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It seems few understand regression to the mean and how and why it works.

Most people (and by most people, I mean most scholars – i.e., the people who should know better) have a vague understanding that it has something to do with IQ. They seem to have the impression it means that the children of smart parents will be less smart. Even more so when those parents come from a population with a low mean IQ.

And *they seem to think this phenomenon goes on forever*, such that grandchildren and great-grandchildren continue this march to mediocrity.

Well, a lot of this is confused to plain old wrong.

Let’s start with what regression to the mean is. Above is an illustration of a bell curve. A set of parents that lie out on the curve away from the mean will indeed *tend* to have children that are closer to the average. Hence, if a set of parents are +2 standard deviations for a trait, their children will be typically some degree closer to the mean.

The first thing to clear up is that **regression to the mean operates in both directions.** Just as parents +2σ will have children some degree less far off to the right on the curve, **parents –2σ will have children some degree less far off to the left. **That is,

**children of parents who are**

*below*average for a trait*regress up.*To clear up some additional confusion, let’s look at *what causes regression to the mean.* The root of the phenomenon goes back to behavioral genetics, or more broadly heritability. Human traits have several components that contribute to trait variance. They are:

A: Additive heredity

D: Non-additive heredity (D from “dominance”)

C: Shared environment (C from “common environment”)

E: “Unshared” or “unique” environment.

As we’ve seen before, we know that A is typically 50-60%, D 10-20%, C is 0%, and E the remaining 20-30%.

The key fact is that for the transmission of a trait from parent to child, **only A and C carry over to the next generation.** But, as we know, C is 0; so that only leaves A. The rest, including non-additive heredity (which is basically fortuitous combinations of alleles) and whatever remaining “non-genetic” factors that constitute E (and all the things that comprise that, see Environmental Hereditarianism) **are essentially luck. **And since we can’t expect lightning to strike twice (as improper as that metaphor is), **regression to the mean happens because luck goes away.**

This is governed by the breeder’s equation.

R = h

^{2}S.R is the response to selection, S is the selection differential, and h

^{2}is the narrow-sense heritability. This is the workhorse equation for quantitative genetics. The selective differential S, is the difference between the population mean and the mean of the parental population (some subset of the total population).

This equation can be used in different ways depending on whether we’re talking about whole populations or individual pairs of parents (though fundamentally for the same reason).

Let’s start with individuals. If two parents (let’s say White Americans) are +2σ for a trait, let’s say IQ, or 130, and we give the additive heritability of IQ to be about 0.6, we can expect their children to collectively have an average IQ of

0.6 • +2 = +1.2σ

…or 118. Now, *this was assuming that their families had a mean IQ of 100*. If their families had a different mean IQ, lets say 120 (+1.333σ), the breeder’s equation would give

0.6 • (2 – 1.333)σ = +0.4σ

…or a mean IQ of 126 for the children. (That’s because it’s +0.4σ plus the family mean IQ of +1.333σ.)

What’s better, here’s another illustration. Let’s say the parents’ families have a mean IQ of 120, but the parents themselves have IQs of 110. Given the breeder’s equation,

0.6 • (+0.6667 – 1.333)σ = –0.4σ

…for a mean IQ of 114 for their children (family mean IQ of +1.333σ minus 0.4σ). In other words, even though the parents (with IQs of 110) are above the mean of the population, because their *families* are well above average, their **children regress up.**

It’s important to make clear that **the breeder’s equation, and hence regression to mean, works the same way for any quantitative trait, not just IQ. **This includes political orientation, height, body weight, personality, etc. All you need to know are the values to fit the variables in the equation.

For populations, the equation works similarly. Hence, if a group of people with a mean IQ of 130 (who come from population with a mean IQ of 100) go off somewhere and have children, the next generation will have a mean IQ of 118. **Now here’s the part that gives a lot of people trouble: **the children of the children of this group, the third generation, **will also have a mean IQ of 118. **Why? Because the initial event **changed the mean. **The new “population mean”, as far as the breeder’s equation is concerned, **is 118.** As long as they mate endogamously, there will be no change in their average IQ thanks to regression (only through selection)**.**

This is should illustrate the flaw in thinking that regression happens forever. If daughter populations regressed back to the mean of their original source populations indefinitely, **how could there be any selection for quantitative traits?** Think about it.

Now let’s return to individuals. Some think OK, if populations don’t regress forever, surely the descendants of any one pair of parents do, yes? **Well, not necessarily.** Let’s return to our example of the offspring of IQ 130 parents from mean IQ 120 families. When it comes time for their children (the second generation), with a mean IQ 126, to have children, we do again run the breeder’s equation. But the key fact here is that the *mean value the** third generation of children are regressing to is the mean of their respective families. *If all of the 2nd generation parents mated with spouses from high mean IQ families,

**there would be little to no regression for the third**. In other words,

**regression to the mean for individuals can be slowed or halted by assortative mating.**This is why wealthy parents have concerned themselves with the family backgrounds of their children’s mates. And this is why Gregory Clark found what he found (see The Son Also Rises | West Hunter) – namely, very slow regression (around 10 generations, in many cases) to the population mean for families (indeed, virtually none in Indian castes, who only mate within caste).

Indeed, as I mentioned, the reason for regression is the same for individuals and populations. You see regression in populations because the exceptional individuals who comprise whatever select group in question are going to be coming from families of all different averages for whatever trait under consideration. The sum of all these individual regressions is going to be add up to regression towards the mean of the source population. (But as mentioned before, this only happens once.)

Hopefully, this serves to clear up the confusion on regression to the mean.

Clever people might notice that all of HBD is based on just two concepts: behavioral genetics (or again, more broadly, heritability) and the breeder’s equation. Know those two things and most of the rest follows.

How do we know that C is 0?

Replies:@JayManRegression to the mean in statistics in general is not a causal effect or process. It is a sampling effect.

