control.ergm: Auxiliary for Controlling ERGM Fitting

View source: R/control.ergm.R

control.ergmR Documentation

Auxiliary for Controlling ERGM Fitting


Auxiliary function as user interface for fine-tuning 'ergm' fitting.


  drop = TRUE,
  init = NULL,
  init.method = NULL,
  main.method = c("MCMLE", "Stochastic-Approximation"),
  force.main = FALSE,
  main.hessian = TRUE,
  checkpoint = NULL,
  resume = NULL,
  MPLE.samplesize = .Machine$integer.max,
  init.MPLE.samplesize = function(d, e) max(sqrt(d), e, 40) * 8,
  MPLE.type = c("glm", "penalized", "logitreg"),
  MPLE.maxit = 10000,
  MPLE.nonvar = c("warning", "message", "error"),
  MPLE.nonident = c("warning", "message", "error"),
  MPLE.nonident.tol = 1e-10,
  MPLE.covariance.samplesize = 500,
  MPLE.covariance.method = "invHess",
  MPLE.covariance.sim.burnin = 1024,
  MPLE.covariance.sim.interval = 1024,
  MPLE.constraints.ignore = FALSE,
  MCMC.prop = trim_env(~sparse),
  MCMC.prop.weights = "default",
  MCMC.prop.args = list(),
  MCMC.interval = NULL,
  MCMC.burnin = EVL(MCMC.interval * 16),
  MCMC.samplesize = NULL,
  MCMC.effectiveSize = NULL,
  MCMC.effectiveSize.damp = 10,
  MCMC.effectiveSize.maxruns = 16,
  MCMC.effectiveSize.burnin.pval = 0.2,
  MCMC.effectiveSize.burnin.min = 0.05,
  MCMC.effectiveSize.burnin.max = 0.5,
  MCMC.effectiveSize.burnin.nmin = 16,
  MCMC.effectiveSize.burnin.nmax = 128,
  MCMC.effectiveSize.burnin.PC = FALSE,
  MCMC.effectiveSize.burnin.scl = 32,
  MCMC.effectiveSize.order.max = NULL,
  MCMC.return.stats = 2^12,
  MCMC.runtime.traceplot = FALSE,
  MCMC.maxedges = Inf, = TRUE,
  MCMC.packagenames = c(),
  SAN.maxit = 4,
  SAN.nsteps.times = 8,
  SAN = control.san(term.options = term.options, SAN.maxit = SAN.maxit, SAN.prop.weights
    = MCMC.prop.weights, SAN.prop.args = MCMC.prop.args, SAN.nsteps = EVL(MCMC.burnin,
    16384) * SAN.nsteps.times, SAN.samplesize = EVL(MCMC.samplesize, 1024),
    SAN.packagenames = MCMC.packagenames, parallel = parallel, parallel.type =
    parallel.type, parallel.version.check = parallel.version.check),
  MCMLE.termination = c("confidence", "Hummel", "Hotelling", "precision", "none"),
  MCMLE.maxit = 60,
  MCMLE.conv.min.pval = 0.5,
  MCMLE.confidence = 0.99,
  MCMLE.confidence.boost = 2,
  MCMLE.confidence.boost.threshold = 1,
  MCMLE.confidence.boost.lag = 4,
  MCMLE.NR.maxit = 100,
  MCMLE.NR.reltol = sqrt(.Machine$double.eps),
  obs.MCMC.mul = 1/4,
  obs.MCMC.samplesize.mul = sqrt(obs.MCMC.mul),
  obs.MCMC.samplesize = EVL(round(MCMC.samplesize * obs.MCMC.samplesize.mul)),
  obs.MCMC.effectiveSize = NVL3(MCMC.effectiveSize, . * obs.MCMC.mul),
  obs.MCMC.interval.mul = sqrt(obs.MCMC.mul),
  obs.MCMC.interval = EVL(round(MCMC.interval * obs.MCMC.interval.mul)),
  obs.MCMC.burnin.mul = sqrt(obs.MCMC.mul),
  obs.MCMC.burnin = EVL(round(MCMC.burnin * obs.MCMC.burnin.mul)),
  obs.MCMC.prop = MCMC.prop,
  obs.MCMC.prop.weights = MCMC.prop.weights,
  obs.MCMC.prop.args = MCMC.prop.args,
