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. 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 = ~.,
      observational = FALSE,
      monitor = NULL,
      statsonly = FALSE,
      esteq = FALSE,
      output = c("network", "stats", "edgelist", "ergm_state"),
      simplify = TRUE,
      sequential = TRUE,
      control = control.simulate.formula(),
      verbose = FALSE,
      ...,
      basis = ergm.getnetwork(object),
      do.sim = NULL,
      return.args = NULL
    )

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

    ## S3 method for class 'ergm_model'
    simulate(
      object,
      nsim = 1,
      seed = NULL,
      coef,
      reference = if (is(constraints, "ergm_proposal")) NULL else trim_env(~Bernoulli),
      constraints = trim_env(~.),
      observational = FALSE,
      monitor = NULL,
      basis = NULL,
      esteq = FALSE,
      output = c("network", "stats", "edgelist", "ergm_state"),
      simplify = TRUE,
      sequential = TRUE,
      control = control.simulate.formula(),
      verbose = FALSE,
      ...,
      do.sim = NULL,
      return.args = NULL
    )

    ## S3 method for class 'ergm_state_full'
    simulate(
      object,
      nsim = 1,
      seed = NULL,
      coef,
      esteq = FALSE,
      output = c("network", "stats", "edgelist", "ergm_state"),
      simplify = TRUE,
      sequential = TRUE,
      control = control.simulate.formula(),
      verbose = FALSE,
      ...,
      return.args = NULL
    )

    ## S3 method for class 'ergm'
    simulate(
      object,
      nsim = 1,
      seed = NULL,
      coef = coefficients(object),
      response = object$network %ergmlhs% "response",
      reference = object$reference,
      constraints = list(object$constraints, object$obs.constraints),
      observational = FALSE,
      monitor = NULL,
      basis = object$newnetwork,
      statsonly = FALSE,
      esteq = FALSE,
      output = c("network", "stats", "edgelist", "ergm_state"),
      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 `ergmTerm`. 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. Can be set to `NULL` to bypass, but only if `return.args` below is used.
`response` | Either a character string, a formula, or `NULL` (the default), to specify the response attributes and whether the ERGM is binary or valued. Interpreted as follows: `NULL` Model simple presence or absence, via a binary ERGM. character string The name of the edge attribute whose value is to be modeled. Type of ERGM will be determined by whether the attribute is `logical` (`TRUE`/`FALSE`) for binary or `numeric` for valued. a formula must be of the form `NAME~EXPR|TYPE` (with `|` being literal). `EXPR` is evaluated in the formula's environment with the network's edge attributes accessible as variables. The optional `NAME` specifies the name of the edge attribute into which the results should be stored, with the default being a concise version of `EXPR`. Normally, the type of ERGM is determined by whether the result of evaluating `EXPR` is logical or numeric, but the optional `TYPE` can be used to override by specifying a scalar of the type involved (e.g., `TRUE` for binary and `1` for valued).
`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.
`observational` | Inherit observational constraints rather than model constraints.
`monitor` | A one-sided formula specifying one or more terms whose value is to be monitored. These terms are appended 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 `"ergm_state"`: determines the output format. Partial matching is performed. Alternatively, a function with prototype `function(ergm_state, 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, typically constructed with `control.simulate.ergm()` or `control.simulate.formula()`, which have different defaults. Their documentation gives the the list of recognized control parameters and their meaning. The more generic utility `snctrl()` (StatNet ConTRoL) also provides argument completion for the available control functions and limited argument name checking.
`verbose` | A logical or an integer to control the amount of progress and diagnostic information to be printed. `FALSE`/`0` produces minimal output, wit higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
`do.sim` | Logical; a deprecated interface superseded by `return.args`, that saves the inputs to the next level of the function.
`return.args` | Character; if not `NULL`, the `simulate` method for that particular class will, instead of proceeding for simulation, instead return its arguments as a list that can be passed as a second argument to `do.call()` or a lower-level function such as `ergm_MCMC_sample()`. This can be useful if, for example, one wants to run several simulations with varying coefficients and does not want to reinitialize the model and the proposal every time. Valid inputs at this time are `"formula"`, "ergm_model", and one of the `"ergm_state"` classes, for the three respective stopping points.

### 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`.

`"ergm_state"`

  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.

### Functions

- `simulate.ergm_state_full`: a low-level function to simulate from an `ergm_state` object.

### 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.

### See Also

`ergm`, `network`, `ergm_MCMC_sample()` for a demonstration of `return.args=`.

### 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)

[Package ergm version 4.2.1 Index]