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R: Model terms

hergm-terms

R Documentation

Model terms

Description

Hierarchical exponential-family random graph models with local dependence can be specified by calling the function hergm(formula), where formula is a formula of the form network ~ terms. By specifying suitable terms, it is possible to specify a wide range of models: see hergm. hergm.terms can be found here. In addition, ergm.terms can be used to include covariates.

Arguments

`edges_i(k) (undirected network)`	adding the term `edges_i` to the model adds node-dependent edge terms to the model; the optional argument `k` is the maximum number of blocks (default: the number of nodes).
`arcs_i(k) (directed network)`	adding the term `arcs_i` to the model adds node-dependent outdegree terms to the model; the optional argument `k` is the maximum number of blocks (default: the number of nodes).
`arcs_j(k) (directed network)`	adding the term `arcs_j` to the model adds node-dependent indegree terms to the model; the optional argument `k` is the maximum number of blocks (default: the number of nodes).
`edges_ij(k) (undirected, directed network)`	adding the term `edges_ij` to the model adds block-dependent edge terms to the model; the optional argument `k` is the maximum number of blocks (default: the number of nodes).
`mutual_i(k) (directed network)`	adding the term `mutual_i` to the model adds additive, block-dependent mutual edge terms to the model; the optional argument `k` is the maximum number of blocks (default: the number of nodes).
`mutual_ij(k) (directed network)`	adding the term `mutual_ij` to the model adds block-dependent mutual edge terms to the model; the optional argument `k` is the maximum number of blocks (default: the number of nodes).
`transedges (undirected network)`	adding the term `transedges` to the model adds the number of transitive edges to the model.
`twostar_ijk(k) (undirected network)`	adding the term `twostar_ijk` to the model adds block-dependent two-star terms to the model; the optional argument `k` is the maximum number of blocks (default: the number of nodes).
`triangle_ijk(k) (undirected, directed network)`	adding the term `triangle_ijk` to the model adds block-dependent triangle terms to the model; the optional argument `k` is the maximum number of blocks (default: the number of nodes).
`ttriple_ijk(k) (directed network)`	adding the term `ttriple_ijk` to the model adds block-dependent transitive triple terms to the model; the optional argument `k` is the maximum number of blocks (default: the number of nodes).
`ctriple_ijk(k) (directed network)`	adding the term `ctriple_ijk` to the model adds block-dependent cyclic triple terms to the model; the optional argument `k` is the maximum number of blocks (default: the number of nodes).

References

Handcock, M. S. (2003). Assessing degeneracy in statistical models of social networks. Technical report, Center for Statistics and the Social Sciences, University of Washington, Seattle, http://www.csss.washington.edu/Papers.

Holland, P. W. and S. Leinhardt (1981). An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association, Theory & Methods, 76, 33–65.

Nowicki, K. and T. A. B. Snijders (2001). Estimation and prediction for stochastic blockstructures. Journal of the American Statistical Association, Theory & Methods, 96, 1077–1087.

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.

Schweinberger, M. (2011). Instability, sensitivity, and degeneracy of discrete exponential families. Journal of the American Statistical Association, Theory & Methods, 106, 1361–1370.

Schweinberger, M. and M. S. Handcock (2015). Local dependence in random graph models: characterization, properties, and statistical Inference. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 7, 1-30, in press.

Schweinberger, M., Petrescu-Prahova, M. and D. Q. Vu (2014). Disaster response on September 11, 2001 through the lens of statistical network analysis. Social Networks, 37, 42–55.

Vu, D. Q., Hunter, D. R. and M. Schweinberger (2013). Model-based clustering of large networks. Annals of Applied Statistics, 7, 1010–1039.

Examples

## Not run: 
data(example)
# p_1 model: undirected network
hergm(d ~ edges_i)

data(sampson) 
# p_1 model: directed network
hergm(samplike ~ arcs_i + arcs_j + mutual)

data(example)
# Stochastic block model: undirected network 
hergm(d ~ edges_ij)

data(sampson) 
# Stochastic block model: directed network 
hergm(samplike ~ edges_ij + mutual)

data(example)
# Exponential-family random graph model with local dependence: undirected network
hergm(d ~ edges_ij + triangle_ijk)

data(sampson) 
# Exponential-family random graph model with local dependence: directed network
hergm(samplike ~ edges + mutual + ttriple_ijk)

## End(Not run)

Model terms

Description

Arguments

References

See Also

Examples

Results