[statnet_help] statnet_help Digest, Vol 167, Issue 7

Adam Haber adamhaber at gmail.com
Sun Jul 19 12:43:48 PDT 2020


Hi Carter,

Thanks (again!) for the detailed response. I’m probably missing something, but I’m not sure I understand why mutuality would be the relevant term here. Let’s say that my nodes are embedded in 2D, and node i is at the origin. I also have two other nodes - node j at (1,0) and node k at (1.001, 0) - such that j and k are very close, relative to i. I’m trying to build a model in which the edges (i->j) and (i->k) are dependent - if one of them exists, the other is more likely to exists as well. Mathematically, I think a good way to denote what I’m trying to achieve is P(i->k | i->j, j and k are very close) > P(i->k), where P(i->k) is the marginal probability that an edge from i to k exists (already taking into account their distance and potentially the effects of other terms).

If I understand correctly, mutuality would affect P(j->i | i->j), or P(i->k | k-> i), but not P(i->k | i->j). But again, maybe I’m missing something - I’m quite new to ERGMs.

Regarding interaction - I thought one possible way to do this is to “discretise” the close/far into categories (clusters of nodes), and then add an interaction term between this new “cluster factor” and relevant triad-related terms, as these seem to capture this dependence I’m after. Like you said, I’m not sure ERGM exposes such functionality.

Thanks again!
Best,
Adam


> On 19 Jul 2020, at 22:01, statnet_help-request at mailman13.u.washington.edu wrote:

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> Today's Topics:

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> 1. Interactions in a distance-dependent model (Adam Haber)

> 2. Re: Interactions in a distance-dependent model (Carter T. Butts)

>

> From: Adam Haber <adamhaber at gmail.com>

> Subject: [statnet_help] Interactions in a distance-dependent model

> Date: 19 July 2020 at 13:07:23 GMT+3

> To: statnet_help at u.washington.edu

>

>

> Hello,

>

> Following a recent question I’ve posted here (and got very helpful responses - thank you!), I’m trying to add more “domain knowledge” into the model. Specifically, the nodes in the network we're studying are embedded in 3D, and we’ve seen that (as expected) adding distance-dependence to the model (via an edgecov(x) term such that x is the distance matrix) indeed improves the GOF.

>

> I want to take this one step further: I know that if there’s a (directed) edge i->j, and j and k are “close” (spatially), it should increase the probability that there’s an edge i->k. Another option would be to “discretize” the distances and group nodes into groups of “spatial loci", and add a term that if there’s an edge i->j and j and k are in the same spatial cluster (a binary indicator function), than this should increase the probability of the edge i->k.

>

> Is there a way to incorporate this sort of reasoning into an ergm model using any of the available terms? I went over the examples I could find and did not encounter anything similar...

>

> Thanks again,

> Respectfully,

> Adam Haber

>

>

>

>

>

> From: "Carter T. Butts" <buttsc at uci.edu>

> Subject: Re: [statnet_help] Interactions in a distance-dependent model

> Date: 19 July 2020 at 14:15:20 GMT+3

> To: statnet_help at u.washington.edu

>

>

> Hi, Adam -

>

> If you have a mutuality term in the model, it already accounts for that effect. Do you intend to say that you expect proximate vertices to reciprocate at higher rates - above and beyond the propinquity effect - than distant vertices? (Again, if you have a propinquity effect, it will already be the case that, ceteris paribus, reciprocation will be more likely for proximate vertices.)

>

> If you want this type of effect, it can be realized with the dyadcov term, or by creating an interaction term between mutual and edgecov. I don't think the user-level functionality for the latter option is yet exposed, though it's pretty easy to code it using ergm.userterms; however, dyadcov will probably suit your purposes.

>

> Hope that helps,

>

> -Carter

>

> On 7/19/20 3:07 AM, Adam Haber wrote:

>> Hello,

>>

>> Following a recent question I’ve posted here (and got very helpful responses - thank you!), I’m trying to add more “domain knowledge” into the model. Specifically, the nodes in the network we're studying are embedded in 3D, and we’ve seen that (as expected) adding distance-dependence to the model (via an edgecov(x) term such that x is the distance matrix) indeed improves the GOF.

>>

>> I want to take this one step further: I know that if there’s a (directed) edge i->j, and j and k are “close” (spatially), it should increase the probability that there’s an edge i->k. Another option would be to “discretize” the distances and group nodes into groups of “spatial loci", and add a term that if there’s an edge i->j and j and k are in the same spatial cluster (a binary indicator function), than this should increase the probability of the edge i->k.

>>

>> Is there a way to incorporate this sort of reasoning into an ergm model using any of the available terms? I went over the examples I could find and did not encounter anything similar...

>>

>> Thanks again,

>> Respectfully,

>> Adam Haber

>>

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