Auxiliary function as user interface for fine-tuning 'ergm' fitting.
control.ergm(drop = TRUE, init = NULL, init.method = NULL,
main.method = c("MCMLE", "Robbins-Monro", "Stochastic-Approximation",
"Stepping"), force.main = FALSE, main.hessian = TRUE,
MPLE.max.dyad.types = 1e+06, MPLE.samplesize = 50000,
MPLE.type = c("glm", "penalized"), MCMC.prop.weights = "default",
MCMC.prop.args = list(), MCMC.interval = 1024,
MCMC.burnin = MCMC.interval * 16, MCMC.samplesize = 1024,
MCMC.effectiveSize = NULL, MCMC.effectiveSize.damp = 10,
MCMC.effectiveSize.maxruns = 1000, MCMC.effectiveSize.base = 1/2,
MCMC.effectiveSize.points = 5, MCMC.effectiveSize.order = 1,
MCMC.return.stats = TRUE, MCMC.runtime.traceplot = FALSE,
MCMC.init.maxedges = 20000, MCMC.max.maxedges = Inf,
MCMC.addto.se = TRUE, MCMC.compress = FALSE,
MCMC.packagenames = c(), SAN.maxit = 10, SAN.burnin.times = 10,
SAN.control = control.san(coef = init, term.options = term.options,
SAN.prop.weights = MCMC.prop.weights, SAN.prop.args = MCMC.prop.args,
SAN.init.maxedges = MCMC.init.maxedges, SAN.burnin = MCMC.burnin *
SAN.burnin.times, SAN.interval = MCMC.interval, SAN.packagenames =
MCMC.packagenames, MPLE.max.dyad.types = MPLE.max.dyad.types, parallel =
parallel, parallel.type = parallel.type, parallel.version.check =
parallel.version.check), MCMLE.termination = c("Hummel", "Hotelling",
"precision", "none"), MCMLE.maxit = 20, MCMLE.conv.min.pval = 0.5,
MCMLE.NR.maxit = 100, MCMLE.NR.reltol = sqrt(.Machine$double.eps),
obs.MCMC.samplesize = MCMC.samplesize,
obs.MCMC.interval = MCMC.interval, obs.MCMC.burnin = MCMC.burnin,
obs.MCMC.burnin.min = obs.MCMC.burnin/10,
obs.MCMC.prop.weights = MCMC.prop.weights,
obs.MCMC.prop.args = MCMC.prop.args,
obs.MCMC.impute.min_informative = function(nw) network.size(nw)/4,
obs.MCMC.impute.default_density = function(nw) 2/network.size(nw),
MCMLE.check.degeneracy = FALSE, MCMLE.MCMC.precision = 0.005,
MCMLE.MCMC.max.ESS.frac = 0.1, MCMLE.metric = c("lognormal",
"logtaylor", "Median.Likelihood", "EF.Likelihood", "naive"),
MCMLE.method = c("BFGS", "Nelder-Mead"), MCMLE.trustregion = 20,
MCMLE.dampening = FALSE, MCMLE.dampening.min.ess = 20,
MCMLE.dampening.level = 0.1, MCMLE.steplength.margin = 0.05,
MCMLE.steplength = NVL2(MCMLE.steplength.margin, 1, 0.5),
MCMLE.adaptive.trustregion = 3, MCMLE.sequential = TRUE,
MCMLE.density.guard.min = 10000, MCMLE.density.guard = exp(3),
MCMLE.effectiveSize = NULL, MCMLE.last.boost = 4,
MCMLE.Hummel.esteq = TRUE, MCMLE.Hummel.miss.sample = 100,
MCMLE.Hummel.maxit = 25, MCMLE.steplength.min = 1e-04,
MCMLE.effectiveSize.interval_drop = 2,
MCMLE.save_intermediates = NULL, SA.phase1_n = NULL,
SA.initial_gain = NULL, SA.nsubphases = 4, SA.niterations = NULL,
SA.phase3_n = NULL, SA.trustregion = 0.5, RM.phase1n_base = 7,
RM.phase2n_base = 100, RM.phase2sub = 7, RM.init_gain = 0.5,
RM.phase3n = 500, Step.MCMC.samplesize = 100, Step.maxit = 50,
Step.gridsize = 100, CD.nsteps = 8, CD.multiplicity = 1,
CD.nsteps.obs = 128, CD.multiplicity.obs = 1, CD.maxit = 60,
CD.conv.min.pval = 0.5, CD.NR.maxit = 100,
CD.NR.reltol = sqrt(.Machine$double.eps), CD.metric = c("naive",
"lognormal", "logtaylor", "Median.Likelihood", "EF.Likelihood"),
CD.method = c("BFGS", "Nelder-Mead"), CD.trustregion = 20,
CD.dampening = FALSE, CD.dampening.min.ess = 20,
CD.dampening.level = 0.1, CD.steplength.margin = 0.5,
CD.steplength = 1, CD.adaptive.trustregion = 3,
CD.adaptive.epsilon = 0.01, CD.Hummel.esteq = TRUE,
CD.Hummel.miss.sample = 100, CD.Hummel.maxit = 25,
CD.steplength.min = 1e-04, loglik.control = control.logLik.ergm(),
term.options = NULL, seed = NULL, parallel = 0,
