Bergm (version 2.4)

bergmS: Bayesian model selection for exponential random graph models

Description

Bayesian model selection for exponential random graphs models using the auto-RJ exchange algorithm. The algorithm consists of two steps: the first step (offline) is used to sample from the posterior of each competing model using the bergm function and then approximated by normal distributions determined by the moments of each sample. The second step (online step) of the algorithm makes use of the normal posterior proposal estimated in the offline step as within-model proposals for the RJ-MCMC computation.

Usage

bergmS(formulae, 
       iters = 10000, 
       m.priors = NULL, 
       sigma.priors = NULL, 
       gammas = NULL, 
       nchains = NULL, 
       sigma.epsilons = NULL, 
       aux.iters = 1000, 
       main.iters = NULL,
       burn.ins=NULL,
       save=FALSE, 
       ...)

Arguments

formulae

list; R formula objects (competing models) of the form ~ , see ergm-terms.

iters

count; number of iterations for auto-RJ exchange algorithm (online step).

m.priors

list; vectors of means of the multivariate Normal priors for each competing model. By default set to a list of vectors (one for each competing model) of 0's.

sigma.priors

list; variance /covariance matrices of the multivariate Normal priors for each competing model. By default set to a list of diagonal matrices (one for each competing model) with every diagonal entry equal to 100.

gammas

vector; ``parallel ADS move factors'' for each competing model (offline step). By default set to a vector of 0.5's.

nchains

vector; number of MCMC chains for each competing model (offline step). By default set to a vector with entries (one for each competing model) equal to twice the dimensions of the competing models.

sigma.epsilons

list; containing variance/covariance matrices for the multivariate Normal proposals or ``parallel ADS move parameters'' for each competing model (offline step). By default set to a list of diagonal matrices (one for each competing model) with every diagon

aux.iters

count; number of auxiliary iterations for network simulation.

main.iters

vector; number of iterations for the MCMC chain(s) for each competing model (offline step). By default set to a vector of 1000's.

burn.ins

vector; number of burn-in iterations at the beginning of an MCMC run for each competing model (offline step). By default set to a vector of 100's.

save

logical; if TRUE a file called "bergmS.out" is saved in the working directory.

...

additional arguments, to be passed to lower-level functions.

References

Caimo, A. and Friel, N., (submitted) ``Bayesian model selection for exponential random graph models.''

See Also

bergm.

Examples

# load the Florentine marriage network 
# included with the ergm package

data(florentine)
y <- flomarriage

# Competing models:

formulae <- c(y ~ edges, 
              y ~ edges + gwesp(log(2),fixed=TRUE),
              y ~ edges + gwdegree(log(2),fixed=TRUE))

# Model selection via auto-RJ exchange algorithm
# (this should take about 1.5 minutes)

flo <- bergmS(formulae,
              iters=10000,
              aux.iters=1000,
              main.iters=rep(1000,3),
              burn.in=rep(100,3),
              gammas=c(0.8,1,1))

# MCMC diagnostics

flo.out <- bergmS.output(flo)

# Bayesian goodness-of-fit test (for the best model)

bgof(flo.out,
     lags=200,
     n.sim=100,
     n.deg=10,
     n.dist=10,
     n.esp=5)