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Dear Zak,

I think it will be very difficult indeed to model such a network by an ERGM. Related to this, I think it would be much better to analyze the original two-mode by year network, rather than some one-mode projection.
Furthermore, I do not think that changes (from year to year) in estimated ERGM parameters for such a one-mode or two-mode network are an adequate reflection or operationalisation of "changes in homophily". I do not yet have a clear answer to the question "then what else would be an adequate reflection?".

Cheers,
Tom

=========================================
Tom A.B. Snijders
Professor of Statistics and Methodology, Dept of Sociology, University of Groningen
Emeritus Fellow, Nuffield College, University of Oxford
http://www.stats.ox.ac.uk/~snijders


On Wed, Jun 10, 2020 at 1:37 PM Neal, Zachary <[log in to unmask]> wrote:
Dear Tom,

Thanks for the feedback. 

The data are constructed via projection of two-mode data (in this case, bill co-sponsorship). But, we've used a null model to identify and retain only significant edges in the projection, so the one-mode network does not contain the kinds of artifacts normally generated by projection.

That said, the network does still contain numerous large cliques, which isn't surprising given the high transitivity. In this case, because the network represents ties between US legislators, its structure is primarily driven by clusters of republicans and democrats. The goal is to estimate both party and gender homophily, examining changes in both over time.

Do you have any suggestions on how to estimate an ERGM on such a network, or is it likely not possible?

Best,
Zak

–––
Zachary Neal, PhD
Associate Professor, Michigan State University
Twitter: @zpneal
Zoom: Click here

On Jun 8, 2020, at 11:33 AM, Snijders, T.A.B. <[log in to unmask]> wrote:

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Dear Zachary,

It is hard to say something meaningful without further information.
But a network with 450 nodes and density about 0.1 has average degree 45. That is extremely large and dense for an ERGM to fit well.
If you say transitivity is in the order of 0.6 then a model without gwesp (or similar) terms is sure to have a poor fit.
Just as a note, if the network was constructed as a one-mode projection of a two-mode network, then it probably will contain many cliques of order higher than 4, which is not in line with the idea of an ERGM, and is bound to lead to problems in estimation. (I bring this up just because I saw this issue earlier today.)

Cheers,
Tom

=========================================
Tom A.B. Snijders
Professor of Statistics and Methodology, Dept of Sociology, University of Groningen
Emeritus Fellow, Nuffield College, University of Oxford
http://www.stats.ox.ac.uk/~snijders


On Thu, Jun 4, 2020 at 10:06 PM Michał Bojanowski <[log in to unmask]> wrote:
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Poster:       =?UTF-8?Q?Micha=C5=82_Bojanowski?= <[log in to unmask]>
Subject:      Re: Help with EGRM non-convergence when using GWESP
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I should add that what I wrote before should not explain
non-convergence per se but rather guide you towards identifying the
problem of the model specification vs data. Looking at GOF plots for
the most complex model that you fit which converged should help you
understand why it stops converging when you add GWESP.

~Michal

On Thu, Jun 4, 2020 at 9:54 PM Michał Bojanowski <[log in to unmask]> wrote:
>
> Zachary,
>
> > I haven't spent much time looking at model GOF since I don't have a good comparison. The models that include nodematch terms obviously fit better than a null model that only contains the edges term, but that didn't seem particularly informative. If a model without GWESP appears to fit well, would it be acceptable to simply use it and ignore any structural effects.
>
> I guess the most important question is whether the model without GWESP
> accounts well for the ESP distribution. If it does, then you do not
> need GWESP term in the model. Folding this onto Goodreau et al
> exposition it would mean that the differential homophily you have in
> your model accounts for higher density within groups, and that already
> also accounts for the amount of transitivity in the network as whole
> (with higher density some transitivity will happen within groups "by
> accident"). Consequently, there would be not much transitivity left to
> "explain" by GWESP on top of the terms you already have in the model.
>
> Ad whether it is acceptable to go with a model without any structural
> (i.e. network endogeneous effects):
>
> This is of course a matter if it makes sense substantively. From a
> purely data-driven standpoint if a model with "demographic" effects
> only (attribute-related terms such as dyadcov, nodecov, nodefactor,
> nodematch, nodemix etc.) accounts for the network structure well in
> the sense of reproducing the important features in the data (degree
> distribution, ESP distribution and so on), then I would say yes.
>
> hth,
> Michal

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