[statnet_help] Improving convergence for valued-ERGMs

Yaxin Cui yaxincui2023 at u.northwestern.edu
Fri Dec 25 09:39:02 PST 2020

Thank you so much, Cart! I really appreciate your sharing!

A follow-up question. What should be a good criterion for selecting the
reference distribution? In my understanding, if the link strength of my
network is discrete and bounded (e.g., 0,1,2,3,4), I can only choose from
DisUnif and Binomial distribution. Do I need to select the reference
distribution based on my link strength distribution? Or as long as my data
is enough, I can use any reference distribution (prior) as in many other
Bayesian scenarios.

Thank you so much for your help again.


On Thu, Dec 24, 2020 at 8:13 PM Carter T. Butts <buttsc at uci.edu> wrote:

> Hi, Yaxin -


> Valued ERGMs are (in general) much more complex than binary ERGMs, and

> much less well-understood. The tools embedded in ergm() for binary

> networks by now have the accumulated wisdom of many years of hard work by

> lots of folks, which has made them much easier to use than they were when

> the tools were first released, but in the valued world things are still in

> their infancy. One side effect of that is that you may need to do more

> tinkering with the model settings to get good convergence in valued models,

> and indeed it can be more difficult in some cases. A lot here depends upon

> your support (i.e., what types of edge values you are dealing with), your

> reference measure, your model terms, and the distribution of your edge

> values. For instance, if you are dealing with count ERGMs with highly

> skewed edge variables covering a large range (e.g., several orders of

> magnitude), then it is very hard to squeeze good performance out of the

> current generation of MCMC algorithms - we expect to have some results to

> show at the upcoming NASN conference regarding practical techniques for

> dealing with this large network/large edge variation regime, so stay tuned

> on that front.


> Absent more details, my initial advice would be as follows. First, check

> your model specification (and remember that valued terms are not the same

> as valued terms), and dial back any sources of dependence. (In fact, if

> you can't get the model to work well, start with no dependence, and add it

> back sparingly.) You may find that for things like mutuality, the "min"

> specification leads to more stable models, though that's a heuristic - in

> any event, bear in mind that terms that are trivial in the binary setting

> can have non-trivial behavior (and require non-trivial parameterization

> choices) in the valued setting. Second, inspect your trace plots, and make

> sure that you're running long enough chains. You may need very, very long

> chains. My rule of thumb for recalcitrant models is that you want a

> thinning interval (and burn-in) of around N^2*k iterations, where N is the

> number of vertices and k is a "big enough number" that depends on the

> application. The intuition is that this is enough draws to visit every

> edge variable an average of roughly k times (or approximately 2k, in the

> undirected case, but what's a factor of two between friends?) - with TNT

> sampling, those "visits" will not *actually* be allocated evenly, but the

> heuristic is still a helpful starting point. With valued graphs, it's not

> enough to merely "toggle" an edge (you need to be able to sample over the

> distribution of edge values), so k might need to be appreciable. Ideally,

> you find settings that give you reasonable mixing for a low-dependence

> model; at that point, you can then try to dial dependence back in. If that

> still fails, I would (third heuristic) revisit the marginal distribution of

> your edge values, and see if you need to rethink your reference measure.

> This may help in some cases (though it is not a panacea).


> Hope that helps!


> -Carter

> On 12/24/20 5:22 PM, Yaxin Cui wrote:


> Hello,


> I am working on valued-ERGM models and feel it is very hard to get the

> model converged. Given my network is quite sparse, where I have around 400

> nodes and a density of 0.14, are there any general suggestions to make the

> model converged via "control. ergm"?


> Any resources are welcomed! Thanks so much!


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