ergm: ergm.exact – R documentation

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ergm.exact

Calculate the exact loglikelihood for an ERGM

Description

ergm.exact calculates the exact loglikelihood, evaluated at eta, for the statnet exponential-family random graph model represented by formula.

Usage

ergm.exact(eta, formula, statmat = NULL, weights = NULL, ...)

Arguments

`eta`	vector of canonical parameter values at which the loglikelihood should be evaluated.
`formula`	an `link{formula}` object of the form `y ~ <model terms>`, where `y` is a network object or a matrix that can be coerced to a `network` object. For the details on the possible `<model terms>`, see `ergm-terms`. To create a `network` object in , use the `network()` function, then add nodal attributes to it using the `%v%` operator if necessary.
`statmat`	if NULL, call `ergm.allstats` to generate all possible graph statistics for the networks in this model.
`weights`	In case `statmat` is not `NULL`, this should be the vector of counts corresponding to the rows of `statmat`. If `statmat` is `NULL`, this is generated by the call to `ergm.allstats`.
`...`	further arguments; not currently used.

Details

ergm.exact should only be used for small networks, since the number of possible networks grows extremely fast with the number of nodes. An error results if it is used on a directed network of more than 6 nodes or an undirected network of more than 8 nodes; use force=TRUE to override this error.

In case this function is to be called repeatedly, for instance by an optimization routine, it is preferable to call ergm.allstats first, then pass statmat and weights explicitly to avoid repeatedly calculating these objects.

Value

Returns the value of the exact loglikelihood, evaluated at eta, for the statnet exponential-family random graph model represented by formula.

Examples

# Count by brute force all the edge statistics possible for a 7-node 
# undirected network
mynw <- network(matrix(0,7,7),dir=FALSE)
system.time(a <- ergm.allstats(mynw~edges))

# Summarize results
rbind(t(a$statmat),a$weights)

# Each value of a$weights is equal to 21-choose-k, 
# where k is the corresponding statistic (and 21 is 
# the number of dyads in an 7-node undirected network).  
# Here's a check of that fact:
as.vector(a$weights - choose(21, t(a$statmat)))

# Simple ergm.exact outpuf for this network.  
# We know that the loglikelihood for my empty 7-node network
# should simply be -21*log(1+exp(eta)), so we may check that
# the following two values agree:
-21*log(1+exp(.1234)) 
ergm.exact(.1234, mynw~edges, statmat=a$statmat, weights=a$weights)

ergm

Fit, Simulate and Diagnose Exponential-Family Models for Networks

v3.11.0

GPL-3 + file LICENSE

Authors

Mark S. Handcock [aut], David R. Hunter [aut], Carter T. Butts [aut], Steven M. Goodreau [aut], Pavel N. Krivitsky [aut, cre] (<https://orcid.org/0000-0002-9101-3362>), Martina Morris [aut], Li Wang [ctb], Kirk Li [ctb], Skye Bender-deMoll [ctb], Chad Klumb [ctb], Michał Bojanowski [ctb], Ben Bolker [ctb]

Initial release

2020-10-14