  obs.MCMC.impute.min_informative = function(nw) network.size(nw)/4,
  obs.MCMC.impute.default_density = function(nw) 2/network.size(nw),
  MCMLE.min.depfac = 2,
  MCMLE.sampsize.boost.pow = 0.5,
  MCMLE.MCMC.precision = if (startsWith("confidence", MCMLE.termination[1])) 0.1 else
  MCMLE.MCMC.max.ESS.frac = 0.1,
  MCMLE.metric = c("lognormal", "logtaylor", "Median.Likelihood", "EF.Likelihood",
  MCMLE.method = c("BFGS", "Nelder-Mead"),
  MCMLE.dampening = FALSE,
  MCMLE.dampening.min.ess = 20,
  MCMLE.dampening.level = 0.1,
  MCMLE.steplength.margin = 0.05,
  MCMLE.steplength = NVL2(MCMLE.steplength.margin, 1, 0.5),
  MCMLE.steplength.parallel = c("observational", "never"),
  MCMLE.sequential = TRUE,
  MCMLE.density.guard.min = 10000,
  MCMLE.density.guard = exp(3),
  MCMLE.effectiveSize = 64,
  obs.MCMLE.effectiveSize = NVL3(MCMLE.effectiveSize, . * obs.MCMC.mul),
  MCMLE.interval = 1024,
  MCMLE.burnin = MCMLE.interval * 16,
  MCMLE.samplesize.per_theta = 32,
  MCMLE.samplesize.min = 256,
  MCMLE.samplesize = NULL,
  obs.MCMLE.samplesize.per_theta = round(MCMLE.samplesize.per_theta *
  obs.MCMLE.samplesize.min = 256,
  obs.MCMLE.samplesize = NULL,
  obs.MCMLE.interval = round(MCMLE.interval * obs.MCMC.interval.mul),
  obs.MCMLE.burnin = round(MCMLE.burnin * obs.MCMC.burnin.mul),
  MCMLE.steplength.solver = c("glpk", "lpsolve"),
  MCMLE.last.boost = 4,
  MCMLE.steplength.esteq = TRUE,
  MCMLE.steplength.miss.sample = function(x1) ceiling(sqrt(ncol(rbind(x1)))),
  MCMLE.steplength.min = 1e-04,
  MCMLE.effectiveSize.interval_drop = 2,
  MCMLE.save_intermediates = NULL,
  MCMLE.nonvar = c("message", "warning", "error"),
  MCMLE.nonident = c("warning", "message", "error"),
  MCMLE.nonident.tol = 1e-10,
  SA.phase1_n = function(q, ...) max(200, 7 + 3 * q),
  SA.initial_gain = 0.1,
  SA.nsubphases = 4,
  SA.min_iterations = function(q, ...) (7 + q),
  SA.max_iterations = function(q, ...) (207 + q),
  SA.phase3_n = 1000,
  SA.interval = 1024,
  SA.burnin = SA.interval * 16,
  SA.samplesize = 1024,
  CD.samplesize.per_theta = 128,
  obs.CD.samplesize.per_theta = 128,
  CD.nsteps = 8,
  CD.multiplicity = 1,
  CD.nsteps.obs = 128,
  CD.multiplicity.obs = 1,
  CD.maxit = 60,
  CD.conv.min.pval = 0.5,
  CD.NR.maxit = 100,
  CD.NR.reltol = sqrt(.Machine$double.eps),
  CD.metric = c("naive", "lognormal", "logtaylor", "Median.Likelihood", "EF.Likelihood"),
  CD.method = c("BFGS", "Nelder-Mead"),
  CD.dampening = FALSE,
  CD.dampening.min.ess = 20,
  CD.dampening.level = 0.1,
  CD.steplength.margin = 0.5,
  CD.steplength = 1,
  CD.adaptive.epsilon = 0.01,
  CD.steplength.esteq = TRUE,
  CD.steplength.miss.sample = function(x1) ceiling(sqrt(ncol(rbind(x1)))),
  CD.steplength.min = 1e-04,
  CD.steplength.parallel = c("observational", "always", "never"),
  CD.steplength.solver = c("glpk", "lpsolve"),
  loglik = control.logLik.ergm(),
  term.options = NULL,
  seed = NULL,
  parallel = 0,
  parallel.type = NULL,
  parallel.version.check = TRUE,
  parallel.inherit.MT = FALSE,



