General factor of intelligence g, a Statistical Myth

http://cscs.umich.edu/~crshalizi/weblog/523.html

by eru • 15 years ago

42 33 15 years ago

cscs.umich.edu

I wish there were more Cosma Shalizis in the world. Somehow, statistics has become the ultimate in cargo cult mathematics. We need more statisticians who can write clearly to set fire to our thatched airplanes.

brent• 15 years ago

Pardon my naivety, but what do you mean by "thatched airplanes"?

Nogwater• 15 years ago

See: http://en.wikipedia.org/wiki/Cargo_cult

"Thatched airplanes" being an imitation of the real thing.

MichaelSalib2• 15 years ago

Nogwater nails it below.

Specifically, I'm think of things like http://cscs.umich.edu/~crshalizi/weblog/491.html and http://cscs.umich.edu/~crshalizi/weblog/656.html

EugeneG• 15 years ago

Cosma was one of my very favorite professors at CMU

honm4• 15 years ago

Even if we can't measure it, what makes it so hard to believe that intelligence is inheritable? Is height inheritable? Yes. Is eye color inheritable? Yes. Is skin color inheritable? Yes. Is physical strength....? Yes. Why wouldn't a human characteristic that has provided one of the biggest advantages through evolution not be inheritable too?

Almaviva• 15 years ago

What if we postulate a general factor "b" that correlates with a superior body, is that inheritable? It's not that certain characteristics of the brain aren't inheritable, it's that "intelligence" is very diffuse and hard to define.

It's not even so clear that what many of us would call intelligence is mainly an evolutionary advantage, either.

Symmetry2• 15 years ago

The author isn't saying that intelligence isn't heritable. He just showed that we can measure heritability in things that don't exist (the sum of a persons weight and height in some units) as well as things that exist like their actual weight and height. Therefore, the fact that g is heritable doesn't mean that its a thing that exists.

Except I think the author would point out that there isn't just _one_ heritability for things like height because height would be much more heritable in environments where everyone has adequate nutrition as opposed to in environments where nutrition was a matter of luck, for instance.

All of this assumes a certain philosophical veiwpoint on what it means to "really exist" which I don't agree with, but which I do recognize as coherent.

ramses• 15 years ago

Because that would contradict their political ideology.

honm4• 15 years ago

Yes, I think that might be it. Unfortunately, there isn't much evidence any side can put on the table. Genetics will advance a lot in the coming years, so that might put an end to the debate and that ideology will be shattered. If that same ideology impedes that we study heritability in the West, I'm sure China will still study it.

Groxx3• 15 years ago

Is height entirely inherited? No, diet makes extraordinary differences. Is physical strength entirely inherited? No, exercise builds muscle.

There are of course factors on both sides, but for mental / physical strength I'll happily argue for landing waaaay towards the what-you-do-with-it, not-what-you-have side.

honm4• 15 years ago

Where I live you honestly can't say that diet stunts people's growth. That would apply in places where food isn't readily available, but certainly not in the western world. From looking at people I know I can tell you too, that the differences in muscle size is more related to how much muscle they had before going to the gym than how much time they spend there.

Can you start going to the gym and get stronger than your friends who don't go? No. Out of 10 friends maybe you'll pass 1 or 2 of them in strength, but that's it. That is what I have seen but I'd say it is pretty far from what you suggest.

tokenadult• 15 years ago

The example of the German monozygotic twins Otto and Ewald, both well nourished but sportsmen who pursued different sports, show that physique is exquisitely sensitive to environmental influences even between two individuals who share a genome and a prenatal environment in the same mother's womb. Take a look at the photos.

http://www.marksdailyapple.com/control-gene-expression/

http://www.joebower.org/2010/05/we-inherit-and-we-also-becom...

