Monday, January 28, 2013

Regression toward the mean and IQ

From Steve Sailer's blog

A reader sends Steve an Excel file for calculating expected IQs of children based on their parents' IQs. 

As I've been pointing out for a long time, these questions are of particular interest to the infertile and to lesbians. (I coined the term "lesbian eugenics" to summarize the issues that lesbian would-be mothers confront in picking a sperm donor, but it hasn't caught on. After all, as we all know, lesbians are Good and eugenics is Bad, so ... Does Not Compute!)
I am an avid reader of your site for ~10 years (not even sure since when) and wanted to email you about a Steve Sailer / Steve Hsu inspired analysis I did over the weekend ... The topics are intelligence, heredity and mating (I am 32 year old single male considering the best course of action).

The best course of action is probably to find somebody you like talking to because you are going to be doing that for a long time. But, all this stuff is definitely interesting.
This is is based on a presentation by Steve Hsu entitled "Investigating the genetic basis for intelligence".

On slide 19 of the presentation, with the header "Your kids and regression" Steve writes "Assuming a parental midpoint of n standard deviations above the population average the kids' IQ will be normally distributed about a mean which is around +0.6n with residual standard deviation of about 12 points." He also gives a helpful example immediately below "So, e.g., for n=4 (parental midpoint of 160 - very smart parents!), the mean for the kids would be 136 with only a few percent chance of any kid to surpass 160 (requires +2 standard deviation fluctuation)."

I've seen estimates of the "narrow sense heritability" of IQ ranging from0.34 to 0.86. At the lowest figure, the two 160 IQ parents' children would average 120 and at the highest, 152. But, as my reader points out, for most values in the middle of that range, the implications he draws are still more or less true.

Another thing to keep in mind is that this assumes that the IQs of grandparents and earlier ancestors are unknown. In contrast, theDarwin-Wedgwood-Galton-Keynes-Benn-Vaughan Williams extended family seems to regress toward a higher IQ than 100, as do the Huxley-Arnolds.

Here are some implications the reader draws, assuming a 0.6 figure.
1) Mating insight

Many nerdy or high achieving men bent on reproducing are troubled by the fact that most intelligent women want a career and likely do not want to have children (or want to adopt orphan baby at age 50, once they have “made it”). Women who are slightly less intelligent may want to have families and even to have bigger families. The above Excel file lets one see the impact of say a man with an IQ of 140 marrying a woman with an IQ of 140 and having only one child (whose expected IQ would be 124) vs. that same man marrying a woman with an IQ of 120 and having three children. The second man's highest IQ child will have an expected mean IQ of 128 which is higher than the man who married the smarter woman but had only one child. Even if the smarter woman chooses to have two children the two smartest children out of the three children that the less intelligent woman had will have approximately the same expected IQ as the two children of the high IQ woman.

Takeaway - twenty IQ points is a lot: 120 vs. 140 is a big difference and it will be by definition much harder to find a woman with an IQ of 140+ (one in 261) vs. one with an IQ of 120+ (one in 11) and it will be much more difficult to persuade your wife to give up IQ 140-career track (Fortune 500 CEO, Ivey League tenured professorship etc.) than IQ 120-career track (nurse, high school teacher etc.) for changing diapers in the middle of the night. If one is concerned about having one or two competent kids to whom one can leave the family business to one might consider finding a slightly less intelligent woman who is willing to have a few kids. Of course there are other factors. Having more children means giving each child less attention but spacing births helps mitigate this and we know that nature dominates over nurture in this matter anyhow. Not to mention that having only one child can result in tragedy if god forbid something was to happen to it.

2) The speed of the regression to the mean.

If one starts with two parents whose IQs are 160 and looks at the average IQs across generations the speed of the regression to the mean is quite fast.

Parents 160, 160
Children average 136 (assume these mate with a 136)
Grandchildren average 122 (assume these mate with a 122)
Greatgrandchildren average 113 (assume these mate with a 113)

There is already a huge drop between the grandparents and the grandchildren. So in just 4 generations the regression to the mean has brought down the Nobel-prize-level grandparents to the pretty much average intelligence. (all this is of course "on average")

This might be a reason why the intellectual elite might want to pay more attention to making America a country where those with IQs of 110-115 can still live satisfying lives with good middle class jobs and publicly funded services. Chances are that most of their descendants will need those jobs and services only century from now; after all “fool and his money are soon parted” – even if dimmer kids inherit billions chances are that they will not have what it takes to keep the wealth in the long run.  

3) "Geniuses belong to the people"

Imagine that with two parents with IQs of 160 set out to produce one child with the same IQ. How many kids we can expect them to have before they succeed?They would have to have 44 kids to have one kid whose IQ would be 160 or higher on average! This is clearly impossible.And if they set standard to IQ 170 - they would require 434 kids!!! Thus geniuses are really borne out of a people and not out of any two particular parents. Having smart parents helps, a lot, but even then, the chances that your little one is going to be the next Newton are small. Very, very small. On the other hand, according to historians none of Newton’s paternal kinsfolk were able to even sign their names. 
4) "The advantage of the rich - buying IQ points through marriage?"

Say you have a family scion with an IQ of 160 who marries a woman with an IQ of 132 (so top 2%). And then their kid perhaps regresses but he leverages family fortune and name to marry a woman with an IQ of 132 and so on and so on. (Sure he might not be the smartest but he's rich so why not marry him). Assume other generations repeat the same trick. What happens?

In just three generations the IQ falls to 114 and stays there. The 132 woman helps keep it at 114 vs. falling back down but it doesn't go up.

