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For a paper, I've ran an ergm model. A reviewer has requested that to run a sensitivity analyses on the model, with the goal of checking how strong the effect of an unobserved and unmeasured confounding variable has to be in order to explain away the effect of the independent variable. The reviewer specifically pointed to this paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4288024/.

I don't really an idea how to go about this. So any and all help is much appreciated. I have provided a reproducible example below.

library(statnet)
data(flo)
flomarriage <- network(flo,directed=FALSE)
flomarriage

flomarriage %v% "wealth" <- c(10,36,27,146,55,44,20,8,42,103,48,49,10,48,32,3)
flomarriage
gest <- ergm(flomarriage ~ edges + 
               absdiff("wealth"))
summary(gest)

Based on the model, it is estimated that a wealth difference of 10 corresponds to a 0.182511 probability of a tie. How can I estimate how strong an unmeasured confouders needs to be in order for this effect to dissapear?

I have looked into several packages such as the tipr package (https://cran.r-project.org/web/packages/tipr/index.html), but I'm not sure this is what I'm looking for or if it is, how to apply it to my model.

Christophe Lesschaeve
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  • are you having trouble with the statistics or the programming part? – Mike Apr 05 '23 at 20:55
  • I guess a bit of both. Is it enough to simulate dyadic covariates that correlate to various degrees with the likelihood of a tie and add them to the model? And if so, how do you simulate such covariates? – Christophe Lesschaeve Apr 14 '23 at 13:28

1 Answers1

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The paper you linked is about network contagion. In the context of modeling network structure it is IMHO less clear what one would mean by a "confounder"... Especially that all sorts of network features are correlated "by construction" (eg density and clustering -- the denser the network the more triangles). Still, I guess I can imagine generating e.g. dyadic covariates with variable effect on tie probability, including them via dyadcov or edgecov term, and hoping the effect in question will vanish in such extended model. IMHO you would have to argue though that it makes sense to consider only confounders in the form of dyadic covariates, because this is by far not the only form of a "confounder" one could think of.

Michał
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