"2) We didn't adjust for assortative mating. Assortative mating makes siblings more genetically similar for the assorted phenotype than expected (more than .50 correlated). I am not exactly sure how this would affect the ratio of the between/within family slope, but maybe it would."
It would affect the between/within ratio because they haven't yet captured the entire heritability of educational attainment.
Let EAPGS refer to the heritability that is captured by the EA PGS. Now clearly this can only capture some education genes and not all of them, e.g. it doesn't capture rare variants or most non-SNP forms of variation. So you've got a secondary latent heritability, covering all of the EA heritability that isn't captured under EAPGS. We could call this latent heritability EALH.
Now here's the critical bit: Due to assortative mating, EAPGS and EALH are correlated with each other between families. So when you use between-family regression to test for the effect of EAPGS, its correlation with EALH also gets counted as part of the effect. However, within families, the correlation between EAPGS and EALH gets broken, since you have your genes randomly assigned from your parents. This means that the within-family regression doesn't count any of the EALH effect.
Just eyeing the effect sizes involved, I would intuit that this could account for a good chunk of the drop in accuracy. However, my intuition might be wrong; when I asked gwern about it, he claimed that they had tested for assortative mating (in an earlier paper) and that this couldn't explain the drop in heritability. I wonder if they tested incorrectly, though. I couldn't find an easily comprehensible explanation of how they did it, and I haven't gotten around to just forcing myself through the advanced model, so I don't know. One possible flaw that I could imagine is that maybe they only considered assortative mating on the phenotype, even though it's known that EA has more assortative mating on the genotype.
I asked James Lee about this in 2018 or so when he presented EA3 at ISIR. I think it was in Toronto. Anyway, he said they had looked real hard into the measurement error aspect of the sibling vs. singleton issue. I don't recall seeing any simple explanation somewhere. Maybe just do your own simulations and see.
I didn't examine their analysis about dominance not being found but i pretty much doubt it.
You can have dominance effects where each allele's p-value doesn't reach Bufferoni threshold, but all of them taken together do improve score.
Maybe it's worth to establish ad hoc corrections for index based on number of rare alleles in individual's genome and heterozygosity?
An allele with 50% frequency is almost certainly neutral but a rare novel allele is likely negative.
Just for fun, how does this tie to (sorry for referencing other newsletters, they are all cool):
Rates of reproduction?
https://wyclif.substack.com/p/the-natural-selection-paper-part
https://wyclif.substack.com/p/the-natural-selection-paper-part-908
Personality (Noncognitive Ability) and risky behaviors (possibly dark traits)?
https://astralcodexten.substack.com/p/non-cognitive-skills-for-educational
"2) We didn't adjust for assortative mating. Assortative mating makes siblings more genetically similar for the assorted phenotype than expected (more than .50 correlated). I am not exactly sure how this would affect the ratio of the between/within family slope, but maybe it would."
It would affect the between/within ratio because they haven't yet captured the entire heritability of educational attainment.
Let EAPGS refer to the heritability that is captured by the EA PGS. Now clearly this can only capture some education genes and not all of them, e.g. it doesn't capture rare variants or most non-SNP forms of variation. So you've got a secondary latent heritability, covering all of the EA heritability that isn't captured under EAPGS. We could call this latent heritability EALH.
Now here's the critical bit: Due to assortative mating, EAPGS and EALH are correlated with each other between families. So when you use between-family regression to test for the effect of EAPGS, its correlation with EALH also gets counted as part of the effect. However, within families, the correlation between EAPGS and EALH gets broken, since you have your genes randomly assigned from your parents. This means that the within-family regression doesn't count any of the EALH effect.
Just eyeing the effect sizes involved, I would intuit that this could account for a good chunk of the drop in accuracy. However, my intuition might be wrong; when I asked gwern about it, he claimed that they had tested for assortative mating (in an earlier paper) and that this couldn't explain the drop in heritability. I wonder if they tested incorrectly, though. I couldn't find an easily comprehensible explanation of how they did it, and I haven't gotten around to just forcing myself through the advanced model, so I don't know. One possible flaw that I could imagine is that maybe they only considered assortative mating on the phenotype, even though it's known that EA has more assortative mating on the genotype.
I asked James Lee about this in 2018 or so when he presented EA3 at ISIR. I think it was in Toronto. Anyway, he said they had looked real hard into the measurement error aspect of the sibling vs. singleton issue. I don't recall seeing any simple explanation somewhere. Maybe just do your own simulations and see.