R: Reference Measures for Exponential-Family Random Graph Models

ergmReference {ergm} | R Documentation

## Reference Measures for Exponential-Family Random Graph Models

### Description

This page describes how to specify the reference measures (baseline distributions) (the set of possible networks Y and the baseline weights h(y) to functions in the `ergm` package. It also provides an indexed list of the references visible to the ergm's API.

### Specifying reference measures

In an exponential-family random graph model (ERGM), the probability or density of a given network, y in sample space Y, on a set of nodes is

h(y) exp{eta(theta).g(y)} / c(theta),

where h(y) is the reference distribution (particularly for valued network models), g(y) is a vector of network statistics for y, η(θ) is a natural parameter vector of the same length (with eta(theta)=theta for most terms), . is the dot product, and c(theta) is the normalizing constant for the distribution. A complete ERGM specification requires a list of network statistics g(y) and (if applicable) their η(θ) mappings provided by a formula of `ergmTerm`s; and, optionally, sample space Y and reference distribution h(y) information provided by `ergmConstraint`s and, for valued ERGMs, by `ergmReference`s.

The reference measure (Y,h(y)) is specified on the right-hand side of a one-sided formula passed typically as the `reference` argument.

### Reference measures visible to the package

#### All references

#### References by keywords

### References

- Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M (2008b). ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Journal of Statistical Software, 24(3). doi: 10.18637/jss.v024.i03

- Krivitsky PN (2012). Exponential-Family Random Graph Models for Valued Networks. Electronic Journal of Statistics, 2012, 6, 1100-1128. doi: 10.1214/12-EJS696

### See Also

`ergm`, `network`, `sna`, `summary.ergm`, `print.ergm`, `\%v\%`, `\%n\%`

[Package ergm version 4.2.2 Index]