R: Separable Temporal Exponential Family Random Graph Models

stergm {tergm} | R Documentation

## Separable Temporal Exponential Family Random Graph Models

### Description

`stergm` is used for finding Separable Temporal ERGMs' (STERGMs) Conditional MLE (CMLE) (Krivitsky and Handcock, 2010) and Equilibrium Generalized Method of Moments Estimator (EGMME) (Krivitsky, 2009).

### Usage

      stergm (nw,
              formation,
              dissolution,
              constraints = ~.,
              estimate,
              times=NULL,
              offset.coef.form=NULL,
              offset.coef.diss=NULL,
              targets=NULL,
              target.stats=NULL,
              eval.loglik=TRUE,
              control=control.stergm(),
              verbose=FALSE,
              ...)

### Arguments

`nw` | A `network` object (for EGMME); or `networkDynamic` object, a `network.list` object, or a `list` containing networks (for CMLE and CMPLE). `simulate.network` understands the `lasttoggle` "API".
`formation, dissolution` | One-sided `ergm`-style formulas for the formation and dissolution models, respectively.
`constraints` | A one-sided formula specifying one or more constraints on the support of the distribution of the networks being modeled, using syntax similar to the `formula` argument. Multiple constraints may be given, separated by “+” operators. 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 by passing a string with the function's name. In that case, arguments to the proposal should be specified through the `prop.args` argument to `control.ergm`. The default is `~.`, for an unconstrained model. See the ERGM constraints documentation for the constraints implemented in the `ergm` package. Other packages may add their own constraints. For STERGMs in particular, the constraints apply to the post-formation and the post-dissolution network, rather than the final network. This means, for example, that if the degree of all vertices is constrained to be less than or equal to three, and a vertex begins a time step with three edges, then, even if one of its edges is dissolved during its time step, it won't be able to form another edge until the next time step. This behavior may change in the future. Note that not all possible combinations of constraints are supported.
`estimate` | One of "EGMME" for Equilibrium Generalized Method of Moments Estimation, based on a single network with some temporal information and making an assumption that it is a product of a STERGM process running to its stationary (equilibrium) distribution; "CMLE" for Conditional Maximum Likelihood Estimation, modeling a transition between two networks, or "CMPLE" for Conditional Maximum PseudoLikelihood Estimation, using MPLE instead of MLE. CMPLE is extremely inaccurate at this time.
`times` | For CMLE and CMPLE estimation, times or indexes at which the networks whose transition is to be modeled are observed. Default to `c(0,1)` if `nw` is a `networkDynamic` and to `1:length(nw)` (all transitions) if `nw` is a `network.list` or a `list`. Unused for EGMME.
`offset.coef.form` | Numeric vector to specify offset formation parameters.
`offset.coef.diss` | Numeric vector to specify offset dissolution parameters.
`targets` | One-sided `ergm`-style formula specifying statistics whose moments are used for the EGMME. Unused for CMLE and CMPLE. Targets is required for EGMME estimation. It may contain any valid ergm terms. If specified as "formation" or "dissolution", it copies the formula from the respective model. Any offset terms are removed automatically.
`target.stats` | A vector specifying the values of the `targets` statistics that EGMME will try to match. Defaults to the statistics of `nw`. Unused for CMLE and CMPLE.
`eval.loglik` | Whether or not to calculate the log-likelihood of a CMLE STERGM fit. See `ergm` for details.
`control` | A list of control parameters for algorithm tuning. Constructed using `control.stergm`.
`verbose` | logical or integer; if TRUE or positive, the program will print out progress information. Higher values result in more output.
`...` | Additional arguments, to be passed to lower-level functions.

### Details

Model Terms See `ergm` and `ergm-terms` for details. At this time, only linear ERGM terms are allowed.

- For a brief demonstration, please see the tergm package vignette: `browseVignettes(package='tergm')`

- A more detailed tutorial is avalible on the statnet wiki: http://statnet.csde.washington.edu/workshops/SUNBELT/current/tergm/tergm_tutorial.pdf

- For more usage examples, see the wiki page at https://statnet.csde.washington.edu/trac/wiki/tergmUsage

### Value

`stergm` returns an object of class `stergm` that is a list consisting of the following elements:

`formation, dissolution`

  Formation and dissolution formulas, respectively.

`targets`

  The targets formula.

`target.stats`

  The target statistics.

`estimate`

  The type of estimate.

`opt.history`

  A matrix containing the full trace of the EGMME optimization process: coefficients tried and target statistics simulated.

`sample`

  An `mcmc` object containing target statistics sampled at the estimate.

`covar`

  The full estimated variance-covariance matrix of the parameter estimates for EGMME. (Note that although the CMLE formation parameter estimates are independent of the dissolution parameter estimates due to the separability assumption, this is not necessarily the case for EGMME.)

`formation.fit, dissolution.fit`

  For CMLE and CMPLE, `ergm` objects from fitting formation and dissolution, respectively. For EGMME, stripped down `ergm`-like lists.

`network`

  For `estimate=="EGMME"`, the original network; for `estimate=="CMLE"` or `estimate=="CMPLE"`, a `network.list` (a discrete series of networks) to which the model was fit.

`control`

  The control parameters used to fit the model.

See the method `print.stergm` for details on how an `stergm` object is printed. Note that the method `summary.stergm` returns a summary of the relevant parts of the `stergm` object in concise summary format.

### References

- Krivitsky PN, Handcock MS (2010). A Separable Model for Dynamic Networks. http://arxiv.org/abs/1011.1937

- Krivitsky, P.N. (2012). Modeling of Dynamic Networks based on Egocentric Data with Durational Information. Pennsylvania State University Department of Statistics Technical Report, 2012(2012-01). http://stat.psu.edu/research/technical-report-files/2012-technical-reports/modeling-of-dynamic-networks-based-on-egocentric-data-with-durational-information

### See Also

ergm, network, %v%, %n%, `ergm-terms`

### Examples

    # EGMME Example
    par(ask=FALSE)
    n<-30
    g0<-network.initialize(n,dir=FALSE)

    #                     edges, degree(1), mean.age
    target.stats<-c(      n*1/2,    n*0.6,        20)

    dynfit<-stergm(g0,formation = ~edges+degree(1), dissolution = ~edges,
                   targets = ~edges+degree(1)+mean.age,
                   target.stats=target.stats, estimate="EGMME",
                   control=control.stergm(SA.plot.progress=TRUE))

    par(ask=TRUE)
    mcmc.diagnostics(dynfit)
    summary(dynfit)

    # CMLE Example
    data(samplk)

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

    mcmc.diagnostics(samplk12)
    summary(samplk12)

    # Fit a transition from Time 1 to Time 2 and from Time 2 to Time 3 jointly
    samplk123 <- stergm(list(samplk1, samplk2, samplk3),
                        formation=~edges+mutual+transitiveties+cyclicalties,
                        dissolution=~edges+mutual+transitiveties+cyclicalties,
                        estimate="CMLE")

    mcmc.diagnostics(samplk123)
    summary(samplk123)

[Package tergm version 3.4.1 Index]