Heritability of g

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From Haworth:

I'm going to focus on young adulthood.

While I think this paper is a good survey of the literature, I have a few issues with its analysis. The biggest is that they conflate measured intelligence with actual intelligence. Specifically:

1. The "0.90" test-retest correlation cited comes from The g Factor: The Science of Mental Ability, where the test-retest correlation is mentioned twice:

   The reliability coefficients for multiitem tests of more complex mental processes, such as measured by typical IQ tests, are generally about .90 to .95. This is higher than the reliability of people’s height and weight measured in a doctor’s office!

   For intervals of less than one year, the test-retest correlations are generally above .90.

   This is just a sloppy citation, but it impacts the next point...

2. The authors elide an important definitional/philosophical problem. The fact the test-retest correlation for g is only 0.90 is a result of conflating two different definitions of g: a score on a test to measure g and the platonic ideal of g itself. The latter must, by definition, have a test-retest validity of 1. This suggests the correlation between MZ twin's gs is actually more like 0.89 and that much of the "unshared environment" is, in fact, simply due to measurement error.

3. But, in fact, the problem is worse than that: this still assumes IQ tests are unbiased measure of g - e.g. it assumes your score on the Wechsler is just g plus some random noise. This is probably not the case. This can most easily be seen in the subtests: it doesn't matter how many questions you add to your math subtest, at some point the reason it doesn't perfectly measure g is that g is not just math. Each test has a test-specific factor that isn't g, and unless you take literally infinitely many tests these factors will introduce additional error that can't be estimated via simple retesting.

   For instance Raven's matrices and the WAIS have a correlation of about 0.84 Paul, 0.76 (when corrected for range-restriction) O'Leary, or 0.74 McLaurin, much lower than the ~0.925 you'd expect based on simple test-retest correlations.

   For this reason, it is entirely possible that the correlation between identical twins actual intelligence (as opposed to measured intelligence) is indistinguishable from 1.

   The sceptic will retort that maybe the test-specific factors are even more heritable than g, which would mean traditional analysis of twin studies will overstate g's heritability. To this there are two defenses: (a) even after only accounting for the within-test measurement error, estimates of g's h^2 rise to above ~0.89, which makes it one of the most heritable traits to be measured; it is, a priori, unlikely that the test-specific traits are even more heritable, and (b) more g-loaded tests tend to be more heritable Kan Pedersen Nijenhuis, which means test-specific traits must tend to be less heritable than g.

All the above points suggest the true correlation for MZ intelligence is approximately 1, 22% higher than the measured correlation. The same arguments apply to the DZ correlation: placing the true correlation at about r~0.59 rather than the measured r~0.49. Naively, this DZ correlation would suggest that common environment is still important, even in young adulthood. This brings us to assortative mating.

As the authors, themselves, note: they did not account for assortative mating, which they admit is probably a problem. The correlation between spouse IQs is typically reported to be in the 0.3-0.4 range, with some studies finding values as high as 0.6 Watkins Familial studies of intelligence: A review Mascie-Taylor Watson. Again, though, these correlations run into measurement error issues and, so, I think a conservative estimate of the correlation between spouse intelligence is r~0.4, which would explain away about 7pp of the DZ correlation. It is very much not a stretch to believe assortative mating also explains away the remaining 2pp and brings the DZ correlation down to 0.50, exactly where you'd expect a 100% heritable trait to be.

Moreover, most IQ studies assume non-zero common environment and zero genetic dominance effects: that is they use the ACE model rather than the ADE model. This means they are biased against finding genetic effects. We don't need to appeal to this bias, but it gives yet more evidence that traditional estimations are biased against genetic explanations.

In other words, I think bulk of the evidence suggests that true intelligence is 100% heritable, and that belief to the contrary stems from imperfect measurement and common ACE model assumptions.

That being said, in the name of full disclosure, here is all the evidence I've found against this conclusion:

• Some experts believe common environment can have significant effects on intelligence in adulthood Kaplan.
• Even within identical twins, IQ test scores correlate with income - albeit, they explain only about a quarter the variance Sandewall. This suggests that some of the facets of unshared environment that affect IQ scores also affect ability to earn money, which means such factors can't be mere measurement error. In my opinion, the most parsimonious explanation is that some test-specific factors help on both (imperfect) IQ tests and with earning money.