ergm.eta: Operations to map curved 'ergm()' parameters onto canonical...

In ergm: Fit, Simulate and Diagnose Exponential-Family Models for Networks

Operations to map curved ergm() parameters onto canonical parameters

Description

The 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.

Usage

ergm.eta(theta, etamap)

ergm.etagrad(theta, etamap)

ergm.etagradmult(theta, v, etamap)

Arguments

theta	the curved model parameters
etamap	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: canonical a numeric vector whose ith entry specifies whether the ith component of theta is canonical (via non-negative integers) or curved (via zeroes) offsetmap a logical vector whose ith entry tells whether the ith coefficient of the canonical parameterization was "offset", i.e fixed offset a logical vector whose ith entry tells whether the ith model term was offset/fixed offsettheta a logical vector whose ith entry tells whether the ith curved theta coeffient was offset/fixed; curved a list with one component per curved EF term in the model containing from the indices of the curved theta parameter that are to be mapped from to the indices of the canonical eta parameters to be mapped to map the map provided by InitErgmTerm gradient the gradient function provided by InitErgmTerm cov optional additional covariates to be passed to the map and the gradient functions etalength the length of the eta vector
v	a vector of the same length as the vector of mapped eta parameters

Details

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.

Value

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.

References

• 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.

See Also

ergmTerm

ergm documentation built on Oct. 7, 2024, 5:08 p.m.