New Graphlet Orbit Factor Term for the 'ergm' Package – introduced under 'ergm.graphlets' package
Description
This is a new term for the ergm
package
that links the graphlet orbits of a given type with categorical 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 Factor Term
grorbitFactor(attrname, grorbit, base)

The
grorbitFactor
term adds a relationship between graphlet degrees and a categorical node attribute into an ERGM. The question that the change score function of this term answers is: what is the change in the total graphlet degree (for a given orbit) for those nodes with a given attribute value, for a particular edge change? This term has three arguments:attrname
;grorbit
; andbase
.attrname
is a character vector giving the name of a categorical 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 model. Whengrorbit
is not provided, all graphlet orbits are evaluated by default. The optional base argument is a vector of distinct integers representing the list of categories inattrname
that are going to be omitted. When this argument is set to 0, all categories are evaluated. When this argument is set to 1, the category having the lowest value (or lexicographically first name) is eliminated. The term sorts all values of the categorical attribute lexicographically andbase
term defines the indexes of the categories to be omitted in this sorted list. For example, if the "fruit" attribute has values "orange", "apple", "banana" and "pear",grorbitFactor("fruit" , 0 , 2:3)
will ignore the "banana" and "orange" factors and evaluate the "apple" and "pear" factors. When thebase
argument is not provided, the argument is set to 1 by default. ThegrorbitFactor
term addsa x grorbit
terms into the model wherea
represents the number of attribute values that are evaluated in the model andgrorbit
is the number of graphlet orbits to be evaluated in the model. This term is defined for the 73 graphlet 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 is defined for 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