Thus another conclusion, being multi-generational rich helps, you can buy intelligence and ensure that your kids are one standard deviation higher than the average. That is a lot, but it also allows for a lot of overlap between the populations. (Especially because never dipping under the IQ 132 threshold is an optimistic assumption - it assumes multi-generational saintly resistance to blonde bimbo's charms). Thus, richer kids are on average smarter but plenty of them are dumber than the average Joe. 

Selective coments:

Anonymous said...
At some point there's a floor. An ideal, great environment 140 probably has a neutral/natural 115, all shredded and dried out. It's like weight, you have a "frame" size but the best muscle addition to the frame could vary wildly. Pro fighters of the same frame and merit might be 3 weight classes apart, depending on style and what trainers they got early.

But at some point, the probabilities calculus into nothing. 100 natural 115's might produce 1 130, 1000 of them might produce 1 145, but 10000 aren't going to give you a 160; at some point you are limited by your frame. It's just too under the radar. The national/racial IQ needs to be 103ish for the best mix of fertility and potential brilliance. I might be aiming too high, typical European thinking.

Elites are obsessed with caste and underrate race to an absurd degree. Their time (as in generations here) value is that of average people, not gifted ones. THEY ARE AVERAGE PEOPLE, who just happened to grab more than average frontal cortex mass. But memory, spacial, intuition, and other measurements reveal them as being generally normal range, which is what their children will be.

Sincerely bright people aren't elected. Proles don't like a mismatch of time preference or incentives for corruption (and the juicy pork it leads to). A well rounded mind could make a living in 3243 different ways, so there's far less of a tendency to want to cheat (pure wealth doesn't matter here, because it's about social/sexual status dependent on dominance!). A fluke high IQ (and normal everything else) specialist who could rise to the top, with just a little "extra help", has a vastly greater incentive to cheat than a real renaissance man.

Invariably, the former make it in politics, and the latter retires to Thailand at 34. There's 80% of modernity explained for you.

If you want smart kids, a smart mother is only the beginning. What you really want is a smart mother who isn't terribly exceptional among her family---ie. you want her to have smart parents and grandparents as well. If you marry a smart one-off, as you imply, regression to the mean is going to be brutal. Besides, your wife's parents become your in-laws. You can't pick your own parents, but you most assuredly CAN pick your in-laws (half of your child's grandparents).

Thank you for that insight, though it has depressing implications, since it is high IQ women who are least likely to reproduce. (Also, most of the East Asian men I know believe the opposite, with some strange consequences for their mating strategies.)

Another thing... I grok regression toward the mean but there is still the problem of defining the population whose mean is to be regressed toward. This is why a certain degree of breeding isolation/endogamy defining an otherwise "big enough" (to avoid serious inbreeding depression) population can be so useful-- regression toward a population mean of, say, 105 IQ is a lot less painful than regression toward a population mean of, say, 85 IQ.

Regression toward the mean is the curse of smart parents' lives. It is natural to wish for children as smart as or smarter than oneself but the smarter you are the less likely your wish will come true.

(This all relates to why libertarian economists' views on immigration are so wrong. Libertarian economists have never heard of regression toward the mean, or perhaps are so ideologically blind they don't think it applies to human beings.)
Let's consider the real personalities of high IQ women.

How shall we do this? Well, how about what we know of women in the high IQ populations.

Ashkenazi Jewish women

Women in STEM academia

High IQ Asian women

Now, when you think of these groups, does "great personality for a wife" come to mind?

I am not being sarcastic.

Honest question.
Anonymous said...
The assumed heritability of IQ in the general population is assumed to be 0.6. As I understand it, one would only use this factor if additional information on IQ of previous generations is not known.

For instance, if one knows that both parents are drawn from a limited breeding pool that has been throwing high IQ children for tens of generations, I suspect the heritability factor may be significantly greater than 0.6.

Or, if both high IQ parents are drawn randomly from the general population, and one knows that neither parent has any high IQ ancestors for several generations back, the additional information may imply a heritability factor significantly less than 0.6.

Take home message is that if the aim is to build a population (bloodline) thats breeds selected traits with high levels of certainty, a proven strategy is to line-breed with limited outcrossing under conditions of ruthless culling - environmental or otherwise.

After several generations, breeding within the sub-population will still exhibit regression to the mean for the selected traits, but the mean will have "increased" from the general population mean, and the variance will have decreased. The reduced variance implies greater heritability within the sub-population.
Anonymous said...
Obviously, there are certain sub cultures in the USA where wealthy fathers are able to successfully require their sons to marry when the young man is young. These wealthy fathers are also able to motivate their sons to marry young females with very high IQ. None of this is theoretical. Look at the high genetic IQ of the females that Mitt Romney's sons married, just as an example Or look at the women that the sons of Indian Brahmins marry in the USA. Young men just lack the judgement to select their own wives. It is that simple. The fathers of those young men should be selecting the wives of their sons. I am very interested in hearing about other groups in America in which wealthy men are able to insure that their sons marry females with genetically .

Steve's correspondent mentioned that Newton's father was an illiterate farmer. This is true. Carl Friedrich Gauss's parents were working class people, and his mother was illiterate. Michael Faraday's parents were poor. The Wikipedia mentions his father having been an apprentice to a village blacksmith.

Bill Clinton's mother was a nurse and what I'm going to call here a loose woman. I think I've read that her parents picked cotton for a living. The guy who ended up on Bill Clinton's birth certificate was a traveling salesman, a son of poor farmers. John Lennon's parents were irresponsible, lower-class people. It's not typical for very smart people to be first-generation descendants of riff-raff, but it happens..

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