[statnet_help] standardized coefficients in ERGMs

[Krause, Robert]

Dear Jing,


In general terms, it is extremely difficult to compare parameters across models. Carina Mood (2010) showed this in detail for simple logistic regression models. Her results very much hold for ergms but are much more pronounced here due to the increased complexity and the connectedness, of well, everything.

If you go to the mail that Carter wrote this morning and take the example he used, that you might have subgroups based on some covariate which have high levels of transitive closure within the groups but relatively fewer ties (and thus also fewer transitive ties) between groups. And now compare this to a network where the same covariates exert a far weaker influence on homophilic clustering. If the transitivity (gwesp...) parameters are the same across the two networks (but density is different so that overall degree is the same), for most people the real contribution on probability for creating a tie due to shared partners will be different.

If you take the odds ratios, as I often see as a reviewer, than they are (as Mood 2010 shows!!) not a good idea, because, say your have a reciprocity/mutual effect of '2', then this effect will matter very differently for a dyad that shares several covariates and has many friends in common, having the incoming tie will increase the probability, but the real effect might be relatively small, given that the probability to connect was already high. On the other hand, two nodes that do not share any covariates or friends in common might be much stronger affected if one send a tie to another. If a certain parameter now primarily occurs together with other parameters in one network or one part of a network (e.g., where there are subgroups there is also clustering - but no interaction between groups and clustering), then this is very difficult to compare to another network.


So, in short, no the parameters are not standardized and there is no easy way to do this.

Average marginal effect would be great to have but no one has, as far as I know, implemented them or something similar for ergms and the computational power required will probably be very large in all but trivial models or very small graphs (SAOMs have Relative Importance, see Indlekofer & Brandes 2013, and something similar could probably be implemented in ergm).

One option would be to create a few example cases and vary the statistics for the parameters to see the effects on tie probability, something like Marginal Effect at Representative values (MER)?


Sorry :/ I do not have a better answer - and sorry for the late response, I saw the mail last month but forgot to reply...


Cheers from a (way too) sunny Berlin,

Robert

________________________________
Von: statnet_help <statnet_help-bounces at mailman13.u.washington.edu> im Auftrag von Jing Chen <chenj.chenjing at outlook.com>
Gesendet: Donnerstag, 16. Juni 2022 13:43:57
An: statnet_help at u.washington.edu
Betreff: [statnet_help] standardized coefficients in ERGMs

Dear Statnet community,

I am posting this question again – not sure if the previous one was sent successfully.

I am trying to compare the strength of an edge effect across ERGMs (the identical model specification, but the outcome objects are different). I am wondering how do we talk about effect sizes in the ERGM world? Are the “regression” coefficients presented in the ERGM output standardized? If not, is there a way to do so?

Any information would be appreciated. Thank you!

Jing Chen, Ph.D.
Assistant professor
Shanghai Jiao Tong University


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