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 ergm-terms.

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; and base. attrname is a character vector giving the name of a categorical attribute in the network's vertex attribute list. The optional grorbit argument is a vector of distinct integers representing the list of graphlet orbits to include into the model. When grorbit 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 in attrname 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 and base 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 the base argument is not provided, the argument is set to 1 by default. The grorbitFactor term adds a x |grorbit| terms into the model where a represents the number of attribute values that are evaluated in the model and |grorbit| 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), 1-29, URL http://www.jstatsoft.org/v65/i12/.

See Also

statnet, network, ergm, ergm-terms