parallel.type = NULL, parallel.version.check = TRUE, ...)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(prev.fit)) can be used to ``resume''
an uncoverged ergm() run, but see
enformulate.curved.
A chatacter vector or NULL. The default method
depends on the reference measure used. For the binary ("Bernoulli")
ERGMs, it's maximum pseudo-likelihood estimation (MPLE). Other valid values
include "zeros" for a 0 vector of appropriate length and
"CD" for contrastive divergence.
Valid initial methods for a given reference are set by the InitErgmReference.* function.
One of "MCMLE" (default),"Robbins-Monro",
"Stochastic-Approximation", or "Stepping". Chooses the estimation method
used to find the MLE. MCMLE attempts to maximize an approximation to
the log-likelihood function. Robbins-Monro and
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. Another alternative is a partial
stepping algorithm (Stepping) as in Hummel et al. (2012). 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.
Note that in recent versions of ERGM, the enhancements of Stepping
have been folded into the default MCMLE, which is able to handle more
modeling scenarios.
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.
Maximum number of unique values of change
statistic vectors, which are the predictors in a logistic regression used to
calculate the MPLE. This calculation uses a compression algorithm that
allocates space based on MPLE.max.dyad.types.
Not currently documented; used in conditional-on-degree version of MPLE.
One of "glm" or "penalized". Chooses method of calculating
MPLE. "glm" is the usual formal logistic regression, 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.
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.
The TNT (tie / no tie) option puts roughly equal weight on selecting
a dyad with or without a tie as a candidate for toggling, whereas the
random option puts equal weight on all possible dyads, though the
interpretation of random may change according to the constraints in
place. When no constraints are in place, the default is TNT, which appears
to improve Markov chain mixing particularly for networks with a low edge
density, as is typical of many realistic social networks.
obs.MCMC.prop.weights, if given separately, specifies the weights to
be used for the constrained MCMC when missing dyads are present, defaulting
to the same as MCMC.prop.weights.
An alternative, direct way of
specifying additional arguments to proposal. obs.MCMC.prop.args, if
given separately, specifies the weights to be used for the constrained MCMC
when missing dyads are present, defaulting to the same as
MCMC.prop.args.
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.
Logical: If TRUE, return the matrix of MCMC-sampled
network statistics. This matrix should have MCMC.samplesize rows.
This matrix can be used directly by the coda package to assess MCMC
convergence.
Logical: If TRUE, plot traceplots of the MCMC sample after every MCMC MLE iteration.
These parameters
control how much space is allocated for storing edgelists for
return at the end of MCMC sampling. Allocating more than needed
wastes memory, so MCMC.init.maxedges is the initial amount
allocated, but it will be incremented by a factor of 10 if
exceeded during the simulation, up to MCMC.max.maxedges, at
which point the process will stop with an error.
Whether to add the standard errors induced by the MCMC algorithm to the estimates' standard errors.
Logical: If TRUE, the matrix of sample statistics returned is compressed to the set of unique statistics with a column of frequencies post-pended.
