle and time attributes are also included. Additionally, the same attributes (attr, not network attributes) as with output=="networkDynamic" are attached. When nsim>1, a network.list of these networks is returned.

"ergm_state"

The ergm_state object resulting from the simulation. Attributes are attached as for other output types.

Note that when using simulate_formula.networkDynamic with either "final" or "ergm_state" for output, the nodes included in these objects are those produced by network.collapse at the start time.

Examples

data(samplk)

# Fit a transition from Time 1 to Time 2
samplk12 <- tergm(list(samplk1, samplk2)~
                  Form(~edges+mutual+transitiveties+cyclicalties)+
                  Diss(~edges+mutual+transitiveties+cyclicalties),
                  estimate="CMLE")

# direct simulation from tergm object
sim1 <- simulate(samplk12, nw.start="last")

# equivalent simulation from formula with network LHS;
# must pass dynamic=TRUE for tergm simulation
sim2 <- simulate(samplk2 ~ Form(~edges+mutual+transitiveties+cyclicalties) +
                           Diss(~edges+mutual+transitiveties+cyclicalties),
                           coef = coef(samplk12),
                           dynamic=TRUE)

# the default simulate output is a networkDynamic, and we can simulate
# with a networkDynamic LHS as well
sim3 <- simulate(sim2 ~ Form(~edges+mutual+transitiveties+cyclicalties) +
                        Diss(~edges+mutual+transitiveties+cyclicalties),
                        coef = coef(samplk12),
                        dynamic=TRUE)