triadic-ergmHint-b01cc436: Network with strong clustering (triad-closure) effects

In ergm: Fit, Simulate and Diagnose Exponential-Family Models for Networks

Network with strong clustering (triad-closure) effects

Description

The network has a high clustering coefficient. This typically results in alternating between the Tie-Non-Tie (TNT) proposal and a triad-focused proposal along the lines of that of \insertCiteWaAt13a;textualergm.

Usage

# triadic(triFocus = 0.25, type="OTP")

# .triadic(triFocus = 0.25, type = "OTP")

Arguments

triFocus	A number between 0 and 1, indicating how often triad-focused proposals should be made relative to the standard proposals.
type	A string indicating the type of shared partner or path to be considered for directed networks: "OTP" (default for directed), "ITP", "RTP", "OSP", and "ISP"; has no effect for undirected. See the section below on Shared partner types for details.

Shared partner types

While there is only one shared partner configuration in the undirected case, nine distinct configurations are possible for directed graphs, selected using the type argument. Currently, terms may be defined with respect to five of these configurations; they are defined here as follows (using terminology from Butts (2008) and the relevent package):

• Outgoing Two-path ("OTP"): vertex k is an OTP shared partner of ordered pair (i,j) iff i \to k \to j. Also known as "transitive shared partner".

• Incoming Two-path ("ITP"): vertex k is an ITP shared partner of ordered pair (i,j) iff j \to k \to i. Also known as "cyclical shared partner"

• Reciprocated Two-path ("RTP"): vertex k is an RTP shared partner of ordered pair (i,j) iff i \leftrightarrow k \leftrightarrow j.

• Outgoing Shared Partner ("OSP"): vertex k is an OSP shared partner of ordered pair (i,j) iff i \to k, j \to k.

• Incoming Shared Partner ("ISP"): vertex k is an ISP shared partner of ordered pair (i,j) iff k \to i, k \to j.

By default, outgoing two-paths ("OTP") are calculated. Note that Robins et al. (2009) define closely related statistics to several of the above, using slightly different terminology.

.triadic() versus triadic()

If given a bipartite network, the dotted form will skip silently, whereas the plain form will raise an error, since triadic effects are not possible in bipartite networks. The dotted form is thus suitable as a default argument when the bipartitedness of the network is not known a priori.

References

\insertAllCited

See Also

ergmHint for index of constraints and hints currently visible to the package.

\Sexpr[results=rd,stage=render]{ergm:::.formatTermKeywords("ergmHint", "triadic", "subsection")}

ergm documentation built on Oct. 7, 2024, 5:08 p.m.