Replies:@JayManRead all about it:

The Son Becomes The Father

Replies:@AnonymousQuite correct. I almost put a section on that in my post, but I decided not too. Feel free to explain it in more details for the readers.

Replies:@Aaron Gross”as improper as that metaphor is”

just because you want. 😉

metaphor is much more understandable or didatic because you are putting abstract specific ”things” in the familiar ”things” via logical association.

Something’s gone wrong here. 0.6 • (2 – 1.3333)σ = 0.6 • (0.6667)σ = 0.4σ; by my calculation the second family should have children with mean IQ 126 (= 120 + 0.4*15). Then, 0.6 • (0.6667 – 1.3333)σ = 0.6 • (-0.6667)σ = -0.4σ, 6 points again, but… that makes the figure of mean child IQ 114 correct, which disagrees with the calculation for the middle family.

Regression to the mean in genetics can be viewed as a direct effect, caused by genes that were suppressed by dominant genes coming to the fore in later generations (in individuals that didn’t inherit the dominant genes that suppressed them), but it can also be viewed as a sampling effect, where dominant genes mask stuff that’s really there and make that stuff hard to sample. It all depends on your perspective.

I’ve been wondering about that one-time-only population regression after a selective step. Regression to the mean is a tool for predicting one outcome given a related outcome, and we can straightforwardly predict a child’s IQ (even a distribution for it) from the parents’ IQ. Taking from the example above, we’d predict that the children of 2 130 IQ parents of unknown background would have a normal IQ distribution centered around 118. If the parents were perfect predictors, the children should all have IQ 130 (exactly equal, not normally distributed around), but they’re not and they won’t. I believe (?) it’s standard to think of regression to the mean as reflecting the fact that the parents aren’t perfect predictors.

One-time-only population regression seems to me to be equivalent to the statement that knowing a child’s four grandparents gives you exactly as much predictive power as knowing their two parents. This is hard to swallow; grandparents should be worse predictors than parents — and in fact in the domain of genetics specifically we can observe that, while every child receives exactly half of each parent’s genome, the contribution from each grandparent varies!

Is there a multi-generational data set I could look at for something easy like height that illustrates total-grandparent-knowledge being just as good as total-parent-knowledge?

Replies:@JayManYup, you’re right. I screwed up my math. I’ll fix it.

Among other things (particularly, E). Basically, “luck” is

everythingother than additive genetics.Umm, meiosis? Have we forgotten what sex does?

Actually, grandparents (the average of all four, that is) are

betterpredictors than parents, because they tell you about family background. They control for the “luck” that expressed itself in the parents (non-additive genetics, developmental noise, etc.).Replies:@J2Sorry, I still don’t understand it. The children get the genes only from their parents – why is the wider population relevant?

Let us say that the trait is completely genetically determined, that it is influenced by, say, 10 genes, each of which has two alleles (A1 and B1, … A10 and B10), and each of which counts equally, As giving you higher individual, and Bs shorter. This will give you a Binomial distribution which is approximated by Normal one you plotted.

The more As one has in the genome, the stronger trait one exhibits – if this was height, person with 10 A alleles will be super tall, with 10 Bs super short, etc. In this case, is there a reversion to the mean? I don’t see it… the total genome of the man+woman pair will have, say 16 As and 4 Bs (their average height is 8As out of 10), so the children will be very tall, on average, although an unlucky runt may inherit 4 Bs (and 6 As) and be only slightly taller than average. There is no mean reversion, no?

Replies:@JayManI’m aware that parents aren’t perfect predictors. Obviously, meiosis is a large part of why. I don’t see the relevance to “if the parents were perfect predictors”, though.

Can you point me to a good citation for this, or a good multigenerational data set?

Sorry but that is not all you need to know. Science marches on.

Want to be up to date? Check out Transgenerational epigenetic inheritance. (Easily done on Wiki. More intellectually honest checking out references).

Basically Lemark was at least a little correct. Responses to the environment can be inherited outside the schoolbook notions of neoDarwinism.

And of course any organism who figures out how to do this has a great Darwinian advantage.

Replies:@JayManIn that case, the phenotype would be

completelydetermined by additive heredity (A = 100%, D, C, and E would all = 0). There would be no “luck” to go away. In that case, there would be no regression.Wrong place to bring up that bullshit, buddy (unless you’re being facetious):

Replies:@HitlerFood for thought; it reinforces my view that seeking a mate from “a good family” is among the best ways for sons and daughters to “marry

lucky.” Why anyone would ignore this, given its logical connection to happiness in life, is inscrutable.Does your position shed any light on women who succumb to the current fad of producing children with people whose genetic contribution is probably down-market? This seems like entering Life’s Casino while yearning for

.Bad LuckReplies:@JayMan, @Erik SievenIs that actually what’s happening?

See Idiocracy Can Wait?

There’s something I’ve never understood. We can build categories or collectives of all kinds. For example, we can look at the child of parents as part of the population of American academics or of the white race or of the inhabitants of Detroit. Now I understand that “regression to the mean” means here, above all, regression to the mean of the parents A and B, and “regression to the mean of this or that collective” is only a comprehensive way to speak about all regressions of all individuals comprehended to the mean of their parents.

I also see that “regression to the mean of the population X” is a necessary concept as long as our contrahent Forces it upon us to speak about the future of this or that population. But it seems to be rather nonsensical if we aren’t forced to speak about this or that population.

Replies:@candid_observer, @JimThe outcome that C = 0 approaches being a

reductio ad absurdum.We won’t

knowthat the common environmental variance has no effect for major life outcomes until you explain away the reasons the claim seems patently ridiculous. [For instance, that members of a species that is unique in the amount of long-term care it requires somehow is indifferent to thequalityof that care. And if shared-environment effects IQ across birth cohorts (as by nutrition in advanced countries), what’s the plausibility that there will benoeffect within cohorts?]There seems to be a place where heritability calculations can go wrong: if the gene/common environment interaction differs from the gene/unique environment interaction. A recent exchange in

Criminologysuggests to me that the dispute comes down to a burden of proof argument regarding the equality or inequality of these components.Replies:@JayManGenerally the relevant group for determining these population means will be those groups across which a fair amount of breeding takes place. Obviously, the qualitative term “a fair amount of breeding” can be replaced by a quantitative one.

