# [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.

Best,

Yaxin

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
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>* 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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