Logical: If TRUE, terms whose observed statistic values are at the extremes of their possible ranges are dropped from the fit and their corresponding parameter estimates are set to plus or minus infinity, as appropriate. This is done because maximum likelihood estimates cannot exist when the vector of observed statistic lies on the boundary of the convex hull of possible statistic values.


numeric or NA vector equal in length to the number of parameters in the model or NULL (the default); the initial values for the estimation and coefficient offset terms. If NULL is passed, all of the initial values are computed using the method specified by control$init.method. If a numeric vector is given, the elements of the vector are interpreted as follows:

  • Elements corresponding to terms enclosed in offset() are used as the fixed offset coefficients. Note that offset coefficients alone can be more conveniently specified using ergm() argument offset.coef. If both offset.coef and init arguments are given, values in offset.coef will take precedence.

  • Elements that do not correspond to offset terms and are not NA are used as starting values in the estimation.

  • Initial values for the elements that are NA are fit using the method specified by control$init.method.

Passing control.ergm(init=coef( can be used to “resume” an uncoverged ergm() run, though checkpoint and 'resume' would be better under most circumstances.


A chatacter vector or NULL. The default method depends on the reference measure used. For the binary ("Bernoulli") ERGMs, with dyad-independent constraints, it's maximum pseudo-likelihood estimation (MPLE). Other valid values include "zeros" for a 0 vector of appropriate length and "CD" for contrastive divergence. If passed explicitly, this setting overrides the reference's limitations.

Valid initial methods for a given reference are set by the ⁠InitErgmReference.*⁠ function.


One of "MCMLE" (default) or "Stochastic-Approximation". Chooses the estimation method used to find the MLE. MCMLE attempts to maximize an approximation to the log-likelihood function. Stochastic-Approximation are both stochastic approximation algorithms that try to solve the method of moments equation that yields the MLE in the case of an exponential family model. The direct use of the likelihood function has many theoretical advantages over stochastic approximation, but the choice will depend on the model and data being fit. See Handcock (2000) and Hunter and Handcock (2006) for details.


Logical: If TRUE, then force MCMC-based estimation method, even if the exact MLE can be computed via maximum pseudolikelihood estimation.


Logical: If TRUE, then an approximate Hessian matrix is used in the MCMC-based estimation method.


At the start of every iteration, save the state of the optimizer in a way that will allow it to be resumed. The name is passed through sprintf() with iteration number as the second argument. (For example, checkpoint="step_%03d.RData" will save to step_001.RData, step_002.RData, etc.)


If given a file name of an RData file produced by checkpoint, the optimizer will attempt to resume after restoring the state. Control parameters from the saved state will be reused, except for those whose value passed via control.ergm() had change from the saved run. Note that if the network, the model, or some critical settings differ between runs, the results may be undefined.

MPLE.samplesize, init.MPLE.samplesize

These parameters control the maximum number of dyads (potential ties) that will be used by the MPLE to construct the predictor matrix for its logistic regression. In general, the algorithm visits dyads in a systematic sample that, if it does not hit one of these limits, will visit every informative dyad. If a limit is exceeded, case-control approximation to the likelihood, comprising all edges and those non-edges that have been visited by the algorithm before the limit was exceeded will be used.

MPLE.samplesize limits the number of dyads visited, unless the MPLE is being computed for the purpose of being the initial value for MCMC-based estimation, in which case init.MPLE.samplesize is used instead, All of these can be specified either as numbers or as ⁠function(d,e)⁠ taking the number of informative dyads and informative edges. Specifying or returning a larger number than the number of informative dyads is safe.