But, for example, there has been very little such breeding between any groups in SubSaharan Africa and those in Europe. Between countries in Europe, there’s been more such breeding, although it may be fair in many cases to treat each nationality as mostly a distinct group for these purposes — but, on still another hand, there may be relatively little difference on the relevant trait (such as IQ) in any case, for various obvious reasons (either both nationalities derived their IQs importantly from common ancestors, and/or they were subjected to very similar selection pressures.)

Replies:@StogumberLook, measure after measure (see my above comment)

findsthat C = 0. This is an empirical matter. And the case is closed.You know, this is an interesting point. If the shared environment has no effect

withincohorts (and there’s a whole lot of variation between families), then that greatly narrows down the type of environmental effects that could lead to observed differencesbetweencohorts.Don’t pin your hopes on interactions. It just don’t fly.

Replies:@szopen, @Aaron Gross, @Stephen R. DiamondThere is a regression to the intellectual mean by three out of four offspring – but one in four offspring gets the best genes of both parents. This does not work for Newton and Darwin grate intellects – but it does for most others.

What do you think about the claim that adoption studies are not really representative, because foster parents are selected, i.e. they do not show the whole variation possible within a population? I know you were very critical of this guy who claimed shared environment influence was higher when he researched poor families, but I can’t remember you have ever addressed this point (that parents in adoption studies are selected group with limited variability of environments).

Nice article. We could talk about regression to the mean with professional athletes, and everybody would immediately get it, there would be no argument. But toss in intelligence as the example of luck evening out in the next generation and some folks get confused and positively cranky. Anyway keep up the good work Jayman.

At an individual level all probabilities are zero or one.

candid observer #17,

As long as we are speaking about the breeder’s equation, we certainly have to look for groups with a tendency to inbreed. But even then it’s questionable if “academics” or “white race” or “Detroiters” would be the group of our choice. Of all three groups we can assume that they in a way tend to inbreed, but their “mean” would be completely different.

Even more so, if we are speaking about mathematical “regression to the mean” (I didn’t understand if Jayman looks at the “breeder’s equation” (or rather its outcome) as a variant of the mathematical regression or something completely different which only accidentally is subsumized under the same term).

Lets imagine two people having a kid who are both mixed race.

The father half white and half black. The mother is half Korean and half Ashkenazi Jew.

Would it be appropriate to just average these populations?

So if African American mean IQ is 85 and white is 100, take for the father’s mean 92.5. And if Ashkenazi mean IQ is 110 and Korean 105, take for the mother’s populational mean 107.5. Then average those two numbers out to 100, and expect 100 to be the mean that their kids would regress to?

Replies:@JayManFor start to understand regression to mean you just need look for people around.

Family, friends, etc

IQ is not everything. An extreme high share of german women have children with westafrican males. Those kids might on average become uni professors quite seldom, but popular culture, professional sports, etc. have a high demand for half-black kids, who are because of that in fact on average more successful than white german kids

Jay

I have been arguing against cognitive elitism in the reactophere on the basis that in addition to other benefits proles are a larger producer of high IQ people than elites are partly because of regression [which i now understand a bit better } but mostly because greater numbers and since these prole sired high IQs will meet and mate at university etc they will soon stabilize and improve their trait. can you calculate if this is true and to what degree. say for whites in the US or europe. my view is considered lefty which im not but you as a liberal might enjoy liberalizing the far right a bit

Replies:@JayManIf you knew nothing about their respective family backgrounds, yes. If you do, that changes a lot.

I’m not sure that’s true.

In general, assortative mating stalls regression. That’s how castes (or near castes) form.

Replies:@Wizard of Oz, @AnonymousIt should be “towards the mean.”

Replies:@Emil O. W. KirkegaardFor populations, the equation works similarly. Hence, if a group of people with a mean IQ of 130 (who come from population with a mean IQ of 100) go off somewhere and have children, the next generation will have a mean IQ of 118. Now here’s the part that gives a lot of people trouble: the children of the children of this group, the third generation, will also have a mean IQ of 118. Why? Because the initial event changed the mean.Isn’t it important to stress here that the first two individuals “come from population about which we know nothing more than that the entire population has a mean IQ of 100”? In particular, you have to be ignorant about their parent’s IQ. That would help people’s “trouble” with the statistics of the next generation.

I think the point so many miss is that this is for averages for sufficiently large groups. We can all tell anecdotes about friends who are average height but their son is 6’5″ or some such.

Regression to the mean is generally true and true for sufficiently large groups. There are outliers.

So, Joe is the smartest from his family and Susie the smartest of her family. If they have ten kids, the average of those kids will regress toward the mean, but any given child could be quite far from the mean.

Replies:@JayManMay I ask you to turn your attention to a Hbd matter which is perhaps not an order of magnitude less important than IQ but rarely treated as a normally distributed characteristic?

I refer to the number of hours sleep different individuals need and the approximate inverse number of constructive hours work they can put in each day.

My starting point is countless articles and interviews telling us that we need (as adults) 7.5 or 8 hours sleep for various restorative and other housekeeping functions and that, ever since Thomas Edison became famous for only needing four hours sleep Western civilization has been infected with chronic sleep deficits. Well, maybe, but…..

It seems clear that our hours of sleep allow a great many different functions to occur from recharging some endocrine/hormone supplies or their glandular sources to arranging and consolidating memories to repairing muscle fibre damage and much more.

