esp-ergmTerm-d2e07fc8: Directed edgewise shared partners

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

Directed edgewise shared partners

Description

This term adds one network statistic to the model for each element in d where the i th such statistic equals the number of edges in the network with exactly d[i] shared partners.

Usage

# binary: desp(d, type="OTP")

# binary: esp(d, type="OTP")

Arguments

d	a vector of distinct integers
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.

Note

This term takes an additional term option (see options?ergm), cache.sp, controlling whether the implementation will cache the number of shared partners for each dyad in the network; this is usually enabled by default.

This term can only be used with directed networks.

See Also

ergmTerm for index of model terms currently visible to the package.

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

statnet/ergm documentation built on April 17, 2024, 12:21 p.m.