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").
ergm:::.formatProposalsHtml(ergm:::.buildProposalsList(), keepProposal=TRUE)
Note that .dyads is a meta-constraint, indicating that the proposal supports an arbitrary dyad-level constraint combination.
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.
Goodreau SM, Handcock MS, Hunter DR, Butts CT, Morris M (2008a). A statnet Tutorial. Journal of Statistical Software, 24(8). 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). 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. 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). tools:::Rd_expr_doi("10.18637/jss.v024.i04")
ergm package, ergm, ergmConstraint, ergmHint, ergm_proposal