Poisson-ergmReference {ergm.count}

Poisson-reference ERGM

Description

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.

Usage

# Poisson

See Also

ergmReference for index of reference distributions currently visible to the package.