R: Metropolis-Hastings Proposal Methods for TERGM MCMC

ergm-proposals {tergm} | R Documentation

## Metropolis-Hastings Proposal Methods for TERGM MCMC

### Description

`tergm` uses a Metropolis-Hastings (MH) algorithm provided by `ergm` to control the behavior of the Markov Chain Monte Carlo (MCMC) for sampling networks. The MCMC chain is intended to step around the sample space of possible networks, selecting a network at regular intervals to evaluate the statistics in the model. For each MCMC step, n (n=1 in the simple case) toggles are proposed to change the dyad(s) to the opposite value. The probability of accepting the proposed change is determined by the MH acceptance ratio. The role of the different MH methods implemented in `tergm` is to vary how the sets of dyads are selected for toggle proposals. This is used in some cases to improve the performance (speed and mixing) of the algorithm, and in other cases to constrain the sample space.

The user may specify proposals directly if need be, but is encouraged to utilize the hints and constraints UI instead.

### Details

#### MH proposal methods implemented in the `tergm` package

- `InitErgmProposal.staticDiscordTNT`

  A version of `TNT` appropriate for CMLE fitting, with proposals stratified both by discordance status and edge status. The argument `ref` specifies the data relative to which discordance status is defined.

- `InitErgmProposal.discordTNT`

  A temporal version of `TNT`, with approximately `discordance_fraction` of proposed toggles being made on the set of discordant dyads, and approximately `1 - discordance_fraction` of proposed toggles being TNT proposals from the network. The value of `discordance_fraction` can be set by the user as a proposal argument, and defaults to `0.5`.

- `InitErgmProposal.discordBDStratTNT`

  A temporal version of `BDStratTNT`. Within each strat mixing type, approximately 50% of proposed toggles are made on discordant dyads, and approximately 50% of proposed toggles are TNT proposals from the network, all subject to the bounded degree and mixing type constraints. The degree bound constraint is imposed on the instantaneous network state (rather than the temporal operator networks).

  Proposal arguments are the same as for `BDStratTNT`, and should be passed in via the `bd` and `blocks` constraints and the `Strat` hint.

### References

Goodreau SM, Handcock MS, Hunter DR, Butts CT, Morris M (2008a). A statnet Tutorial. Journal of Statistical Software, 24(8). https://www.jstatsoft.org/v24/i08/.

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

Hunter DR, Handcock MS, Butts CT, Goodreau SM, Morris M (2008b). ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Journal of Statistical Software, 24(3). https://www.jstatsoft.org/v24/i03/.

Krivitsky PN (2012). Exponential-Family Random Graph Models for Valued Networks. Electronic Journal of Statistics, 2012, 6, 1100-1128. doi: 10.1214/12-EJS696

Morris M, Handcock MS, Hunter DR (2008). Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects. Journal of Statistical Software, 24(4). https://www.jstatsoft.org/v24/i04/.

### See Also

`tergm` package, `ergm`, `ergm-constraints`, and ergm's `ergm_proposal` help page

[Package tergm version 4.0.2 Index]