Valid constraints for non-binary references?

[tylerandrewscott]

Hello, I'm having a little trouble figuring out how the constraints=~ options work/do not work in the context of, say, a Unif(0,1) reference ergm. Ideally I would like to constrain for the density of nonzero dyads or fix the degree of only a few high nonzero-degree nodes, but those sorts of options don't seem to work (or perhaps I'm just missing something obvious?).

[krivit]

Briefly, the way estimation works is that ergm takes the combination of constraints you've given it, plus the reference distribution and a few other things, and tries to figure out if it has a Metropolis-Hastings proposal that can sample from a space of networks that satisfies those constraints. If it doesn't, it stops with an error. At the moment, there are relatively few valued ERGM proposals that properly enforce constraints in ergm.

More generally, I don't know whether Unif(0,1) reference makes sense if you are going to have dyads that are 0 but are not fixed at 0. This is because for a continuous random variable X~Unif(0,1), Pr(X = 0) = 0 (and, more generally Pr(X = x) = 0 for any constant x). Your problem therefore probably requires a custom Metropolis-Hastings proposal.

[tylerandrewscott]

Ah, that makes total sense and is super helpful, thanks! -tyler

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On Sun, May 16, 2021 at 1:21 AM Pavel N. Krivitsky ***@***.***> wrote: Briefly, the way estimation works is that ergm takes the combination of constraints you've given it, plus the reference distribution and a few other things, and tries to figure out if it has a Metropolis-Hastings proposal that can sample from a space of networks that satisfies those constraints. If it doesn't, it stops with an error. At the moment, there are relatively few valued ERGM proposals that properly enforce constraints in ergm. More generally, I don't know whether Unif(0,1) reference makes sense if you are going to have dyads that are 0 but are not fixed at 0. This is because for a continuous random variable *X*~Unif(0,1), Pr(*X* = 0) = 0 (and, more generally Pr(*X* = *x*) = 0 for any constant *x*). Your problem therefore probably requires a custom Metropolis-Hastings proposal. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <#295 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AA4G7X4ANBTTCPFYHEPHNJLTN557LANCNFSM446WQ3CA> .

-- Tyler Scott ***@***.*** Department of Environmental Science and Policy University of California, Davis