Presumably these processes are controlled by a large number of genes plus epigenesis and there is no reason to suppose that their identity and efficacy wouldn’t be distributed normally in much the same way as genes for IQ and other mental characteristics. A point which I have not heard raised but which seems prima facie correct is that there would be only a loose connection – if any – between genes for one restorative function and another. Thus there is no reason to suppose that the clever person who was blessed with being able to use his brain effectively for 17 hours a day (and become Chief Justice let us suppose) is necessarily going to be able to keep his cardio-vascular system healthy without another two hours sleep.

My guess is that the healthy adult’s requirement is on average about 7.5 hours and that the SD is about 50 minutes. Have you an opinion on this, even evidence? And do you know of anything bearing on my hypothesis that not all sleep’s functions would be performed equally effectively in the average individual? It could certainly help explain the collapse in health of some people whose brains had achieved great things although it is my experience that the imagination and lateral thinking which I really enjoy tends to fail me when I am forced to push myself without sleep to keep on exerting expertise in some reasonably testing situation in which one can perform satisfactorily because of practice and experience.

Replies:@JayManHand waving away a whole new area of scientific study? You do realize that they have done DIRECT experiments that prove transgenerational epigenetics right?

Replies:@JayManThat doesn’t seem right. First of all, any

newenvironment will by definition not have affected the variation within the previous cohort, although maybe that’s what you meant by “greatly narrows.”But it’s not just new effects that can cause a big change between cohorts. For instance, suppose hypothetically that playing a certain obscure work by Mozart to infants greatly increases their IQs. If only a minuscule number of parents currently play that music, then the shared environmental effect will be negligible. But if everyone started playing that music, then there might be a huge difference between cohorts.

This goes back to a statistical or logical fallacy that lots of people make, including famous people like Judith Rich Harris. All variances – those explained by genes, shared environment, etc. – are

averages. It’s a fallacy to say, “The shared environment effect is negligible, therefore none of the shared environments today have a strong effect on the trait.” But that’s exactly what some people say or imply.Finally, your statement seems wrong for a much more general reason. While for a given cohort the mean is fixed, between cohorts the mean is changing. You have no way of knowing

a prioriwhat effects a change in the mean will have.Replies:@JayManOne very easy way to see that it’s not a causal effect or process is to remember that it goes both forwards and backwards in time. For instance, just as our children regress towards the mean compared to us, our parents regress towards the mean compared to us as well. I think that fact can give people a better intuitive understanding of regression toward the mean.

Yup. For individuals, the breeder’s equation only helps you predict probabilities. Statistics of small numbers is very much in play.

Something I almost added to the post, but I (correctly) figured someone would mention it.

Probably something like that. Yes, there is great variation in the minimum amount of sleep individuals need to function normally.

No idea about group variation in such.

Maybe it’s time for me to write an epigenetics (shitting on such) post?

Replies:@Hitler, @szopen, @RaceRealist88Except that for the shared environment, the fact of the matter is we have reason to believe that zero means zero. See: Apples, Oranges, and Lesbians: The Nurture Assumption Just Will Not Die

We know it means nothing for behavioral genetic studies.

Replies:@Aaron GrossPlease do.

I think we also have look for regression to the mean as individual proportion of favorable biological variables that produce a set of intelligence phenotypes spectrum. Everyone inherited a certain favorable proportion if intelligence(s) is(are) polygenic.

Would be interesting look for families with only sons and with only girls. Are there significant trends between couples of different sex ratio among their children?

I don’t know if it’s correct to say but we will go try…

Regression to the mean metaphorically speaking is like you threw a little quantity of red paint into a bucket with blue paint. The red color will appear occasionally, if you mix the paint.

The more red ink in the bucket you play, the greater will be your quantitative presence.

Another metaphor. Duplication of a cell. Do you have a population ” with ” average IQ of 90. So the smartest begin to interbreed, we think they decided to found a divergent worship where they secretly only those who score 3 digits in IQ can participate.

Initially, there will be many cases of regression to the mean, by logic, because you have many individuals with unfavorable mutational load for greater intelligence who are getting married to each other. Then, over time, going with progressive segregation those with (contextually, i mean intelligence) favorable mutational load and over time, it will occur to fixation / prevalence of these favorable genes.

First we have the emergence of a genetic insularity within a larger gene pool. Then over time, you have the separation of this deviant group until the moment they are not as related as before.

Let’s assume that you ‘have’ a iq 130 within a community where the average IQ is 90.

First, you’re likely to marry within this community, especially if the community is inbreeding,

Second, you will have trouble finding a spouse with the same average IQ than you,

Third, it is likely that you will have low genetic load for greater intelligence, especially if you’re a cognitive outlier within your family (one Lisa Simpson), because, high levels of inbreeding tend to depress ” intelligence ” (or type of intelligence that tends to be related to IQ and fluid moral intelligence, if it exists),

Room, you also need to know if the spouse to choose comes from a family with greater intelligence. Generally, families tend to cluster by social class,

Fifth, it is possible to conclude that heredity vary with its age. So, the older you are, the better the chances to pass mutant genes, which may or may not depress intelligence (this should also be investigated more hard). Having children too soon also may cause problems or reduce the biologic potential of its progeny.

I’m very curious about the Nazi experiment in a city in southern Brazil (and Argentina) where, it seems, an hour to the other, began to be born twins in a large percentage. If this was really true or if there were an excessive history of twins in this city.

It seems that there is an inheritance hierarchy, as did the experiment (quasi-unethical, but valid, not to cause suffering to the ” animal ”) with the mouse, it just got smarter.

Maybe you can make a recessive gene or even of polygenic nature, in a dominant gene. Anyway, I’m not a geneticist, just curious.

I’d prefer that you would rather write a detailed explanation on methodology behind twin studies. For example, after reading both Hanscombe, Trzaskowski et al article (about heritability in UK twins) and wikipedia articles on twin studies, I feel dumber than before.

