ergmProposal: Metropolis-Hastings Proposal Methods for ERGM MCMC
In ergm: Fit, Simulate and Diagnose Exponential-Family Models for Networks

ergmProposal

R Documentation

Metropolis-Hastings Proposal Methods for ERGM MCMC

Description

This page describes the low-level Metropolis–Hastings (MH) proposal algorithms. They are rarely invoked directly by the user but are rather selected based on the provided sample space constraints and hints about the network process. They can also be searched via search.ergmProposals, and help for an individual proposal can be obtained with ⁠ergmProposal?<proposal>⁠ or help("<proposal>-ergmProposal").

Details

ergm uses a Metropolis-Hastings (MH) algorithm 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, generating a network at regular intervals to evaluate the statistics in the model. For each MCMC step, one or more toggles are proposed to change the dyads 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 ergm() 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.

Proposals available to the package

\ergmCSS \Sexpr[results=rd,stage=render]{ergm:::.formatProposalsHtml(ergm:::.buildProposalsList(), keepProposal=TRUE)}

Note that .dyads is a meta-constraint, indicating that the proposal supports an arbitrary dyad-level constraint combination.

References

Goodreau SM, Handcock MS, Hunter DR, Butts CT, Morris M (2008a). A statnet Tutorial. Journal of Statistical Software, 24(8). \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v024.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). \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v024.i03")}
Krivitsky PN (2012). Exponential-Family Random Graph Models for Valued Networks. Electronic Journal of Statistics, 2012, 6, 1100-1128. \Sexpr[results=rd]{tools:::Rd_expr_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). \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v024.i04")}