AFTER EDIT: I'm asked in a reply below what my point was, and it's partly to point out that the term "heritable" means something far, far different from "determined by genes." There are whole books

http://www.amazon.com/Nature-Nurture-Environmental-Influence...

http://www.amazon.com/Genes-Behavior-Nature-Nurture-Interpla...

http://www.amazon.com/Dependent-Gene-Fallacy-Nature-Nurture/...

by professional geneticists, medical doctors, and psychologists patiently refuting the confusion in most popular literature about what "heritability" means, but the main point in this thread is that Shalizi is correct, and many psychologists are wrong, about what heritability figures mean in relation to IQ.

xiaoma• 15 years ago

Not really sure what your point is there. It's natural two people with virtually identical genes subjected to vastly different training would have different body-types. It's also natural that two people with vastly different genes would respond differently to virtually identical training.

Consider someone like this boy vs his classmates: http://www.sciencentral.com/articles/view.php3?type=article&...

yummyfajitas5• 15 years ago

It's a great article. But it's a bit more philosophical than practical, and I particularly take issue with the author's use of the term "statistical myth".

Near as I can tell, Thompson's model is the following: there are lots of abilities, and any test uses many (232+) of them at random. Individuals have a random selection of abilities.The author then declares that any individual ability is not g, since no specific ability describes performance very well. All very true.

But there is a single, explanatory variable in this model: g = # of abilities an individual has [1]! Moreover, Thompson's model makes a specific prediction about g - it should be normally distributed. So overall, I agree with the author's scientific argument: g is very likely to be decomposable into subfactors.

But I don't agree with his claim that g is a "statistical myth". Let me give an argument illustrating the fallacy he is making. Suppose I want to explain the thermodynamic law PV=nT. I can build a moderately more complicated statistical model [2] involving only 10^23 newtonian particles, with normally distributed velocities, and completely reproduce all the predictions of the thermodynamics. But not a single one of those particle positions explains pressure or temperature! Thus, thermodynamics is just a statistical myth.

Thermodynamics and g are simplified models of the world, based on the fact that the macroscale is dependent primarily on the sum of a large number of microscale variables [1]. They both have decent, though imperfect, predictive power. There is almost certainly a more complicated underlying theory, which will reproduce thermo/g as theorems about statistical aggregates. (For example, g may eventually be explained as the interaction of neurons.) Does this make them "statistical myths"? Of course not. Just macroscale models which have an underlying microscale explanation.

[1] Or perhaps a weighted average based on how frequently abilities are used in tests.

[2] http://en.wikipedia.org/wiki/Statistical_mechanics

[3] For example, pressure is the the average force imparted by particles colliding with the side of a vessel divided by the area on which the collisions occur.

Symmetry2• 15 years ago

The authors viewpoint seems to be that things that can be directly measured do exist. So I would think that the author would be find with talking about temperature the same way he's ok with talking about IQ ("That thing that IQ tests measure").

I would agree with you personally, and say that really any measurement involves some implicit figuring so there really isn't any difference between IQ and T.

Dn_Ab5• 15 years ago

A flaw with your argument is that biology is harder than physics. That is, the interactions of the elementary constituents of biology are many orders of magnitude vastly more complex than those of the point particles found in newtonian physics. Which makes sense considering the compositional hierarchy involved from atom -> cells -> humans. Hence reductionists statistical methods are likely to be far less useful/meaningful than in thermodynamics.

Dn_Ab5• 15 years ago

I do not care about the downvoting. But I am guessing it is due to my saying that biology is harder than physics [1]. Perhaps I should clarify to say that a broad mathematical understanding of biology is a harder problem than doing so for your typical system studied in physics. In biology, systems can only be modeled and not understood or derived from fundemental principles, as the interactions of the basic entities are too complex. Or consider: Quantum mechanics, it is a straight forward linear theory (just conceptually difficult) while much of biology is analytically and computationally hard, often involving things like non-linear dynamical systems. A further difficulty here is that the behaviour of the whole of the things studied in biology cannot be inferred by studying its constituents - due to feedback-dissipation processes leading to self organization.