I mean I understand that you prefer not to answer to question you think are stupid, or your first reaction to someone writing “I feel dumber than before” may be “maybe it’s because you are dumb”, but still quite a lot of readers would gain a lot from simple (simplified?) explanation of the twin studies models.

Replies:@HitlerNo, no please I want to see this great shitting refutation of epigenetics.

…Please.

True but wouldn’t proles contribute at least as many high IQ university students as the elites?

{ Say elites produce 100% high IQ students and all go to university, and proles produce 1 out of 100 of the prole population with a plus 130 IQ and they all go to university, and prole pop is is 100x the elite population of over 130 IQ} I chose >130 IQ because i think that’s the 1%, adjust if im off.

So now we have an equal number of stabilized high IQ elite children and regression prone prole High IQ children at university together. Even without any further mating proles have doubled the number of the nations high IQ quotient. Further assuming the elites can and want to still mate only with their class, and the prole university kids all marry out of the prole elites group to average prole mates. The proles will continue to add as many cognitive elites every year as the elites do.

BUT what I think will/ does actually happen is elites have a much harder time identifying each other at university and very little interest in perpetuating a class division and so in reality they are mating as often with high IQ proles as high IQ elites.

Now if you agree with me so far the question I am not informed enough to answer is how much regression are the elites picking up and how much are the proles losing in these mixed mating’s what is the net gain or loss in the next generation as measure against a pure bred model.

I would think if it is even a wash its still quite a gain because the elite pool is growing but it could be there’s a increase in breadth and a loss of height to be considered, but I suspect the diminishing odds of of super high IQs in the long run benefit more from larger pools than more concentrated input.

Replies:@JayManOk, about supposed nazi experiment, is very very likely to be a BS. 😉

But the rest is right, is not??

You didn’t express this degree of certainty when responding to Aaron Gross: “Except that for the shared environment, the fact of the matter is we have reason to believe that zero means zero. See:

Apples, Oranges, and Lesbians: The Nurture Assumption Just Will Not Die.”I’ll read your piece before commenting on interactions; here I only seek clarification as to which position expresses your real degree of confidence. I doubt the degree of confidence you expressed in reply to me can be justified, when an informed and objective commenter like Ron Unz has concluded that there must be some undiscovered error behind the c = 0 conclusion. [Why isn’t c = 0 for height – to interject a question of my own.]

On the other hand, if the heritability studies only “give us reason to believe,” other evidence might give us greater reason to believe otherwise. Speaking now only hypothetically.

Pointing out that the issue is “empirical” is … I don’t know .. a bit demagogic. Of course it’s empirical. What else might it be? Logical? Metaphysical? But heritability studies aren’t the only relevant empirical evidence, good scientists don’t

ignoreevidence that hasn’t been scientifically verified.Replies:@JayManI read your article you linked to, and I don’t see what it has to do with my point. It says that if the additive effects are negligible, in practice we can expect that the interactive effects will be negligible as well (though they don’t have to be), because it would be surprising for the mechanism to exactly balance out additively.

I agree, but that doesn’t apply to my point. If there’s a (currently) rare treatment, then because it’s rare, we would

expectthe overall shared-environment effect to be negligible, even if the treatment had a strong effect.Re your reply that a change in means over time “means nothing for behavioral genetic studies”: Well, it’s a type of environmental effect that’s totally invisible to the kind of studies your talking about. That says only that the studies themselves are limited, nothing wrong with that. But it also says that many people (including you, but you’re in good company) interpret the findings of the studies wrongly, by drawing conclusions that go far beyond what the data imply. By the way, there are plenty of people who have pointed this out, I’m not claiming any originality here.

Replies:@JayManHolding out hope a little

toomuch, aren’t we?OK let’s say that this is real. The moral? The vast majority of parents don’t need to be concerned with it, because it’s so rare it won’t matter to most.

No, not if they include several generations and/or are extended twin studies.

Why do people insist on grasping at straws? Go get cigarettes and drinks, this one has flatlined.

If you haven’t read my relevant pieces on the matter, why are you commenting now? Hint, hint. Last warning.

C = 0 for height, by the way. Don’t confuse the shared environment with secular changes.

Replies:@szopenWell, I re-read “All human behaviour is heritable”, and C!=0 for:

#. Asocial behaviour (.09 for adults)

#. Conservatism (yes in females above 20 years old)

#. RWA (0-0.16 in adults)

#. Religiousness (0.2-0.4)

#. Psychological interests (0.08-0.12)

I’d say that this still opens a possibility that for some psychological traits C is non zero.

And I still don’t get twin studies 🙁 (why you can estimate C from difference between monozygotic and dizygotic twins. I would understand that if you would have monozygotic and dizygotic twins sharing the same environment – i.e. from the same family, but I do not get how the formulas can work if they do not share the environment, even if averaged over large number of different twins and environments 🙁 )

Replies:@szopen, @JayManDamn, I waited too long with edit. Sorry Jayman for the additional post.

With twin studies, for example I wonder what would be the impact of more similarity of MZ than DZ twins. MZ twins will have similar interests and will create more similar environments than DZ twins.

Replies:@szopenJayman, please remove my previous post. If I understand correctly, the problem I had with twins making environment more similar would result in inflation of C estimation, right?

I want to second this. The reason to prefer this wording is that it doesn’t suggest that the regression is always complete or will be at some point in later generations. “regression to the mean” makes these misunderstandings more common I think.

First you need define specifically what is “mean”. Where begin where finish the mean.

In my opinion and specially for this iq-context, mean is unlikely to be a single number but a spectrum where majority of people fit. Just look for bell curve that illustrates this post.

That was a summary of behavioral genetic literature way back when Bouchard reviewed it. Newer, larger studies confirm that C=0 for all those traits:

The Son Becomes The Father

Let’s figure it out.

