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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
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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
> Web: https://urldefense.proofpoint.com/v2/url?u=http-3A__www.zacharyneal.com&d=DwIFaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=yQQsvTNAnbvDXGM4nDrXAje4pr0qHX2qIOcCQtJ5k3w&m=E-51WLT-eBxvi-G55o59o93aqgiBexNWHMbfV54IWbA&s=X0fveTY6XE8JEhcxF2b4KQl-3qioZYvw6knSQJcFYPc&e= 
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>
> 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
> https://urldefense.proofpoint.com/v2/url?u=http-3A__www.stats.ox.ac.uk_-7Esnijders&d=DwIFaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=yQQsvTNAnbvDXGM4nDrXAje4pr0qHX2qIOcCQtJ5k3w&m=E-51WLT-eBxvi-G55o59o93aqgiBexNWHMbfV54IWbA&s=nLFQZJa15-5EMqu2jnUm_2tq8JgaV5hvYpN3uRSWq70&e= 
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>
>
> On Thu, Jun 4, 2020 at 10:06 PM Michał Bojanowski <[log in to unmask]>
> wrote:
>
>> ---------------------- Information from the mail header
>> -----------------------
>> Sender:       Social Networks Discussion Forum <[log in to unmask]>
>> 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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