One of "glm", "penalized", or "logitreg". Chooses method of calculating MPLE. "glm" is the usual formal logistic regression called via glm, whereas "penalized" uses the bias-reduced method of Firth (1993) as originally implemented by Meinhard Ploner, Daniela Dunkler, Harry Southworth, and Georg Heinze in the "logistf" package. "logitreg" is an "in-house" implementation that is slower and probably less stable but supports nonlinear logistic regression. It is invoked automatically when the model has curved terms.


Maximum number of iterations for "logitreg" implementation of MPLE.

MPLE.nonident, MPLE.nonident.tol, MPLE.nonvar, MCMLE.nonident, MCMLE.nonident.tol, MCMLE.nonvar

A rudimentary nonidentifiability/multicollinearity diagnostic. If MPLE.nonident.tol > 0, test the MPLE covariate matrix or the CD statistics matrix has linearly dependent columns via QR decomposition with tolerance MPLE.nonident.tol. This is often (not always) indicative of a non-identifiable (multicollinear) model. If nonidentifiable, depending on MPLE.nonident issue a warning, an error, or a message specifying the potentially redundant statistics. Before the diagnostic is performed, covariates that do not vary (i.e., all-zero columns) are dropped, with their handling controlled by MPLE.nonvar. The corresponding ⁠MCMLE.*⁠ arguments provide a similar diagnostic for the unconstrained MCMC sample's estimating functions.

MPLE.covariance.method, MPLE.covariance.samplesize, MPLE.covariance.sim.burnin, MPLE.covariance.sim.interval

Controls for estimating the MPLE covariance matrix. ⁠MPLE.covariance method⁠ determines the method, with invHess (the default) returning the covariance estimate obtained from the glm(). Godambe estimates the covariance matrix using the Godambe-matrix \insertCiteScHu23cergm. This method is recommended for dyad-dependent models. Alternatively, bootstrap estimates standard deviations using a parametric bootstrapping approach \insertCite@see @ScDe17eergm. The other parameters control, respectively, the number of networks to simulate, the MCMC burn-in, and the MCMC interval for Godambe and bootstrap methods.


If TRUE, MPLE will ignore all dyad-independent constraints except for those due to attributes missingness. This can be used to avert evaluating and storing the rlebdms for very large networks except where absolutely necessary. Note that this can be very dangerous unless you know what you are doing.


Specifies the proposal (directly) and/or a series of "hints" about the structure of the model being sampled. The specification is in the form of a one-sided formula with hints separated by + operations. If the LHS exists and is a string, the proposal to be used is selected directly.

A common and default "hint" is ~sparse, indicating that the network is sparse and that the sample should put roughly equal weight on selecting a dyad with or without a tie as a candidate for toggling.


Specifies the proposal distribution used in the MCMC Metropolis-Hastings algorithm. Possible choices depending on selected reference and constraints arguments of the ergm() function, but often include "TNT" and "random", and the "default" is to use the one with the highest priority available.


An alternative, direct way of specifying additional arguments to proposal.


Number of proposals between sampled statistics. Increasing interval will reduces the autocorrelation in the sample, and may increase the precision in estimates by reducing MCMC error, at the expense of time. Set the interval higher for larger networks.


Number of proposals before any MCMC sampling is done. It typically is set to a fairly large number.


Number of network statistics, randomly drawn from a given distribution on the set of all networks, returned by the Metropolis-Hastings algorithm. Increasing sample size may increase the precision in the estimates by reducing MCMC error, at the expense of time. Set it higher for larger networks, or when using parallel functionality.

MCMC.effectiveSize, MCMC.effectiveSize.damp, MCMC.effectiveSize.maxruns, MCMC.effectiveSize.burnin.pval, MCMC.effectiveSize.burnin.min, MCMC.effectiveSize.burnin.max, MCMC.effectiveSize.burnin.nmin, MCMC.effectiveSize.burnin.nmax, MCMC.effectiveSize.burnin.PC, MCMC.effectiveSize.burnin.scl, MCMC.effectiveSize.order.max

Set MCMC.effectiveSize to a non-NULL value to adaptively determine the burn-in and the MCMC length needed to get the specified effective size; 50 is a reasonable value. In the adaptive MCMC mode, MCMC is run forward repeatedly (MCMC.samplesize*MCMC.interval steps, up to MCMC.effectiveSize.maxruns times) until the target effective sample size is reached or exceeded.

