ergmReference {ergm}

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. References can also be searched via search.ergmReferences(), and help for an individual reference can be obtained with ⁠ergmReference?<reference>⁠ or help("<reference>-ergmReference").

Specifying reference measures

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

h(y) \exp[\eta(\theta) \cdot g(y)] / \kappa(\theta),

where h(y) is the reference distribution (particularly for valued network models), g(y) is a vector of network statistics for y, \eta(\theta) is a natural parameter vector of the same length (with \eta(\theta)\equiv\theta for most terms), \cdot is the dot product, and \kappa(\theta) is the normalizing constant for the distribution. A complete ERGM specification requires a list of network statistics g(y) and (if applicable) their \eta(\theta) mappings provided by a formula of ergmTerms; and, optionally, sample space \mathcal{Y} and reference distribution h(y) information provided by ergmConstraints and, for valued ERGMs, by ergmReferences.

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

Term	Package	Description	Concepts
Bernoulli	ergm	Bernoulli reference	discrete finite nonnegative
DiscUnif(a,b)	ergm	Discrete Uniform reference	discrete finite
StdNormal	ergm	Standard Normal reference	continuous
Unif(a,b)	ergm	Continuous Uniform reference	continuous

All references

Term	bin	discrete	fin	nneg	cont
Bernoulli	✔	✔	✔	✔
DiscUnif		✔	✔
StdNormal					✔
Unif					✔

References by keywords

Jump to keyword: binary discrete finite nonnegative continuous

binary

Bernoulli

discrete

Bernoulli DiscUnif

finite

Bernoulli DiscUnif

nonnegative

Bernoulli

continuous

StdNormal Unif

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\%⁠