R: Operations with 'eta' vector of canonical parameter values...

ergm.eta {ergm} | R Documentation

## Operations with 'eta' vector of canonical parameter values from ergm model

### Description

The `ergm.eta` function calculates and returns eta, mapped from theta using the etamap object created by `ergm.etamap`.

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

The `ergm.etamap` function takes a model object and creates a mapping from the model parameters, theta, to the canonical (linear) eta parameters; the mapping is carried out by `ergm.eta`

### Usage

    ergm.eta(theta, etamap)

    ergm.etagrad(theta, etamap)

    ergm.etagradmult(theta, v, etamap)

    ergm.etamap(model)

### Arguments

`theta` | the curved model parameters
`etamap` | the list of values that constitutes the theta-> eta mapping and is returned by `ergm.etamap`
`v` | a vector of the same length as the vector of mapped eta parameters
`model` | model object, as returned by `ergm.getmodel`

### Details

This function is only 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 sufficient statistics (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`: `eta` the canonical eta parameters as mapped from theta

- for `ergm.etagrad`: `etagrad` a matrix of the gradient of eta

- for `ergm.etagradmult`: `ans` the vector that is the product of the gradient of eta and `v`; infinite values are replaced by (+-)10000

- for `ergm.etamap` the theta -> eta mapping given by a list of the following:

  - 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 : the eta covariance ??, possibly always NULL (no <Init> function creates such an item)

  - etalength : the length of the eta vector

### 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

`ergm-terms`

[Package ergm version 3.8.0 Index]