After each run, the returned statistics are mapped to the estimating function scale, then an exponential decay model is fit to the scaled statistics to find that burn-in which would reduce the difference between the initial values of statistics and their equilibrium values by a factor of MCMC.effectiveSize.burnin.scl of what it initially was, bounded by MCMC.effectiveSize.min and MCMC.effectiveSize.max as proportions of sample size. If the best-fitting decay exceeds MCMC.effectiveSize.max, the exponential model is considered to be unsuitable and MCMC.effectiveSize.min is used.

A Geweke diagnostic is then run, after thinning the sample to MCMC.effectiveSize.burnin.nmax. If this Geweke diagnostic produces a p-value higher than MCMC.effectiveSize.burnin.pval, it is accepted.

If MCMC.effectiveSize.burnin.PC>0, instead of using the full sample for burn-in estimation, at most this many principal components are used instead.

The effective size of the post-burn-in sample is computed via Vats, Flegal, and Jones (2015), and compared to the target effective size. If it is not matched, the MCMC run is resumed, with the additional draws needed linearly extrapolated but weighted in favor of the baseline MCMC.samplesize by the weighting factor MCMC.effectiveSize.damp (higher = less damping). Lastly, if after an MCMC run, the number of samples equals or exceeds 2*MCMC.samplesize, the chain will be thinned by 2 until it falls below that, while doubling MCMC.interval. MCMC.effectiveSize.order.max can be used to set the order of the AR model used to estimate the effective sample size and the variance for the Geweke diagnostic.


Numeric: If positive, include an mcmc.list (two, if observational process was involved) of MCMC network statistics from the last iteration of network of the estimation. They will be thinned to have length of at most MCMC.return.stats. They are used for MCMC diagnostics.


Logical: If TRUE, plot traceplots of the MCMC sample after every MCMC MLE iteration.


The maximum number of edges that may occur during the MCMC sampling. If this number is exceeded at any time, sampling is stopped immediately.

Whether to add the standard errors induced by the MCMC algorithm to the estimates' standard errors.


Names of packages in which to look for change statistic functions in addition to those autodetected. This argument should not be needed outside of very strange setups.


When target.stats argument is passed to ergm(), the maximum number of attempts to use san to obtain a network with statistics close to those specified.


Multiplier for SAN.nsteps relative to MCMC.burnin. This lets one control the amount of SAN burn-in (arguably, the most important of SAN parameters) without overriding the other SAN defaults.


Control arguments to san. See control.san for details.


The criterion used for terminating MCMLE estimation:

  • "Hummel" Terminate when the Hummel step length is 1 for two consecutive iterations. For the last iteration, the sample size is boosted by a factor of MCMLE.last.boost. See Hummel et. al. (2012).

Note that this criterion is incompatible with MCMLE.steplength \ne 1 or MCMLE.steplength.margin = NULL.

  • "Hotelling" After every MCMC sample, an autocorrelation-adjusted Hotelling's T^2 test for equality of MCMC-simulated network statistics to observed is conducted, and if its P-value exceeds MCMLE.conv.min.pval, the estimation is considered to have converged and finishes. This was the default option in ergm version 3.1.

  • "precision" Terminate when the estimated loss in estimating precision due to using MCMC standard errors is below the precision bound specified by MCMLE.MCMC.precision, and the Hummel step length is 1 for two consecutive iterations. See MCMLE.MCMC.precision for details. This feature is in experimental status until we verify the coverage of the standard errors.

Note that this criterion is incompatible with \code{MCMLE.steplength}\ne 1 or \code{MCMLE.steplength.margin}=\code{NULL}.

