ChristianKl comments on Open thread, December 7-13, 2015 - Less Wrong

3 Post author: polymathwannabe 07 December 2015 02:47PM

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Comment author: ChristianKl 09 December 2015 08:02:28PM 1 point [-]

No, actually, genetic studies of both milk production and IQ show them to be mainly linear.

What kind of study do you think shows IQ to be mainly linear?

I would guess that you confuse assumptions that the researchers behind a study make to reduce the amount of factors with finding of the study.

Comment author: Douglas_Knight 09 December 2015 11:20:28PM 0 points [-]

There are decades of studies of the heritability of IQ. Some of them measure H², which is full heritability and some of them measure h², "narrow sense heritability"; and some measure both. Narrow sense heritability is the linear part, a lower bound for the full broad sense heritability. A typical estimate of the nonlinear contribution is H²-h²=10%. In neither case do they make any assumptions about the genetic structure. Often they make assumptions about the relation between genes and environment, but they never assume linear genetics. Measuring h² is not assuming linearity, but measuring linearity.

This paper finds a lower bound for h² of 0.4 and 0.5 for crystallized and fluid intelligence, respectively, in childhood. I say lower bound because it only uses SNP data, not full genomes. It mentions earlier work giving a narrow sense heritability of 0.6 at that age. That earlier work probably has more problems disentangling genes from environment, but is unbiased given its assumptions.

Comment author: ChristianKl 09 December 2015 11:49:39PM *  2 points [-]

The linked paper says:

We fitted a linear mixed model y = µ + g + e, where y is the phenotype, m is the mean term, g is the aggregate additive genetic effect of all the SNPs and e is the residual effect.

If you have 3511 individuals and 549692 SNPs you won't find any nonlinear effects. 3511 observations of 549692 SNPs is already overfitted 3511 observations of 549692 * 549691 gene interactions is even more overfitted and I wouldn't expect that the four four principal components they calculate to find an existing needle in that haystack.

Apart from that it's worth noting that IQ is g fitted to a bell curve. You wouldn't expect a variable that you fit to a bell curve to behave fully linearly.

Comment author: Douglas_Knight 10 December 2015 12:36:45AM -1 points [-]

No, they didn't try to measure non-linear effects. Nor did they try to measure environment. That is all irrelevant to measuring linear effects, which was the main thing I wanted to convey. If you want to understand this, the key phrase is "narrow sense heritability." Try a textbook. Hell, try wikipedia.

That it did well on held-back data should convince you that you don't understand overfitting.

Actually, I would expect a bell curve transformation to be the most linear.

Comment author: ChristianKl 10 December 2015 01:27:49AM 1 point [-]

That it did well on held-back data should convince you that you don't understand overfitting.

They didn't do well on the gene level: Analyses of individual SNPs and genes did not result in any replicable genome-wide significant association

No, they didn't try to measure non-linear effects. Nor did they try to measure environment. That is all irrelevant to measuring linear effects, which was the main thing I wanted to convey.

No, the fact that you can calculate a linear model that predicts h_2 in a way that fits 0.4 or 0.5 of the variance doesn't mean that the underlying reality is structured in a way that gene's have linear effects.

To make a causal statement that genes work in a linear way the summarize statistic of is not enough.

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