R: Bridge sampling to evaluate ERGM log-likelihoods and...

ergm.bridge.llr {ergm} | R Documentation

## Bridge sampling to evaluate ERGM log-likelihoods and log-likelihood ratios

### Description

`ergm.bridge.llr` uses bridge sampling with geometric spacing to estimate the difference between the log-likelihoods of two parameter vectors for an ERGM via repeated calls to `simulate.formula.ergm`.

`ergm.bridge.0.llk` is a convenience wrapper that returns the log-likelihood of configuration θ relative to the reference measure. That is, the configuration with θ=0 is defined as having log-likelihood of 0.

`ergm.bridge.dindstart.llk` is a wrapper that uses a dyad-independent ERGM as a starting point for bridge sampling to estimate the log-likelihood for a given dyad-dependent model and parameter configuration. Note that it only handles binary ERGMs (`response=NULL`) and with constraints (`constraints=`) that that do not induce dyadic dependence.

### Usage

    ergm.bridge.llr(object, response = NULL, constraints = ~., from, to,
      basis = NULL, verbose = FALSE, ..., llronly = FALSE,
      control = control.ergm.bridge())

    ergm.bridge.0.llk(object, response = response, constraints = ~., coef,
      ..., llkonly = TRUE, control = control.ergm.bridge())

    ergm.bridge.dindstart.llk(object, response = NULL, constraints = ~.,
      coef, dind = NULL, coef.dind = NULL, basis = NULL, ...,
      llkonly = TRUE, control = control.ergm.bridge())

### Arguments

`object` | A model formula. See `ergm` for details.
`response` | Name of the edge attribute whose value is to be modeled in the valued ERGM framework. Defaults to `NULL` for simple presence or absence, modeled via a binary ERGM.
`constraints` | A one-sided formula specifying one or more constraints on the support of the distribution of the networks being simulated. See the documentation for a similar argument for `ergm` for more information.
`from, to` | The initial and final parameter vectors.
`basis` | An optional `network` object to start the Markov chain. If omitted, the default is the left-hand-side of the `object`.
`verbose` | Logical: If TRUE, print detailed information.
`...` | Further arguments to `ergm.bridge.llr` and `simulate.formula.ergm`.
`llronly` | Logical: If TRUE, only the estiamted log-ratio will be returned by `ergm.bridge.llr`.
`control` | Control arguments. See `control.ergm.bridge` for details.
`coef` | A vector of coefficients for the configuration of interest.
`llkonly` | Whether only the estiamted log-likelihood should be returned by the `ergm.bridge.0.llk` and `ergm.bridge.dindstart.llk`. (Defaults to TRUE.)
`dind` | A one-sided formula with the dyad-independent model to use as a starting point. Defaults to the dyad-independent terms found in the formula `object` with an overal density term (`edges`) added if not redundant.
`coef.dind` | Parameter configuration for the dyad-independent starting point. Defaults to the MLE of `dind`.

### Value

If `llronly=TRUE` or `llkonly=TRUE`, these functions return the scalar log-likelihood-ratio or the log-likelihood. Otherwise, they return a list with the following components:

`llr` | The estimated log-ratio.
`llrs` | The estimated log-ratios for each of the `nsteps` bridges.
`path` | A numeric matrix with nsteps rows, with each row being the respective bridge's parameter configuration.
`stats` | A numeric matrix with nsteps rows, with each row being the respective bridge's vector of simulated statistics.
`Dtheta.Du` | The gradient vector of the parameter values with respect to position of the bridge.

`ergm.bridge.0.llk` result list also includes an `llk` element, with the log-likelihood itself (with the reference distribution assumed to have likelihood 0).

`ergm.bridge.dindstart.llk` result list also includes an `llk` element, with the log-likelihood itself and an `llk.dind` element, with the log-likelihood of the nearest dyad-independent model.

### References

Hunter, D. R. and Handcock, M. S. (2006) Inference in curved exponential family models for networks, Journal of Computational and Graphical Statistics.

### See Also

`simulate.formula.ergm`

[Package ergm version 3.10.4 Index]