  • "confidence": Performs an equivalence test to prove with level of confidence MCMLE.confidence that the true value of the deviation of the simulated mean value parameter from the observed is within an ellipsoid defined by the inverse-variance-covariance of the sufficient statistics multiplied by a scaling factor control$MCMLE.MCMC.precision (which has a different default).

  • "none" Stop after MCMLE.maxit iterations.


Maximum number of times the parameter for the MCMC should be updated by maximizing the MCMC likelihood. At each step the parameter is changed to the values that maximizes the MCMC likelihood based on the current sample.


The P-value used in the Hotelling test for early termination.


The confidence level for declaring convergence for "confidence" methods.


The maximum increase factor in sample size (or target effective size, if enabled) when the "confidence" termination criterion is either not approaching the tolerance region or is unable to prove convergence.

MCMLE.confidence.boost.threshold, MCMLE.confidence.boost.lag

Sample size or target effective size will be increaed if the distance from the tolerance region fails to decrease more than MCMLE.confidence.boost.threshold in this many successive iterations.

MCMLE.NR.maxit, MCMLE.NR.reltol

The method, maximum number of iterations and relative tolerance to use within the optim rountine in the MLE optimization. Note that by default, ergm uses trust, and falls back to optim only when trust fails.

obs.MCMC.prop, obs.MCMC.prop.weights, obs.MCMC.prop.args, obs.MCMLE.effectiveSize, obs.MCMC.samplesize, obs.MCMC.burnin, obs.MCMC.interval, obs.MCMC.mul, obs.MCMC.samplesize.mul, obs.MCMC.burnin.mul, obs.MCMC.interval.mul, obs.MCMC.effectiveSize, obs.MCMLE.burnin, obs.MCMLE.interval, obs.MCMLE.samplesize, obs.MCMLE.samplesize.per_theta, obs.MCMLE.samplesize.min

Corresponding MCMC parameters and settings used for the constrained sample when unobserved data are present in the estimation routine. By default, they are controlled by the ⁠*.mul⁠ parameters, as fractions of the corresponding settings for the unconstrained (standard) MCMC.

These can, in turn, be controlled by obs.MCMC.mul, which can be used to set the overal multiplier for the number of MCMC steps in the constrained sample; one half of its effect applies to the burn-in and interval and the other half to the total sample size. For example, for obs.MCMC.mul=1/4 (the default), obs.MCMC.samplesize is set to \sqrt{1/4}=1/2 that of obs.MCMC.samplesize, and obs.MCMC.burnin and obs.MCMC.interval are set to \sqrt{1/4}=1/2 of their respective unconstrained sampling parameters. When MCMC.effectiveSize or MCMLE.effectiveSize are given, their corresponding obs parameters are set to them multiplied by obs.MCMC.mul.

obs.MCMC.impute.min_informative, obs.MCMC.impute.default_density

Controls for imputation of missing dyads for initializing MCMC sampling. If numeric, obs.MCMC.impute.min_informative specifies the minimum number dyads that need to be non-missing before sample network density is used as the imputation density. It can also be specified as a function that returns this value. obs.MCMC.impute.default_density similarly controls the imputation density when number of non-missing dyads is too low.

MCMLE.min.depfac, MCMLE.sampsize.boost.pow

When using adaptive MCMC effective size, and methods that increase the MCMC sample size, use MCMLE.sampsize.boost.pow as the power of the boost amount (relative to the boost of the target effective size), but ensure that sample size is no less than MCMLE.min.depfac times the target effective size.

MCMLE.MCMC.precision, MCMLE.MCMC.max.ESS.frac

MCMLE.MCMC.precision is a vector of upper bounds on the standard errors induced by the MCMC algorithm, expressed as a percentage of the total standard error. The MCMLE algorithm will terminate when the MCMC standard errors are below the precision bound, and the Hummel step length is 1 for two consecutive iterations. This is an experimental feature.

If effective sample size is used (see MCMC.effectiveSize), then ergm may increase the target ESS to reduce the MCMC standard error.


Method to calculate the loglikelihood approximation. See Hummel et al (2010) for an explanation of "lognormal" and "naive".


