R: Edgewise shared partners on layers

despL-ergmTerm {ergm.multi}

R Documentation

Edgewise shared partners on layers

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. For a directed network, multiple shared partner definitions are possible.

espL and despL are aliases for consistency with ergm.

Usage

# binary: despL(d, type="OTP", L.base=NULL, Ls.path=NULL, L.in_order=FALSE)

# binary: espL(d, type="OTP", L.base=NULL, Ls.path=NULL, L.in_order=FALSE)

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.
`L.base`	the Layer Logic (c.f. Layer Logic section in the `Layer()` documentation) specification for the base
`Ls.path`, `L.in_order`	a vector of one or two formulas `Ls.path` provides the Layer Logic (c.f. Layer Logic section in the `Layer()` documentation) specifications for the ties of the 2-path or the shared partnership. (If only one formula is given the layers are assumed to be the same.) If `L.in_order==TRUE` , the first tie of the two-path must be the first element of `Ls.path` and the second must be the second; otherwise, any ordering counts, provided there is exactly one of each. (For types `"OSP"` and `"ISP"` , the first tie is considered to be the one incident on the tail of the base tie.)

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.