hergm {hergm} | R Documentation |
The package hergm
implements exponential-family random graph models with Dirichlet process / stick-breaking priors,
including
- the p_1 model for directed networks of Holland and Leinhardt (1981) and its extension to undirected random graph models with Dirichlet process priors (see arcs_i, arcs_j, mutual_i, and edges_i). While the p_1 model for undirected and directed networks with parametric priors contains O(n) parameters (n = number of nodes) and therefore is not parsimonious, the non-parametric Dirichlet process prior encourages a small number of unique parameters and therefore represents an elegant alternative to parametric priors.
- the stochastic block model of Snijders and Nowicki (1997) and Nowicki and Snijders (2001) with natural parameterization (restricted between-block parameters) and Dirichlet process priors (see edges_ij).
- the hierarchical exponential-family models of Schweinberger and Handcock (2009) with stick-breaking priors (see mutual_ij, twostar_ijk, triangle_ijk, ttriple_ijk, ctriple_ijk). Hierarchical exponential-family models replace the strong dependence of simple exponential-family models by weak dependence with an eye to solving the near-degeneracy problem of simple exponential-family model.
The package hergm
implements simulation and Bayesian inference for the mentioned models.
hergm(formula, alpha = NULL, alpha_shape = NULL, alpha_rate = NULL, eta = NULL, eta_mean = NULL, eta_sd = NULL, eta_mean_mean = NULL, eta_mean_sd = NULL, eta_precision_shape = NULL, eta_precision_rate = NULL, indicator = NULL, parallel = 1, simulate = FALSE, seeds = NULL, samplesize = 1e+5, burnin = 1e+4, interval = 1e+2, mh_scale = NULL, output = TRUE, verbose = -1, name = NULL, ...)
formula |
formula of the form |
alpha |
scaling parameter of truncated Dirichlet process / stick-breaking prior of natural parameters of exponential-family model. |
alpha_shape, alpha_rate |
shape and rate (inverse scale) parameter of Gamma prior of scaling parameter. |
eta |
natural parameters of exponential-family model. |
eta_mean, eta_sd |
means and standard deviations of Gaussian baseline distribution of Dirichlet process / stick-breaking prior of natural parameters. |
eta_mean_mean, eta_mean_sd |
means and standard deviations of Gaussian prior of mean of Gaussian baseline distribution of Dirichlet process / stick-breaking prior. |
eta_precision_shape, eta_precision_rate |
shape and rate (inverse scale) parameter of Gamma prior of precision parameter of Gaussian baseline distribution of Dirichlet process / stick-breaking prior. |
indicator |
if |
parallel |
number of processors; if more than one, computing is parallel. |
simulate |
if |
seeds |
seed of pseudo-random number generator; if computing is parallel, number of seeds must equal number of processors. |
samplesize |
if |
burnin |
if |
interval |
if |
mh_scale |
if |
output |
if |
name |
name of project; if |
verbose |
console output: -1: no output; 0: short output; +1: long output. |
... |
additional arguments, to be passed to lower-level functions in the future. |
If called with the option simulate = TRUE
,
the function hergm
returns a sample of networks,
otherwise a raw MCMC sample from the posterior.
To postprocess the sample,
call the function hergm.postprocess
.
Holland, P. W. and S. Leinhardt (1981). An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association 76 (373), 33–65.
Nowicki, K. and T. A. B. Snijders (2001). Estimation and prediction for stochastic blockstructures. Journal of the American Statistical Association 96 (455), 1077–1087.
Schweinberger, M. and M. S. Handcock (2009). Hierarchical exponential-family random graph models. Technical report, Pennsylvania State University. Submitted.
Snijders, T. A. B. and K. Nowicki (1997). Estimation and prediction for stochastic blockmodels for graphs with latent block structure. Journal of Classification 14, 75–100.
network, ergm.terms, hergm.terms, hergm.postprocess
## Not run: # Load undirected network with 15 nodes (see ?example) data(example) # p_1 model for undirected network with Dirichlet process prior hergm(d ~ edges_i) # Stochastic block model for undirected network # with natural parameterization and Dirichlet process prior hergm(d ~ edges_ij) # Hierarchical exponential-family model with stick-breaking prior hergm(d ~ edges + triangle_ijk) ## End(Not run)