Deprecated. By default, ergm uses trust, and falls back to optim with Nelder-Mead method when trust fails.


(logical) Should likelihood dampening be used?


The effective sample size below which dampening is used.


The proportional distance from boundary of the convex hull move.


The extra margin required for a Hummel step to count as being inside the convex hull of the sample. Set this to 0 if the step length gets stuck at the same value over several iteraions. Set it to NULL to use fixed step length. Note that this parameter is required to be non-NULL for MCMLE termination using Hummel or precision criteria.


Multiplier for step length (on the mean-value parameter scale), which may (for values less than one) make fitting more stable at the cost of computational efficiency.

If MCMLE.steplength.margin is not NULL, the step length will be set using the algorithm of Hummel et al. (2010). In that case, it will serve as the maximum step length considered. However, setting it to anything other than 1 will preclude using Hummel or precision as termination criteria.


Whether parallel multisection search (as opposed to a bisection search) for the Hummel step length should be used if running in multiple threads. Possible values (partially matched) are "never", and (default) "observational" (i.e., when missing data MLE is used).


Logical: If TRUE, the next iteration of the fit uses the last network sampled as the starting network. If FALSE, always use the initially passed network. The results should be similar (stochastically), but the TRUE option may help if the target.stats in the ergm() function are far from the initial network.

MCMLE.density.guard.min, MCMLE.density.guard

A simple heuristic to stop optimization if it finds itself in an overly dense region, which usually indicates ERGM degeneracy: if the sampler encounters a network configuration that has more than MCMLE.density.guard.min edges and whose number of edges is exceeds the observed network by more than MCMLE.density.guard, the optimization process will be stopped with an error.

MCMLE.effectiveSize, MCMLE.effectiveSize.interval_drop, MCMLE.burnin, MCMLE.interval, MCMLE.samplesize, MCMLE.samplesize.per_theta, MCMLE.samplesize.min

Sets the corresponding ⁠MCMC.*⁠ parameters when main.method="MCMLE" (the default). Used because defaults may be different for different methods. MCMLE.samplesize.per_theta controls the MCMC sample size (not target effective size) as a function of the number of (curved) parameters in the model, and MCMLE.samplesize.min sets the minimum sample size regardless of their number.


The linear program solver to use for MCMLE step length calculation. Can be either "glpk" to use Rglpk or "lpsolve" to use lpSolveAPI. Rglpk can be orders of magnitude faster, particularly for models with many parameters and with large sample sizes, so it is used where available; but it requires an external library to install under some operating systems, so fallback to lpSolveAPI provided.


For the Hummel termination criterion, increase the MCMC sample size of the last iteration by this factor.


For curved ERGMs, should the estimating function values be used to compute the Hummel step length? This allows the Hummel stepping algorithm converge when some sufficient statistics are at 0.


In fitting the missing data MLE, the rules for step length become more complicated. In short, it is necessary for all points in the constrained sample to be in the convex hull of the unconstrained (though they may be on the border); and it is necessary for their centroid to be in its interior. This requires checking a large number of points against whether they are in the convex hull, so to speed up the procedure, a sample is taken of the points most likely to be outside it. This parameter specifies the sample size or a function of the unconstrained sample matrix to determine the sample size.


Stops MCMLE estimation when the step length gets stuck below this minimum value.


Every iteration, after MCMC sampling, save the MCMC sample and some miscellaneous information to a file with this name. This is mainly useful for diagnostics and debugging. The name is passed through sprintf() with iteration number as the second argument. (For example, MCMLE.save_intermediates="step_%03d.RData" will save to step_001.RData, step_002.RData, etc.)


A constant or a function of number of free parameters q, number of free canonical statistic p, and network size n, giving the number of MCMC samples to draw in Phase 1 of the stochastic approximation algorithm. Defaults to \max(200, 7+3p). See Snijders (2002) for details.


Initial gain to Phase 2 of the stochastic approximation algorithm. Defaults to 0.1. See Snijders (2002) for details.


Number of sub-phases in Phase 2 of the stochastic approximation algorithm. Defaults to MCMLE.maxit. See Snijders (2002) for details.