While I am clarifying, I might as well point out that while I personally believe that the usefulness for looking for broad general factors is meaningless considering the dimensions in consideration, there might be some use for them in aggregrate. However, these should not be taken for more than they are. Statistics. Furthermore, You, yummyfajitas, argue agianst a strawman. Did you read the article? Because if you did you would have seen:

I don't want to be mis-understood as being on some positivist-behaviorist crusade against inferences to latent mental variables or structures. As I said, my deepest research interest is, exactly, how to reconstruct hidden causal structures from data.

...

Similarly, pointing out that factor analysis and related techniques are unreliable guides to causal structure does not establish the non-existence of a one-dimensional latent variable driving the success of almost all human mental performance. It's possible that there is such a thing. But the major supposed evidence for it is irrelevant, and it accords very badly with what we actually know about the functioning of the brain and the mind.

Which leads me to the fact that Shalizi has no qualm against dimensionality reduction. Instead he is against the methodologies used and how the conclusions are drawn:

1) g is almost a tautology. It is due to the correlations in the tests which are made to correlate. When performing such factor analysis on these variables a dominating factor which most explains their variance must appear due to algebraic reasons.

2) No one has tried to explained g directly, experimentally or otherwise. Instead they still argue in terms of correlations.

3) They still use simple correlation matrices - linear models from yestercentury. Other more appropriate or robust methods such as non-parametric statistics have since been refined or developed.

[1] http://metabolism.math.duke.edu/docs/04whyams.pdf

bambax2• 15 years ago

I think what the author means is that g is a statistical necessity, and that being such, doesn't imply that it's an actual reality.

What you seem to be saying is that, in any case, g is a useful proxy for a reality that is difficult to know in detail. This doesn't contradict the author's thesis.

The question remains, does g exist beyond arithmetics, is there such a thing as "general intelligence". Maybe it's a useless question, in that we don't need to know whether g "exists": we only need to know that it works.

But there is a big difference between intelligence and thermodynamics: policies are implemented that impact the lives of millions of people based on an understanding of g that may be completely false. If g is only a statistical artifact and nothing more, then it's still useful for statisticians, but for policy makers, the underlying factors need to be identified and understood.

yummyfajitas5• 15 years ago

That's why I object to the term "statistical myth" - it implies the measure is not useful in cases when it is. If g is a useful proxy, it's useful for policy makers. All they need to know is that low T implies dead homeless, and low g implies a higher probability of unskilled employment.

The fact that g is actually a sum of independent variables, or T is a sum of squares of velocities of particles is irrelevant to them.

bambax2• 15 years ago

Reading the original article further I understand more of what the author meant -- and I agree with him more.

What he means by "statistical myth", I think, is that you can throw any number of measurements into a big bag, even weakly correlated, and you'll always be able to find a general macro-factor that is correlated with all of them and therefore seems to "describe the bag" pretty well... even if the bag itself is absolutely meaningless.

For example, one could throw into the bag height, sexiness, feet length, and BMI, which are all somewhat correlated with one another and with "IQ".

There is a macro factor describing such a bag; but would you call it "general intelligence"?

The fact that we talk about g is because we consider a priori that there actually is such a thing as "general intelligence" and that we are measuring elements of it. Maybe we are, maybe we're not; correlations alone tell us nothing about it.

The analogy with physics, be it temperature or pressure or what have you, is in my opinion quite flawed, because in the case of those entities we know that the elementary events / forces are linked by way of causality with the macro factor, and we know that for reasons other than mere correlation.

In the case of g, on the contrary, the only link between the different elements is the correlation itself. And it gets worse: to be included as a relevant IQ test, a new test has to be correlated with g. To quote from the article:

"By this point, I'd guess it's impossible for something to become accepted as an "intelligence test" if it doesn't correlate well with the Weschler and its kin, no matter how much intelligence, in the ordinary sense, it requires. (...) This is circular and self-confirming, and the real surprise is that it doesn't work better."

So g is at the same time what we're looking for and what we're building upon, having decided it's there already.

This looks much more like religion than science.

Dn_Ab5• 15 years ago

Yes! This is what I am trying to say but in a much more muddled and round about way.

yummyfajitas5• 15 years ago

For example, one could throw into the bag height, sexiness, feet length, and BMI, which are all somewhat correlated with one another and with "IQ".

