[statnet_help] Distance-dependent ERGM model

Carter T. Butts buttsc at uci.edu
Wed Jul 8 18:31:00 PDT 2020


Hi, Adam -

Distance-based models are indeed a thing.  Although there many are other
things you can do, the easiest starting point is usually to calculate
the distances among all vertices in whatever metric is most apposite (in
your case, Euclidean space), and use the distance matrix or some
function thereof as an edgecov.  Using the raw distances as an edge
covariate implicitly models a logistic effect of distances on tie
probability; it can make sense when ties are necessarily local.  In
social settings, it usually makes more sense to work with the log
distances, which approximates a power-law decline in marginal tie
probability as a function of distance.  If you can effectively draw a
sphere around a node and say to yourself (and others), "well, the chance
of there being any ties to nodes outside this sphere is essentially
zero" (i.e., probability small and falling exponentially), then the draw
model is a reasonable approximation.  If not (i.e., there's always some
non-vanishing chance of a long range tie, even if the probability is
very low), then you want the log version.  (Yes, this is heuristic, and
there are other things that one can do.  But I would start with this.)

Hope that helps,

-Carter

On 7/8/20 1:15 PM, Adam Haber wrote:

> Hello,

>

> (Apologies in advance if this is a trivial question - I’m quite new to modelling with ERGMs, and I couldn’t find an answer elsewhere...)

>

> The nodes in the network I’m studying are embedded in 3D, and I have reasons to believe that the spatial organisation plays a major role in the structure of the network, along with a specific node-level attribute. How can one model such a spatial dependency using ergm? AFAIU, it’s not absdiff, since it’a a function of 3 numeric node-level attributes (it’s x-y-z coordinates). Is it also possible to have a different distance-dependence for different levels of some node-level attribute?

>

> Any help would be much appreciated!

>

> Best regards,

> Adam Haber

> Department of Neurobiology

> Weizmann Institute of Science

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