New Graphlet Orbit Covariance Term for the 'ergm' Package – introduced under 'ergm.graphlets' package
Description
This is a new term for the ergm
package
that links the graphlet structures in the network for a given graphlet orbit
with numeric node attributes.
Details
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{θ *
g(y)}/c(θ), where g(y) is a vector of network
statistics for y, θ is a parameter vector of the same
length and c(θ) is the normalizing constant for the distribution.
The network statistics g(y) are entered as terms in the
function call to ergm
. The ergm
package contains
a wide range of terms. For the details on the possible
<model terms>
, see ergmterms
.
The ergm.userterms
package provides a template for
adding new terms. The terms can be used throughout the ergm
package
and behave identically to the supplied terms.
The Graphlet Orbit Covariance Term
grorbitCov(attrName, grOrbit)

The correlation between a node's graphlet degree and a numeric attribute value can be included into an ERGM by using the
grorbitCov
term. The question that the change score function of this term answers is: what is the change in covariance between a vector of nodal attributes and nodal orbit degrees when an edge is changed? This term has two arguments:attrname
andgrorbit
. Theattrname
is a character vector giving the name of a numeric attribute in the network's vertex attribute list. The optionalgrorbit
argument is a vector of distinct integers representing the list of graphlet orbits to include into the ERGM model. Whengrorbit
is not provided, all graphlet orbits are evaluated by default. The term adds one network statistic to the model for each element ingrorbit
. This term is defined for the 73 orbits corresponding to graphlets with up to 5 nodes. Therefore,grorbit
accepts values between 0 and 72. Values outside this range are ignored. This term can only be used with undirected networks.
References
Yaveroglu ON, Fitzhugh SM, Kurant M, Markopoulou A, Butts CT, Przulj N (2015). ergm.graphlets: A Package for ERG Modeling Based on Graphlet Properties, Journal of Statistical Software 65(12), 129, URL http://www.jstatsoft.org/v65/i12/.
See Also
statnet, network, ergm, ergmterms