ergm.bridge.llr: Bridge sampling to evaluate ERGM log-likelihoods and...

In ergm: Fit, Simulate and Diagnose Exponential-Family Models for Networks

Bridge sampling to evaluate ERGM log-likelihoods and log-likelihood ratios

Description

ergm.bridge.llr uses bridge sampling with geometric spacing to estimate the difference between the log-likelihoods of two parameter vectors for an ERGM via repeated calls to simulate.formula.ergm().

ergm.bridge.0.llk is a convenience wrapper that returns the log-likelihood of configuration \theta relative to the reference measure. That is, the configuration with \theta=0 is defined as having log-likelihood of 0.

ergm.bridge.dindstart.llk is a wrapper that uses a dyad-independent ERGM as a starting point for bridge sampling to estimate the log-likelihood for a given dyad-dependent model and parameter configuration. Note that it only handles binary ERGMs (response=NULL) and with constraints (⁠constraints=⁠) that that do not induce dyadic dependence.

Usage

ergm.bridge.llr(
  object,
  response = NULL,
  reference = ~Bernoulli,
  constraints = ~.,
  from,
  to,
  obs.constraints = ~. - observed,
  target.stats = NULL,
  basis = ergm.getnetwork(object),
  verbose = FALSE,
  ...,
  llronly = FALSE,
  control = control.ergm.bridge()
)

ergm.bridge.0.llk(
  object,
  response = NULL,
  reference = ~Bernoulli,
  coef,
  ...,
  llkonly = TRUE,
  control = control.ergm.bridge(),
  basis = ergm.getnetwork(object)
)

ergm.bridge.dindstart.llk(
  object,
  response = NULL,
  constraints = ~.,
  coef,
  obs.constraints = ~. - observed,
  target.stats = NULL,
  dind = NULL,
  coef.dind = NULL,
  basis = ergm.getnetwork(object),
  ...,
  llkonly = TRUE,
  control = control.ergm.bridge(),
  verbose = FALSE
)

Arguments

object	A model formula. See ergm() for details.
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. (Defaults to ~Bernoulli.)
constraints, obs.constraints	One-sided formulas specifying one or more constraints on the support of the distribution of the networks being simulated and on the observation process respectively. See the documentation for similar arguments for ergm() for more information.
from, to	The initial and final parameter vectors.
target.stats	A vector of sufficient statistics to be used in place of those of the network in the formula.
basis	An optional network object to start the Markov chain. If omitted, the default is the left-hand-side of the object.
verbose	A logical or an integer to control the amount of progress and diagnostic information to be printed. FALSE/0 produces minimal output, with higher values producing more detail. Note that very high values (5+) may significantly slow down processing.
...	Further arguments to ergm.bridge.llr and simulate.formula.ergm().
llronly	Logical: If TRUE, only the estiamted log-ratio will be returned by ergm.bridge.llr.
control	A list of control parameters for algorithm tuning, typically constructed with control.ergm.bridge(). Its 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.
coef	A vector of coefficients for the configuration of interest.
llkonly	Whether only the estiamted log-likelihood should be returned by the ergm.bridge.0.llk and ergm.bridge.dindstart.llk. (Defaults to TRUE.)
dind	A one-sided formula with the dyad-independent model to use as a starting point. Defaults to the dyad-independent terms found in the formula object with an overal density term (edges) added if not redundant.
coef.dind	Parameter configuration for the dyad-independent starting point. Defaults to the MLE of dind.

Value

If llronly=TRUE or llkonly=TRUE, these functions return the scalar log-likelihood-ratio or the log-likelihood. Otherwise, they return a list with the following components:

llr	The estimated log-ratio.
llr.vcov	The estimated variance of the log-ratio due to MCMC approximation.
llrs	A list of lists (1 per attempt) of the estimated log-ratios for each of the bridge.nsteps bridges.
llrs.vcov	A list of lists (1 per attempt) of the estimated variances of the estimated log-ratios for each of the bridge.nsteps bridges.
paths	A list of lists (1 per attempt) with two elements: theta, a numeric matrix with bridge.nsteps rows, with each row being the respective bridge's parameter configuration; and weight, a vector of length bridge.nsteps containing its weight.
Dtheta.Du	The gradient vector of the parameter values with respect to position of the bridge.

ergm.bridge.0.llk result list also includes an llk element, with the log-likelihood itself (with the reference distribution assumed to have likelihood 0).

ergm.bridge.dindstart.llk result list also includes an llk element, with the log-likelihood itself and an llk.dind element, with the log-likelihood of the nearest dyad-independent model.

References

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

See Also

simulate.formula.ergm()

ergm documentation built on Oct. 7, 2024, 5:08 p.m.