Specifies each
dyad's baseline distribution to be Poisson with mean 1:
\(h(y)=\prod_{i,j} 1/y_{i,j}!\) , with the support of
\(y_{i,j}\) being natural numbers (and \(0\) ). Using
valued ERGM terms that are
"generalized" from their binary counterparts, with form
"sum" (see previous link for the list) produces Poisson
regression. Using CMP induces a
Conway-Maxwell-Poisson distribution that is Poisson when its
coefficient is \(0\) and geometric when its coefficient is
\(1\) .
@details Three proposal functions are currently implemented, two of them
designed to improve mixing for sparse networks. They can can be
selected via the MCMC.prop.weights= control parameter. The
sparse proposals work by proposing a jump to 0. Both of them take
an optional proposal argument p0 (i.e.,
MCMC.prop.args=list(p0=...) ) specifying the probability of
such a jump. However, the way in which they implement it are
different:
"random": Select a dyad (i,j) at random, and draw the
proposal \(y_{i,j}^\star \sim \mathrm{Poisson}_{\ne
y_{i,j}}(y_{i,j}+0.5)\) (a Poisson distribution with mean
slightly higher than the current value and conditional on not
proposing the current value).
"0inflated": As "random" but, with
probability p0 , propose a jump to 0 instead of a
Poisson jump (if not already at 0). If p0 is not given,
defaults to the "surplus" of 0s in the observed network,
relative to Poisson.
"TNT": (the default) As "0inflated" but
instead of selecting a dyad at random, select a tie with
probability p0 , and a random dyad otherwise, as with
the binary TNT. Currently, p0 defaults to 0.2.
# PoissonergmReference for index of reference distributions currently visible to the package.
ergm:::.formatTermKeywords("ergmReference", "Poisson", "subsection")