ergmm: Fit a Latent Space Random Graph Model

Description

ergmm is used to fit latent space and latent space cluster random network models, as described by Hoff, Raftery and Handcock (2002), Handcock, Raftery and Tantrum (2005), and Krivitsky, Handcock, Raftery, and Hoff (2009). ergmm can return either a Bayesian model fit or the two-stage MLE.

Usage

ergmm(formula, response=NULL, family="Bernoulli",fam.par=NULL,
      control=ergmm.control(), user.start=list(), prior=ergmm.prior(),
      tofit=c("mcmc", "mkl", "mkl.mbc", "procrustes",
      "klswitch"), Z.ref=NULL, Z.K.ref=NULL, seed=NULL,
      verbose=FALSE)

Arguments

formula

An R formula object, of the form g ~ <term 1> + <term 2> ..., where g is a network object or a matrix that can be coerced to a network object, and <term 1>, <term 2>, etc., are each terms for the model. See terms.ergmm for the terms that can be fitted. To create a network object in R, use the network function, then add nodal attributes to it using set.vertex.attribute if necessary.

Note that, as in lm, the model will include an intercept term. This behavior can be overridden by including a -1 or +0 term in the formula, and a 1(mean=...,var=...) term can be used to set a prior different from default.

response

An optional edge attribute that serves as the response variable. By default, presence (1) or absence (0) of an edge in g is used.

family

A character vector specifying the conditional distribution of each edge value. See families.ergmm for the currently implemented families.

fam.par

For those families that require additional parameters, a list.

control

The MCMC parameters that do not affect the posterior distribution such as the sample size, the proposal variances, and tuning parameters, in the form of a named list. See ergmm.control for more information and defaults.

user.start

An optional initial configuration parameters for MCMC in the form of a list. By default, posterior mode conditioned on cluster assignments is used. It is permitted to only supply some of the parameters of a configuration. If this is done, the remaining paramters are fitted conditional on those supplied.

prior

The prior parameters for the model being fitted in the form of a named list. See terms.ergmm for the names to use. If given, will override those given in the formula terms, making it useful as a convenient way to store and reproduce a prior distribution. The list or prior parameters can also be extracted from an ERGMM fit object. See ergmm.prior for more information.

tofit

A character vector listing some subset of "pmode", "mcmc", "mkl", "mkl.mbc", "mle","procrustes", and "klswitch", defaulting to all of the above, instructing ergmm what should be returned as a part of the ERGMM fit object. Omiting can be used to skip particular steps in the fitting process. If the requested procedure or output depends on some other procedure or output not explictly listed, the dependency will be resolved automatically.

Z.ref

If given, used as a reference for Procrustes analysis.

Z.K.ref

If given, used as a reference for label-switching.

seed

If supplied, random number seed.

verbose

If this is TRUE (or 1), causes information to be printed out about the progress of the fitting, particularly initial value generation. Higher values lead to greater verbosity.

Value

ergmm returns an object of class ergmm containing the information about the posterior.

References

Mark S. Handcock, Adrian E. Raftery and Jeremy Tantrum (2002). Model-Based Clustering for Social Networks. Journal of the Royal Statistical Society: Series A, 170(2), 301-354.

Peter D. Hoff, Adrian E. Raftery and Mark S. Handcock (2002). Latent space approaches to social network analysis. Journal of the American Statistical Association, 97(460), 1090-1098.

Pavel N. Krivitsky, Mark S. Handcock, Adrian E. Raftery, and Peter D. Hoff (2009). Representing degree distributions, clustering, and homophily in social networks with latent cluster random effects models. Social Networks, 31(3), 204-213.

Pavel N. Krivitsky and Mark S. Handcock (2008). Fitting Position Latent Cluster Models for Social Networks with latentnet. Journal of Statistical Software, 24(5).

Examples

Run this code

# NOT RUN {
#
# Use 'data(package = "latentnet")' to list the data sets in a
#
data(package="latentnet")
#
# Using Sampson's Monk data, lets fit a 
# simple latent position model
#
data(sampson)
samp.fit <- ergmm(samplike ~ euclidean(d=2))
#
# See if we have convergence in the MCMC
mcmc.diagnostics(samp.fit)
#
# Plot the fit
#
plot(samp.fit)
#
# Using Sampson's Monk data, lets fit a latent clustering random effects model
#
samp.fit2 <- ergmm(samplike ~ euclidean(d=2, G=3)+rreceiver)
#
# See if we have convergence in the MCMC
mcmc.diagnostics(samp.fit2)
#
# Plot the fit.
#
plot(samp.fit2, pie=TRUE)
# }