ergm-hints: Hints for Exponential-Family Random Graph Models

Description Hints implemented in the ergm package

Description

These hints may be used to control proposal probabilities.

Hints implemented in the ergm package

sparse (dyad-independent)

The network is sparse. This typically results in a Tie-Non-Tie (TNT) proposal regime.

strat(attr=NULL, pmat=NULL, empirical=FALSE) (dyad-independent)

The dyads in the network are stratified according to an attribute combination.

This typically results in stratifying proposals by mixing type on a vertex attribute.

Specifically, the user may pass a vertex attribute attr as an argument (the default for attr gives every vertex the same attribute value), and may also pass a matrix of weights pmat (the default for pmat gives equal weight to each mixing type). See Specifying Vertex Attributes and Levels for details on specifying vertex attributes. The matrix pmat, if specified, must have the same dimensions as a mixing matrix for the network and attribute under consideration, and the correspondence between rows and columns of pmat and values of attr is the same as for a mixing matrix.

The interpretation is that pmat[i,j]/sum(pmat) is the probability of proposing a toggle for mixing type (i,j). (For undirected, unipartite networks, pmat is first symmetrized, and then entries below the diagonal are set to zero. Only entries on or above the diagonal of the symmetrized pmat are considered when making proposals. This accounts for the convention that mixing is undirected in an undirected, unipartite network: a tail of type i and a head of type j has the same mixing type as a tail of type j and a head of type i.)

As an alternative way of specifying pmat, the user may pass empirical=TRUE to use the mixing matrix of the network beginning the MCMC chain as pmat. In order for this to work, that network should have a reasonable (in particular, nonempty) edge set.

While some mixing types may be assigned zero proposal probability (either with a direct specification of pmat or with empirical=TRUE), this will not be recognized as a constraint by all components of ergm, and should be used with caution.


ergm documentation built on July 27, 2021, 5:07 p.m.