SA.min_iterations, SA.max_iterations

A constant or a function of number of free parameters q, number of free canonical statistic p, and network size n, giving the baseline numbers of iterations within each subphase of Phase 2 of the stochastic approximation algorithm. Default to 7+p and 207+p, respectively. See Snijders (2002) for details.


Sample size for the MCMC sample in Phase 3 of the stochastic approximation algorithm. See Snijders (2002) for details.

SA.burnin, SA.interval, SA.samplesize

Sets the corresponding ⁠MCMC.*⁠ parameters when main.method="Stochastic-Approximation".

CD.samplesize.per_theta, obs.CD.samplesize.per_theta, CD.maxit, CD.conv.min.pval, CD.NR.maxit, CD.NR.reltol, CD.metric, CD.method, CD.dampening, CD.dampening.min.ess, CD.dampening.level, CD.steplength.margin, CD.steplength, CD.steplength.parallel, CD.adaptive.epsilon, CD.steplength.esteq, CD.steplength.miss.sample, CD.steplength.min, CD.steplength.solver

Miscellaneous tuning parameters of the CD sampler and optimizer. These have the same meaning as their ⁠MCMLE.*⁠ and ⁠MCMC.*⁠ counterparts.

Note that only the Hotelling's stopping criterion is implemented for CD.

CD.nsteps, CD.multiplicity

Main settings for contrastive divergence to obtain initial values for the estimation: respectively, the number of Metropolis–Hastings steps to take before reverting to the starting value and the number of tentative proposals per step. Computational experiments indicate that increasing CD.multiplicity improves the estimate faster than increasing CD.nsteps — up to a point — but it also samples from the wrong distribution, in the sense that while as CD.nsteps\rightarrow\infty, the CD estimate approaches the MLE, this is not the case for CD.multiplicity.

In practice, MPLE, when available, usually outperforms CD for even a very high CD.nsteps (which is, in turn, not very stable), so CD is useful primarily when MPLE is not available. This feature is to be considered experimental and in flux.

The default values have been set experimentally, providing a reasonably stable, if not great, starting values.

CD.nsteps.obs, CD.multiplicity.obs

When there are missing dyads, CD.nsteps and CD.multiplicity must be set to a relatively high value, as the network passed is not necessarily a good start for CD. Therefore, these settings are in effect if there are missing dyads in the observed network, using a higher default number of steps.


See control.ergm.bridge


A list of additional arguments to be passed to term initializers. See ? term.options.


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


Number of threads in which to run the sampling. Defaults to 0 (no parallelism). See the entry on parallel processing for details and troubleshooting.


API to use for parallel processing. Supported values are "MPI" and "PSOCK". Defaults to using the parallel package with PSOCK clusters. See ergm-parallel


Logical: If TRUE, check that the version of ergm running on the slave nodes is the same as that running on the master node.


Logical: If TRUE, slave nodes and processes inherit the set.MT_terms() setting.


A dummy argument to catch deprecated or mistyped control parameters.


This function is only used within a call to the ergm() function. See the usage section in ergm() for details.


A list with arguments as components.


  • Snijders, T.A.B. (2002), Markov Chain Monte Carlo Estimation of Exponential Random Graph Models. Journal of Social Structure. Available from

  • Firth (1993), Bias Reduction in Maximum Likelihood Estimates. Biometrika, 80: 27-38.

  • Hunter, D. R. and M. S. Handcock (2006), Inference in curved exponential family models for networks. Journal of Computational and Graphical Statistics, 15: 565-583.

  • Hummel, R. M., Hunter, D. R., and Handcock, M. S. (2012), Improving Simulation-Based Algorithms for Fitting ERGMs, Journal of Computational and Graphical Statistics, 21: 920-939.

  • Kristoffer Sahlin. Estimating convergence of Markov chain Monte Carlo simulations. Master's Thesis. Stockholm University, 2011.

See Also

ergm(). The control.simulate function performs a similar function for simulate.ergm; control.gof performs a similar function for gof.

ergm documentation built on May 31, 2023, 8:04 p.m.