Change the tie-level link function?

[stouffer]

Currently the code is set up to use the default logit link for the binomial regression that occurs at the tie level. Is there any way to allow the user to change the link function when MPLE.type == "glm". In particular, I am interested in using family = binomial(link = 'cloglog').

Based on what I can see in the code, it would seem like this could be added as an additional option within control.ergm(). Superficially, changing the link function should be fine when that change gets passed to glm() but it's unclear to me what else might break upstream or downstream of the calls to ergm.mple() (which seems like the crucial and possibly only place that the family information and link function are explicitly specified and used).

[mbojan]

Thanks for inquiring. This might be not that trivial to work for both dyad-independent and dyad-dependent models. Still, what you are asking seems simpler than variations with different distributions for tie values/weights (cf https://doi.org/10.1214%2F12-EJS696). @krivit ?

[krivit]

A GLM with a logit link is not a modelling choice here but rather the unique result that emerges when evaluating the pseudolikelihood for a non-curved binary ERGM or the likelihood of a non-curved binary ERGM whose sufficient statistics are weighted sums of edge indicators. This, in turn, is because the logit link is the canonical link for binomial response.

Thus, specifying other links does not make sense in the context of MPLE. And, to be clear, MPLE as it stands has nothing to do with ERGMs for counts.

If you want to use an alternative link to model edge probabilities, my recommendation would be to use ergmMPLE() with appropriate output= argument to obtain the response and predictor matrices, then use glm() on those with your chosen link. This should, at least, produce sensible results for dyad-independent models.