A simple model for estimating this is to cut the normal distribution. By this definition, “prole” = IQ < 115, "elite" = IQ 115+

(This is of course not proper, but it's close enough for this purpose).

"Proles" are 84% of the White population while "elites" are 16%.

Using the formula for a truncated normal distribution, the mean IQ of the “prole” side is 95.7, while the mean of the “elite” side is 123.

For the next generation (assuming there’s no change in the relative proportions of each), allowing for regression (assuming an additive heritability of IQ of 0.6), the mean IQ of the prole side will be 97.4 and the mean IQ of the elite side will be 114. Each is still 84% and 16% of the total population, respectively.

The fraction of those IQ 130 coming from the “prole” side will be 1.5% of all proles. The fraction of those coming from the elites will be 14% of all elites.

So:

“Elite” share of 130+ = 64%

“Prole” share of 130+ = 36%

Two thirds of the high IQ children will originate from the elite class under this model.

This whole discussion is shot through with misunderstanding of H2. The concept has no applicability to individuals. A group can have a mean weight, while the individuals of it have a weight. A group can have a mean H2 for some trait, but no individual has an H2.

So if H2 for some desirable trait T is .8 it is no more likely that a individual will inherit T than if the H2 is .3.

Replies:@JayManthanks ive been wondering about that. even without accounting for proles probably having more children one third is not a trifle contribution ide imagine they also are keeping the blue blood from turning green.

For the individuals, the breeder’s equation only tells you probabilities for expected children. It can’t do much more than that thanks to the statistics of small numbers issue, among other things.

Nicely done, JayMan. My explanation here.

And yes, please do devote a post to tossing & goring overblown claims for epigenetics.

I don’t see how any of the assumptions of this model hold up.

First, there is the idea that shared environment explains roughly nothing in terms of IQ variance. Many researchers who make this claim refer back to McGue’s 1993 review. However, Kaplan 2012 showed that this review was deeply flawed, especially with respect to its calculation of C. Specifically, Kaplan notes that McGue’s data most straightforwardly implied a C of -.06, an impossibility. Rather than finding this data to be problematic, McGue simply subtracted .06 from E to arrive at 0.00 for C. Kaplan was also able to show that the problem lied with elderly samples: if you restrict McGue’s sample to only include twins below the age of 60 you get a mean C value of .17. This is consistent with more contemporary studies, such as Hartworth et al. 2011 and Kendler et al. 2015, both of which showed significant effects for shared environment. Hartworth et al. is especially note worth because its sample size was dramatically larger than McGue’s was. Over all, contemporary intelligence research does not support the idea that C is zero for adults. (And, of course, it never supported this idea for children. This is especially note worth since regression to the mean studies often involve children or adolescents.)

Secondly, the assumption that E is random is counter intuitive and, so far as I know, not backed up by any significant evidence. There is no obvious reason to suppose that parents are totally unable to transmit non-shared environmental abnormalities that they experience to their children.

Lastly, D is certainly not random. If your parents posses some genetic feature which has a non additive impact on a trait you will be more likely than the general population to also posses that genetic feature. The fact that it isn’t assured doesn’t change the fact that the probability will be greater than average.

Replies:@JayManIt’s Jonathan Kaplan, that’s your problem. He’s hardly the most objective voice (by the way, if you read this comment, and claim that was ad hominem, you have failed).

What could push the shared environment term to the negative in a standard twin study? Hmmm…

Why don’t we try this?

More Behavioral Genetic Facts

As for the Kendler study, Swedish adoption during that time wasn’t exactly random. Hence, seeing a tiny “effect” isn’t unexpected.

That said, see this:

Even if the C term for IQ in adults was nonzero (which it’s not), if the effect of E term is clearly not “real”, then neither can the C term.

See above.

Then that would make it additive, right (i.e., A not D)? Think of non-additive heritability like Tetris pieces. The exact effect of each piece depends on the context, but most pieces have a net positive or net negative impact.

Note to you and other commenters: there are over 200 posts of mine here, and they tend to be arranged and linked to in a way that should make them easy to find (if not easy to find, please let me know). Before claiming in a comment that some claim of mine is “not backed up by any significant evidence,” try reading around first.

I don’t think you really give a fair treatment of regression to the mean. A good theoretical model of regression to the mean is that given continuous unimodal symmetric independent random variables A, X, X’ with X, X’ identically distributed and m = A + X > E[A + X] then E[A + X’| A+ X = m] if m < E[A+X]) . In other words if we have some underlying ability (true IQ etc.. etc..) A and some noisy measurement of A then the result of that measurement is an overestimate of how extreme A is.

If we think of genetic outcomes as the result of some heritable component A and non-heritable component X (the effect of enviornment and lucky combinations of genes that aren't practically heritable) then this tells us that if mates are selected to share the same heritable component A then we should expect their offspring to be less smart. This DOES continue indefinitely in the following sense. If your ancestors IQs were m1, m2 … mk and the average m of m1…mk is greater than E[A + X] then your expected IQ conditional on your ancestors having IQs m1…mk is less than m. In other words part of the reason your ancestors are smarter than average is probably luck so you probably won't be as smart.

This isn't incompatible with any kind of selection pressure. Just because each generation is likely to be more average than their ancestors doesn't mean they become arbitrarily average. The size of the regression to the mean effect reduces as you condition on more trials.

In other words if your parents are geniuses you have good reason to think a great deal of that is probably luck and you will be much less smart than they are. If both your parents and grandparents are geniuses then the family intelligence is probably partly luck so you will be somewhat less smart. If the last 10 generations of your family have an average IQ of 121 that is probably only slightly due to luck so you should expect your IQ to be only slightly less than 121.

Of course using this model in genetic can be a bit tricky since deciding what A is to measure and what does and doesn't go into the heritable component isn't obvious (nor a perfect model).