The point is that if those phenomena are all correlated with one another, there is likely to be an underlying reason for that. Maybe it's not general intelligence, but there is something.

Suppose you threw a different set of things into the bag: phase of the moon at birth, whether you were bitten by a wolf, and how good you are with computers. These things almost certainly will not be correlated, because there is indeed no relationship between them. The only reason the author discovered a large principal component in all his models is because he explicitly built one in!

Now, my analogy with physics is not to the physics of today. Rather, it's to physics pre-Boltzman. Before that, we didn't really know how the atomic theory of physics was related to thermodynamics. All we really had were correlations - boiling is correlated with burning, with faster chemical reactions, expansion of solids, with the human perception of warmth, etc. We observed they all occurred together, and postulated an underlying variable T which correlated well with all of them. We then exploited the correlation between this hidden variable T and thermal expansion to design a specific test to measure it (thermometers).

Pre-Boltzman, all we had were correlations between fundamentally different physical phenomena. We had various incorrect theories about why some of them occurred together, but that's about it.

Now suppose Boltzman comes along. He says "what you call a single variable T, I can explain with the sum of many variables." Does that mean it's reasonable to conclude T is a "statistical myth"?

NY_USA_Hacker2• 15 years ago

There's a point he omitted: In curve fitting, exploratory data analysis, data mining, etc., we are looking for X. We don't know if X exists. But if X does exist, then our methods have a shot at finding X. So, we look. Maybe we find something. We test what we find, and it appears to work as we believe X would. So, we start to believe that X exists and we have found it.

Do like following this 'paradigm'? No! But, when people do follow this paradigm and claim to have found X, then I can't be sure they are wrong!

E.g., maybe there is a statistical model that predicts the stock market. So, do a lot of curve fitting. Find something that appears to predict. Then if there is a predictive model, maybe have found it. Test the model on old data not used in constructing the model and see if it works. If it does, then we start to believe that there is a predictive model and that we have found it or something close enough.

When people do such things, I can't say that they are wrong.

NY_USA_Hacker2• 15 years ago

Largely I agree with him, and at times I suspected some such. E.g., just testing some software, I generated some 'random' symmetric, positive definite matrices, found the eigenvalues, and noticed that there was a big one and the sizes went down quickly. So, in linear equations, a few variables constructed from the eigenvectors of the largest few eigenvalues, can make a good approximation to all of many variables. So, factor analysis makes a good data compression technique. Can't find fault with that.

That just a few of the largest eigenvalues/vectors can explain all the data well is curious. So really he might have just used R and some Monte Carlo to show us how variance explained increases with number of factors used. I'm surprised he didn't do this.

Much or all of this has long been clear.

But what I didn't like was his drifting off into old goals of the psychologists. I couldn't figure out if he was a psychologist with an ax to grind or what. Instead, he's a statistical physicist. Curious.

The psychologists looking for 'causality' have a goal that is from tough down to impossible. We should have been concluding that. That he got off into arguing about 'causality' seemed a bit silly. I don't know all what silly stuff the psychos are trying to believe, but arguing with silly psychos is a bit silly.

But it remains: Give a test with some mental puzzle problems, and in just a linear way can explain a lot of the data with just one factor. Curious. Maybe somewhat useful. 'Causality'? Likely not if only because we know that there is a biological and neurological basis and have made no connection with that.

Then I didn't like his use of 'factors': He has some factors correlated. No: The usual approach is that, like all the eigenvectors are orthogonal, the factors are all uncorrelated. Maybe the psychos look for some uncorrelated 'factors' trying to get at some of their guesses about causality, but in this case he should have been more clear.

Finally, he wants Gaussian to justify being interested in means, variances, and covariances. Well, in the Gaussian case, sample mean and variance are 'sufficient' statistics. But even without Gaussian, means and covariances remain important, e.g., for the inner products in the Hilbert space of L^2 real random variables.

General factor of intelligence g, a Statistical Myth

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