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.
# 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)
a vector of distinct integers
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.
the Layer Logic (c.f. Layer Logic section in the
Layer() documentation) specification for the base
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.)
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.
ergmTerm for index of model terms currently visible to the package.
ergm:::.formatTermKeywords("ergmTerm", "despL", "subsection")