This document describes the process by which ergm
and related packages selects the MCMC proposal for a particular analysis. Note that it is not intended to be a tutorial as much as a description of what inputs and outputs different parts of the system expect. Nor does it cover the C API.
There is a number of factors that can affect MCMC sampling, some of them historical and some of them new:
functions and other structures defined in an accessible namespace
ergm_proposal_table()
a function that if called with no arguments returns a table of registered proposals and updates it otherwise. See ? ergm_proposal_table
for documentation and the meaning of its columns. Of particular interest is its Constraints
column, which encodes which constraints the proposal does (always) enforce and which it can enforce.InitErgmReference.<REFERENCE>
a family of initializers for the reference distribution. For the purposes of the proposal selection, among its outputs should be $name
specifying the name of the reference distribution.InitErgmConstraint.<CONSTRAINT>
a family of initializers for constraints, weightings, and other high-level specifiers of the proposal distribution. Hard constraints, probabilistic weights, and hints all use this API. For the purposes of the proposal selection, its outputs include
$constrain
(defaulting to <CONSTRAINT>
) a character vector specifying which constraints are enforced, and can include several semantically nested elements;$dependence
(defaulting to TRUE
) specifying whether the constraint is dyad-dependent;$priority
(defaulting to Inf
) specifying how important it is that the constraint is met (with Inf
meaning that it must be met); and$implies
/$impliedby
specifying which other constraints this constraint enforces or is enforced by, and this can include itself for constraints, such as edges
that can only be applied once.arguments and settings passed to the call or as control parameters.
constraints=
argument (top-level): A one-sided formula containing a +
- or -
-separated list of constraints. +
terms add additional constraints to the model whereas -
constraints relax them. -
constraints are primarily used internally observational process estimation and are not described in detail, except to note that 1) they must be dyad-independent and 2) they necessitate falling back to the RLEBDM sampling API.reference=
argument (top-level): A one-sided formula specifying the ERGM reference distribution, usually as a name with parameters if appropriate.control$MCMC.prop=
control parameter: A formula whose RHS containing +
-separated “hints” to the sampler; an optional LHS may contain the proposal name directly.control$MCMC.prop.weights=
control parameter: A string selecting proposal weighting (probably deprecated)control$MCMC.prop.args=
control parameter: A list specifying information to be passed to the proposalMost of this is implemented in the ergm_proposal.formula()
method:
InitErgmReference.<REFERENCE>
is called with arguments of reference=
’s LHS, obtaining the name of the reference.InitErgmConstraint.<CONSTRAINT>
function is called and their outputs are stored in a list of initialized constraints (an ergm_conlist
object). .dyads
pseudo-constraint is added to dyad-independent constraints (not to hints with $priority < Inf
).
constraints=
MCMC.prop=
$implies
/$impliedby
settings.ergm_proposal_table()
are filtered by Class
, Reference
, Weights
(if MCMC.prop.weights
differs from "default"
), and Proposal
(if the LHS of MCMC.prop
is provided).priority=Inf
, it is discarded.priority<Inf
and that the proposal doesn’t and can’t enforce, its (innate, specified in the column of the ergm_proposal_table()
) Priority
value is penalised by the priority
of that constraint.