[statnet_help] Improving convergence for valued-ERGMs
Carter T. Butts
buttsc at uci.edu
Thu Dec 24 18:11:22 PST 2020
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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