Replies:@JayManThat depends on the family, which was my point. Some families are much smarter than average than others. Assortative mating can brings such families together, stalling regression.

You’re confusion regression considered for individuals with regression considered for populations. When considering a population, after the first regression in the second generation,

you’ve changed the average.Thatis what stalls regression to the mean in subsequent generations.Exactly.

OT:

Bringing Up GeniusH/T: Arts & Letters Daily

Interesting how they are a Hungarian Jewish family.

https://en.wikipedia.org/wiki/Susan_Polgar#Personal_life

Replies:@reiner TorLink in previous comment: http://chronicle.com/article/Bringing-Up-Genius/234061

Great post. Yes, you could have added the fact it’s a sampling effect.

There are at least four caveats here.

1) There was self-selection in the case of László Polgár, he needed to be highly intelligent to even conceive of the idea, and to try to raise his children to become great chess players (as opposed to, say, great swimmers or whatever)

2) There was self-selection in the case of the wife, Klára. Many women would have opposed or obstructed his plan.

3) There was self-selection on the level of the story: we only here about the successful one. There might be a few other families who also planned to raise their kids to be geniuses, but didn’t succeed.

4) The three Polgár sisters’ chess skills are nowhere near each other. Judit Polgár (the youngest of the three) was the strongest female player of all time, Zsuzsanna (Susan) Polgár (the oldest of the three) is a Grandmaster, whereas Zsófia (Sofia) Polgár (the middle sister) is only a Woman Grandmaster. The point is not to belittle the latter title (I’d be proud of my daughter if she achieved that), but simply that they are not nearly all on the same level, in spite of having received the same education and upbringing.

Agree:MEH 0910Regression to the mean happens mainly when some individuals born comparatively more-evolved than its population. They tend to be the first of a novel genetic combinations.

Replies:@JayManNo, not quite.

[…] things I’ve heard in the black-white IQ debate. Hey Chanda, there is something called Regression to the Mean (nice post Jayman), which throws your theory out of the […]

Evo and Proud begs to disagree on 3rd generation resetting of mean:

Regression to the mean is something else. It happens because of genetic change. For instance, a man with above-average IQ will likely marry a woman with above-average IQ. But only part of their above-averageness is genetic. The rest is due to favorable circumstances. Or simply luck. So their children’s IQ will likely be a bit closer to the mean of the overall population. That second generation will in turn marry people with similar IQs. And their children will likewise be closer still to the population mean. Eventually, several generations later, the descendants of that original couple will have a mean IQ that matches the population mean.I’d like to see more plain english confirmations of Jayman’s position on this important point. If Jayman is right it would be HUGE. But I am dubious.

Replies:@JayManFrost is wrong here. That second generation will only regress if they choose mates from lower average IQ population. When assortative mating is perfect, there is no regression. Look at Gregory Clark’s work.

Replies:@Luke LeaOk, I contacted Peter Frost and also found a link to Greg Cochran and you are correct it seems. That would be enough to explain Aschenazi IQ right there then, wouldn’t it, assuming differential birth and survival rates for the merchant/scholar class and perhaps some out migration on the part of the poorest, least successful members of these endogenous communities (schtetls) in Eastern Europe?

Replies:@JayManBasic application of the breeder’s equation, as well as the fact that it’s what we see across the world.

Steven Pinker has this to say on epigenetics:

https://www.edge.org/response-detail/25337

If you haven’t picked that book up yet, I recommend it JayMan. It’s a great read.

Is there not some inheritance of luck also, that is, the parents of IQ 130 are probably better off than average and give a better environment, so the breeder equation should not only take the genetic inheritance, set here to 0.6, but inverited environment set to something, like 0.2 maybe. If so, the prediction from two parents is better than from four grandparents.

Replies:@JayManShared environment is taken into account. But as I noted, the effect of shared environment (C in the ADCE system) is zero, so it doesn’t matter.

Replies:@J2I can’t believe you actually answered to a discussion from 2015!!! That’s very good and probably rare. So I have to comment in some way, I guess.

Assume the father (or the average or the parents) has IQ 130 and the son has IQ 155 (I know such a

case), so the son inherited 118 points by additive heritance of IQ and 37 point, that is 67% of his IQ

(about 3.6 SD) from non-additive heritance and nonshared environment. But you say nonshared environment is typically 20-30% and non-additive heritance is 10-20%, together 30-50%, somewhat

smaller than 67%. Is it so that the numbers you give are means and they still have some variance, or

can one count with them as constants and at the end assign some confidence to the result, such as:

in this case the son should have IQ 100+x, where x<=18+0.5x with probability y (y=?). To simplify,

x<=36 with probability y, and consequently x can be 155 with some probability y2. Is this what you

mean?

But there is another error here: in this calculation that follows your example the father has 130 in

additive heritance, since 0.6 of 130 is inherited, but actually the father has 130 as a sum of all his

three IQ components A,B,D (as C=0). So one could calculate as above only in the case of an average

father, where B and D are zero. Is this also as you mean it?

If you do not care to answer, do not do it, who cares anyway. I already was impressed finding an answer to my first comment.

Or let me present the question in a clearer way. Assume fathers/parents IQ is 2SD (130), son has

3.6 SD (about 155). Does it mean that father/parents additive IQ heritage is 142 and non-additive

heritage or environment lowered it to 130? This is because if additive is additive, there should not

be any distribution any more. Genes are inherited. The reasons for distribution are A,B,C,D, not

so that each or them has a distribution. Thus, father additive IQ 130 is inherited as son IQ od about

118. Then comes max 50% other effects, which do not raise son’s IQ to 155. So, father’s real additive

IQ is higher than 130. Is this what you mean?

Or as I suspect, none of these is what you mean, because this is pseudoscience and one cannot make

calculations with these half ready theories. If one does, very soon one can get to contradictions. Maybe

this is what you mean?

