ergm() parameters onto canonical parametersThe ergm.eta function calculates and returns eta, mapped
from theta using the etamap object, usually attached as the
$etamap element of an ergm_model object.
The ergm.etagrad function caculates and returns
the gradient of eta mapped from theta using the etamap object
created by ergm.etamap. If the gradient is only intended
to be a multiplier for some vector, the more efficient
ergm.etagradmult is recommended.
The ergm.etagradmult function calculates and
returns the product of the gradient of eta with a vector v.
ergm.eta(theta, etamap)ergm.etagrad(theta, etamap)
ergm.etagradmult(theta, v, etamap)
For ergm.eta, the canonical eta parameters as mapped
from theta.
For ergm.etagrad, a matrix of the gradient of eta
with respect to theta.
For ergm.etagradmult, the vector that is the product
of the gradient of eta and v.
the curved model parameters
the list of values that describes the theta -> eta
mapping, usually attached as $etamap element of an ergm_model
object. At this time, it is a list with the following elements:
canonicala numeric vector whose ith entry specifies whether the ith component of theta is canonical (via non-negative integers) or curved (via zeroes)
offsetmapa logical vector whose ith entry tells whether the ith coefficient of the canonical parameterization was "offset", i.e fixed
offseta logical vector whose ith entry tells whether the ith model term was offset/fixed
offsetthetaa logical vector whose ith entry tells whether the ith curved theta coeffient was offset/fixed;
curveda list with one component per curved EF term in the model containing
fromthe indices of the curved theta parameter that are to be mapped from
tothe indices of the canonical eta parameters to be mapped to
mapthe map provided by InitErgmTerm
gradientthe gradient function provided by InitErgmTerm
covoptional additional covariates to be passed to the map and the gradient functions
etalengththe length of the eta vector
a vector of the same length as the vector of mapped eta parameters
These functions are mainly important in the case of curved exponential family models, i.e., those in which the parameter of interest (theta) is not a linear function of the natural parameters (eta) in the exponential-family model. In non-curved models, we may assume without loss of generality that eta(theta)=theta.
A succinct description of how eta(theta) is incorporated into an ERGM is given by equation (5) of Hunter (2007). See Hunter and Handcock (2006) and Hunter (2007) for further details about how eta and its derivatives are used in the estimation process.
Hunter, D. R. and M. S. Handcock (2006). Inference in curved exponential family models for networks. Journal of Computational and Graphical Statistics, 15: 565--583.
Hunter, D. R. (2007). Curved exponential family models for social networks. Social Networks, 29: 216--230.
ergmTerm