ergm (version 3.0-3)

ergm-terms: Terms used in Exponential Family Random Graph Models

Description

The function ergm is used to fit linear exponential random graph models, in which the probability of a given network, $y$, on a set of nodes is $\exp{\theta{\cdot}g(y)}/c(\theta)$, where $g(y)$ is a vector of network statistics for $y$, $\theta$ is a parameter vector of the same length and $c(\theta)$ is the normalizing constant for the distribution.

The network statistics $g(y)$ are entered as terms in the function call to ergm.

This page describes the possible terms (and hence network statistics).

Specifying models

Terms to ergm are specified by a formula to represent the network and network statistics. This is done via a formula, that is, an Rformula object, of the form y ~ + ..., where y is a network object or a matrix that can be coerced to a network object, and , , etc, are each terms chosen from the list given below. To create a network object in R, use the network function, then add nodal attributes to it using the %v% operator if necessary.

References

• Davis, J.A. and Leinhardt, S. (1972). The Structure of Positive Interpersonal Relations in Small Groups. In J. Berger (Ed.),Sociological Theories in Progress, Volume 2, 218--251. Boston: Houghton Mifflin.
• Holland, P. W. and S. Leinhardt (1981). An exponential family of probability distributions for directed graphs.Journal of the American Statistical Association, 76: 33--50.
• Hunter, D. R. and M. S. Handcock (2006). Inference in curved exponential family models for networks.Journal of Computational and Graphical Statistics, 15: 565--583.
• Hunter, D. R. (2007). Curved exponential family models for social networks.Social Networks, 29: 216--230.
• Krackhardt, D. and Handcock, M. S. (2007). Heider versus Simmel: Emergent Features in Dynamic Structures.Lecture Notes in Computer Science, 4503, 14--27.
• Snijders, T. A. B., P. E. Pattison, G. L. Robins, and M. S. Handcock (2006). New specifications for exponential random graph models,Sociological Methodology, 36(1): 99-153.

See Also

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

Examples

ergm(flomarriage ~ kstar(1:2) + absdiff("wealth") + triangle)

ergm(molecule ~ edges + kstar(2:3) + triangle
                      + nodematch("atomic type",diff=TRUE)
                      + triangle + absdiff("atomic type"))