# 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 (undirected network)` |
adding the term |

`arcs_i (directed network)` |
adding the term |

`arcs_j (directed network)` |
adding the term |

`edges_ij (undirected, directed network)` |
adding the term |

`mutual_i (directed network)` |
adding the term |

`mutual_ij (directed network)` |
adding the term |

`twostar_ijk (undirected network)` |
adding the term |

`transitiveties_ijk (directed network)` |
adding the term |

`triangle_ijk (undirected, directed network)` |
adding the term |

`ttriple_ijk (directed network)` |
adding the term |

`ctriple_ijk (directed network)` |
adding the term |

### 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, 647-676.

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.

### See Also

hergm, ergm.terms

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ```
## 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)
``` |