R: Draw from the distribution of an Exponential Family Random...

simulate.ergm {ergm}

R Documentation

Draw from the distribution of an Exponential Family Random Graph Model

Description

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

Usage

## S3 method for class 'formula'
simulate(object, nsim=1, seed=NULL,
                           coef, 
                           response=NULL, reference=~Bernoulli,
                           constraints=~.,
                           monitor=NULL,
                           basis=NULL,
                           statsonly=FALSE,
                           esteq=FALSE,
                           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,
                        statsonly=FALSE,
                        esteq=FALSE,
                        sequential=TRUE,
                        control=control.simulate.ergm(),
                        verbose=FALSE, 
                        ...)

Arguments

`object`	an R 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 R, 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`	Random number integer seed. See `set.seed`.
`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`	EXPERIMENTAL. Name of the edge attribute whose value is to be modeled. Defaults to `NULL` for simple presence or absence, modeled via binary ERGM terms. Passing anything but `NULL` uses valued ERGM terms.
`reference`	EXPERIMENTAL. A one-sided formula specifying the reference measure (h(y)) to be used. (Defaults to `~Bernoulli`.) 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.
`basis`	An optional `network` object to start the Markov chain. If omitted, the default is the left-hand-side of the `formula`. If neither a left-hand-side nor a `basis` is present, an error results because the characteristics of the network (e.g., size and directedness) must be specified.
`statsonly`	Logical: If TRUE, return only the network statistics, not the network(s) themselves.
`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.
`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.
`...`	Further arguments passed to or used by methods.

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 + interval 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 statsonly==TRUE a matrix containing the simulated network statistics. If control$parallel>0, the statistics from each Markov chain are stacked.

Otherwise, 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 following attr-style attributes on the list:

`formula`	The `formula` used to generate the sample.
`stats`	The \code{nsim}\times p matrix of network statistics, where p is the number of network statistics specified in the model.
`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.

If statsonly==FALSE && control$parallel>0 the returned networks are "interleaved", in the sense that for y[i,j] is the jth network from MCMC chain i, the sequence returned if control$parallel==2 is list(y[1,1], y[2,1], y[1,2], y[2,2], y[1,3], y[2,3], ...). This is different from the behavior when statsonly==TRUE. This detail may change in the future.

This object has summary and print methods.

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 (satatistics only), and observe the number
# of triangles as well.
#
g.sim <- simulate(gest, nsim=10, 
            monitor=~triangles, statsonly=TRUE,
            control=control.simulate.ergm(MCMC.burnin=1000, MCMC.interval=100))
g.sim

[Package ergm version 3.4.0 Index]