Anyway, I read your article and finally did not understand anything of regression to the mean.

Replies:@JayManIn Rushton,Jensen 30 year of studies Section 9 (in the web) there is a more simple and maybe

better verified version of regression to the mean. Assuming that an individual has IQ equal group mean+x, then full sibling (or parent-child) has IQ close to group mean=x/2. Using this one would

calculate, group mean=100, son IQ 155, thus father IQ is close to 100=55/2, which is quite fine.

Rushton, Jenkins claim the relation is linear and works from IQ 50 to 150, so there is no need to

make the more compilated calculation with A,B,C,D, which probably works less well.

The components are A, D, C, and E

A = additive heredity

D = non-additive heredity

C = Shared (common) environment

E = Unique (or non-shared) evironment

The breeder’s equation, when applied to individuals, gives you probabilities. For parents of combined average of a trait +2σ, their offspring are expected to average (0.6 • 2 = +1.2)σ for the trait. But they will be normally distributed about that average (assuming a large number of offspring).

But this is assuming you know nothing about the parents’s family background. It is how far the parents are off from their

families’averages that matters.The contribution of A,D, and E to a trait varies from family to family. Some families have very little non-additive genetics behind a given trait, while others have a lot. The values I used is for the population as a whole. In short, there’s a lot that goes into trait prediction for a given individual.

Thanks for this answer. It is good enough. The simple formula actually is not the “real” formula,

since it does not take everything into account (women are supposed to have a narrower IQ distribution, parents also should have IQ composed of these parts etc.) but let it be. Rushton and Jensen use a

simpler formula, let it be. I guess this field is still too far from having any really correct formulas for anything.

By the way, I read this your article of ivy collage admissions and the endless discussion of Jewish

overrepresentation. Quite a discussion, so I will not continue this discussion any longer. Must be hard being a blogger.

Replies:@JayManThe breeder’s equation is correct. You’re asking it do something it can’t do. Within families, there will be individual variation about the predicted mean. That is, you can’t perfectly predict individual IQs from it, only probabilities.

That wasn’t by me.

Jayman,

I still have a question of your article regression to the mean. I accept the breeder equation to be correct if the model underlying it is accepted, but that may not be the case. You answered before, which was kind, I hope you answer still to this one. Let us take a selected population, say by an IQ test we discard

half, all below 100. The accepted half has the mean sigma*sqrt(2/pi), where sigma is the standard deviation. Thus, with mean 100 and sigma=15, the mean is about 12. The variance is Var(1-2/pi),

where Var=sigma*sigma. Clearly, the selection has reduced the variance, while if we measure SD

from the higher part, it will seem to be 15 and there will be twice as many over any level, like 150,

than in the general population. Then the regression to the mean reduces the mean for one generation,

and we get the mean to 110. Hope this reminds you of the US Ashkenazi. Terman has twice as many Ashkenazi over 150 than non-Jewish whites and Lynn estimated the average to be 110, while before it was measured to about 12. Now the question.

The distribution is truncated normal distribution with below 100 cut off. It cannot stay like that. For each pair of parents, the mean of the children is the mean of the parents, but is the distribution of

the children IQ normal with SD=15, or is it more probably so that for very high IQ, or very low IQ,

the distribution is skewed, because if genetic IQ is polygenic characteristics and both parents have

the good or the bad genes, the offspring cannot have too wide a range, there is nothing to cause

high variation. If so, the distribution is skewed, and therefore the average may actually not be the

mean of the average of the parents, but there may be exactly what you tried to deny, regression

to the mean over several generations.

To say is again. Your breeder equation is correct, provided that the model under it is correct. If

at the high and low ends of the distribition, the variance of IQ, or any property, is skewed, because

the property is polygenic and there is nothing to vary if both parents have all good or bad, then there is a push to the center because of this distribution and it is not true that the average of the children is the average of the parents.

hope I made this question clear enough. thanks for your previous answers, think if this is the case with the Ashkenazi.

Regression to the means happens due to unassortative mating. Regression to the mean is a statistical phenomenon not a biological one, there is no evidence IQ regresses towards the mean, it happens because highly intelligent and wealthy men marry attractive but less intelligent women, i see it everywhere around me. If mating is 100% assortative there will be NO regression. What happens is very simple, a man is born with a high IQ, his IQ puts him in a high status job, he marries a very attractive woman, with an above average IQ but not as high as his, and his offspring regress back to the mean of he and his wife’s IQ level. I’ll guarantee that since women don’t marry attractive and less intelligent men, that most offspring of very high IQ women don’t regress to the mean.

Wouldn’t assortative mating show itself in certain college populations such as the creation of traditional Black colleges creating an environment where higher IQ than average students tending to marry within the population and then sending their children to the same colleges create sustained increase in average IQ for the group? That would be a strong argument for certain types of environments supporting increased IQ, since assortative mating can be an environmental factor.

Replies:@JayManThe genetic impact of assortative mating is to decrease the non-additive genetic variance and increase the additive variance.

I agree with your conclusion that the rate of regression is 0.6. However, I don’t agree that shared environment has no effect. Heritability is not inheritance blah blah blah.

Let’s say I live in a favorable environment that raises my IQ. When I have kids, I’ll pass on some of this environment to them—we might go to the same school and live in the same neighborhood for example. Our shared environment prevents regression toward the mean. However, it doesn’t cause any of the variation between us.

If everyone goes to the same school and lives in the same neighbourhood, it would of course cause little variation between them. (After all, they’re the same!) If only a few people go to a great school and live in a great neighborhood and they pass this on to their children, preventing regression to the mean, but causing none of the variation between us.

I can’t find your sources on the percentage of the different contributors to trait variance. However, the additive heritability (narrow-sense heritability) of fluid intelligence and crystallized intelligence are actually 40% and 51% respectively. What raises the rate of regression to the mean to (allegedly) 60% may actually be shared environments.