If separately there is cor(g_ij, e_ij) that requires its own solution. But all these issues are present for standard analysis of complete genotyped pairs as well...
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In my reading they present the model as equivalent (in terms of bias) to a family fixed effects model. And that model also solves the issue of cor(g_ij, e_ij). But then we agree that they are only equivalent in a world with cor(g_ij, e_j) but no cor(g_ij, e_ij)?
I agree the goal is a sibs fixed effects model (potentially could do family trickier i think) where the right hand side is a genotype, as you'd require knowledge of the correlation between siblings on the right hand side. I'll have to spend some time to figure out whether I understand your point.
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