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 = NVL(getOption("tergm.eval.loglik"), getOption("ergm.eval.loglik")),
  control = control.stergm(),
  verbose = FALSE,
  ...,
  SAN.offsets = NULL
)

Arguments

nw

A network object (for EGMME); or networkDynamic object, a network.list object, or a list containing networks (for CMLE and CMPLE).

stergm understands the lasttoggle "API".

formation, dissolution

One-sided ergm-style formulas for the formation and dissolution models, respectively. In stergm, the dissolution formula is parameterized in terms of tie persistence: negative coefficients imply lower rates of persistence and postive coefficients imply higher rates. The dissolution effects are simply the negation of these coefficients.

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.

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.

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. Note that at this time, the selected time points will be treated as temporally adjacent. Irregularly spaced time series are not supported at this time.

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. Any offset terms are used only during the preliminary SAN run; they are removed automatically for the EGMME proper. If targets is specified as a character (one of "formation" and "dissolution") then the function .extract.fd.formulae is used to determine the corresponding formula; the user should be aware of its behavior and limitations.

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. Can be set globally via option(tergm.eval.loglik=...), falling back to getOption("ergm.eval.loglik") if not set.

control

A list of control parameters for algorithm tuning. Constructed using control.stergm. Remapped to control.tergm.

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.

SAN.offsets

Offset coefficients (if any) to use during the SAN run.

Details

This function is included for backwards compatibility, and users are encouraged to use the new tergm family of functions instead.

The stergm function uses a pair of formulas, formation and dissolution to model tie-dynamics. The dissolution formula, however, is parameterized in terms of tie persistence: negative coefficients imply lower rates of persistence and postive coefficients imply higher rates. The dissolution effects are simply the negation of these coefficients, but the discrepancy between the terminology and interpretation has always been unfortunate, and we have fixed this in the new tergm function.

If you are making the transition from old stergm to new tergm, note that the dissolution formula in stergm maps to the new Persist() operator in the tergm function, NOT the Diss() operator.

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

Value

stergm returns an object of class tergm; see tergm() for details and methods.

References

Krivitsky P.N. and Handcock M.S. (2014) A Separable Model for Dynamic Networks. Journal of the Royal Statistical Society, Series B, 76(1): 29-46. doi: 10.1111/rssb.12014

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). https://web.archive.org/web/20170830053722/https://stat.psu.edu/research/technical-report-files/2012-technical-reports/TR1201A.pdf

See Also

ergm, network, \

Examples

## Not run: 
# 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)

## End(Not run)


# 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 4.0.2 Index]