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.
Multiplier for SAN.burnin 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.control 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 \(\code{MCMLE.steplength.margin}=\code{NULL}\).
"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 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.
Sample size, burnin, and interval parameters for the MCMC sampling used when unobserved data are present in the estimation routine.
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.
Logical: If TRUE, employ a check for model degeneracy.
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.
Maximum increase the algorithm will allow for the approximated likelihood at a given iteration. See Snijders (2002) for details.
Note that not all metrics abide by it.
(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, which may (for values
less than one) make fitting more stable at the cost of computational
efficiency. Can be set to "adaptive"; see
MCMLE.adaptive.trustregion.
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.
Maximum increase the algorithm will allow
for the approximated loglikelihood at a given iteration when
MCMLE.steplength="adaptive".
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.
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.
Set MCMLE.effectiveSize to non-NULL value to adaptively determine the
burn-in and the MCMC length needed to get the specified effective size using
the method of Sahlin (2011); 50 is a reasonable value. This feature is in
experimental status until we verify the coverage of the standard errors.
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.
Maximum number of iterations in searching for the best step length.
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. The name is passed through sprintf()
with iteration number as the second argument. (So, for example,
MCMLE.save_intermediates="step_%03d.RData" will save to
step_001.RData, step_002.RData, etc.)
Number of MCMC samples to draw in Phase 1 of the stochastic approximation algorithm. Defaults to 7 plus 3 times the number of terms in the model. See Snijders (2002) for details.
Initial gain to Phase 2 of the stochastic approximation algorithm. 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.
Number of MCMC samples to draw in Phase 2 of the stochastic approximation algorithm. Defaults to 7 plus the number of terms in the model. See Snijders (2002) for details.
Sample size for the MCMC sample in Phase 3 of the stochastic approximation algorithm. See Snijders (2002) for details.
The trust region parameter for the likelihood functions, used in the stochastic approximation algorithm.
The Robbins-Monro control parameters are not yet documented.
MCMC sample size for the preliminary steps of
the "Stepping" method of optimization. This is usually chosen to be smaller
than the final MCMC sample size (which equals MCMC.samplesize). See
Hummel et al. (2012) for details.
Maximum number of iterations (steps) allowed by the "Stepping" method.
Integer \(N\) such that the "Stepping" style of optimization chooses a step length equal to the largest possible multiple of \(1/N\). See Hummel et al. (2012) for details.
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.
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.
Miscellaneous tuning parameters of the CD sampler and optimizer. These have
the same meaning as their MCMC.* counterparts.
Note that only the Hotelling's stopping criterion is implemented for CD.
Miscellaneous tuning parameters of the CD sampler and optimizer. These have
the same meaning as their MCMC.* counterparts.
Note that only the Hotelling's stopping criterion is implemented for CD.
Miscellaneous tuning parameters of the CD sampler and optimizer. These have
the same meaning as their MCMC.* counterparts.
Note that only the Hotelling's stopping criterion is implemented for CD.
Miscellaneous tuning parameters of the CD sampler and optimizer. These have
the same meaning as their MCMC.* counterparts.
Note that only the Hotelling's stopping criterion is implemented for CD.
Miscellaneous tuning parameters of
the CD sampler and optimizer. These have the same meaning as their
MCMC.* counterparts.
Note that only the Hotelling's stopping criterion is implemented for CD.
A list of additional arguments to be passed to term initializers. It can also be set globally via option(ergm.term=list(...)).
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.
Additional arguments, passed to other functions This argument is helpful because it collects any control parameters that have been deprecated; a warning message is printed in case of deprecated arguments.
A list with arguments as components.
This function is only used within a call to the ergm() function.
See the usage section in ergm() for details.
Snijders, T.A.B. (2002), Markov Chain Monte Carlo Estimation of Exponential Random Graph Models. Journal of Social Structure. Available from http://www.cmu.edu/joss/content/articles/volume3/Snijders.pdf.
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. http://www2.math.su.se/matstat/reports/master/2011/rep2/report.pdf
ergm(). The control.simulate function
performs a similar function for simulate.ergm;
control.gof performs a similar function for gof.