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August 28, 2003

CHC, g, & Intelligence

I have received a few questions on g, John Carroll's Theory (technically the Cattell-Horn-Carroll (CHC) Theory, named after Raymond Cattell, John Horn and John Carroll), and intelligence.

While the field is far from in total agreement, I think these points are safe to say.

1. Intelligence is too broad and nebulous a term to use, except for common parlance. Moreover, it often evokes visceral reaction, which often hinders more than helps. Consequently, most use the term g, which stands for general intelligence (named by Charles Spearman). Spearman, like Galton and others before him, noticed that when he administered tests to kids that required cognitive ability (e.g., pitch discrimination, math facts), the zero-order correlations were all positive. Because of his rigorous math background (he was en engineer) he was able to use his correlation matrix to invent the technique of principal factor analysis (well, an early version of it anyway), which, basically, just took the first eigenroot and used the first set of eigenvectors. This gave him 2 things: a principal factor (which he called general intelligence, or g) and test-specific variance. There was lots of "controversy" over whether g was embedded in every cognitive task, and two of the main opponents were Raymond Cattell and John Horn. While over simplified, they said there were two general factors, Gf and Gc, which stand for fluid and crystallized general abilities, respectively, and not one common g. Gf was meant to denote the skills it takes to do tasks that require minimal previous knowledge (repeat numbers backwards, solve matrix analogies), and Gc was meant to denote the skills it takes to do tasks that do require specific content knowledge (vocabulary, math). While there was a debate on the specific hierarchy (i.e., whether g alone stood on top, or whether it was Gf and Gc), they all agreed that tasks could be broken down into specific (i.e., stuff that was unique to it alone) and general (i.e., stuff it shared with similar tests) parts. Well, this debate went on for a while until John Carroll came along with his 1993 classic, Human Cognitive Abilities, it which he re-factor analyzed hundreds of published cognitive test data sets (akin to a meta-analysis), using a factor analysis procedure that allows one to factor analyze correlated factors. The details are a little too complex to go into here (although he Carroll outlines it well in his book), but what he found was that when there were enough tests to analyze, g existed by itself as the higher order factor, but that there were 8 sub-factors (Gf and Gc being two of them) and under each subfactors were about 60 narrower abilities. See here for pictorial model. Because he had three different strata of abilities, ranging from specific to general, it is sometimes called the three-strata theory of cognitive abilities. Hands down, this is the most data-based and supported theory of cognitive ability currently viable.

2. Some researchers are more interested in g (e.g., Arthur Jensen), as it permeates all tests of cognitive ability, while others are more interested in some of the specific second order abilities (especially when working with those with learning difficulties) (e.g., the folks at IAP). Consequently, both study "intelligence", but with different goals for their research (i.e., differential psychology vs. clinical/practice-oriented psychology).

3. g, a subset of CHC theory, is probably the most researched aspect of the theory. After decades of research (about 100 years), these "facts" seem to have ample support, although new data is always being published:

a. g permeates every test that involves cognitive ability. Test is broadly defined and can mean regular daily activities (see Robert Gordon's work), health and occupational outcomes (see Linda Gottfredson's work---who, IMHO, ranks right up there with Arthur Jensen, Cyril Burt, and Charles Spearman for prolific research on g), reaction time (Mental Chronometric) tasks (see Arthur Jensen and Ian Deary's work) or regular scholastic tasks.

b. g's heritability is about .5, with it increasing as tasks get harder, and decreasing as tasks get easier. When you extract g from any body of tests, the heritability of performance goes to almost zero, which tends to show that it is the g component of a given task that is heritable, not the specific tasks themselves. Tony Vernon has done a lot here, as has Robert Plomin.

c. Race differences on cognitive ability tests tend to be primarily on the g factor. Phil Rushton has done oodles of work here. (some also say there is a sex difference, with men slightly higher, but I have not seen enough evidence to think it viable....at least at this time).

d. There appears to be a biological and neurological basis for g. The reason for this is that g correlates (and substantially so!) with a ton of biological variables. The best, although now a little dated, piece in this area was: Jensen, A. R., & Sinha, S. N. (1993). Physical correlates of human intelligence. In P.A. Vernon (Ed.) Biological approaches to the study of human intelligence (pp. 139-242). Norwood, NJ: Ablex. Although, also see Jensen's Psycoloquy posts, and the second section of the new Jensen festschrift.

I am not a biologist by training, so I cannot critique the literature here as well as most of the folks who will read this post. From my readings though, the purponderance of evidence seems indicate that g does have a biological basis.


Posted by A. Beaujean at 08:50 PM

What's the narrow-sense heritability of g?

Posted by: gcochran at August 28, 2003 09:38 PM

Some 65 or so narrow abilities. Talk about multiple intelligences!

I can't get over how there are still Gouldians who attack real data and math-loving g-men such as Carroll and Jensen as "pseudo-scientists" [ ! ] while latching on to data-less fakers like Gardner. It's sad.

As for Sternberg, I have much more respect, but he still has little to offer as any sort of alternative to g.

Posted by: Jason Malloy at August 29, 2003 07:31 AM

Any suggestions as to why ability to attract a mate as a teenager is not considered a cognitive task? How about military leadership under pressure, or whatever real-time monitoring of all of the other players is necessary in team athletic contests. These are all tasks at which people with substantially above average g do noticably poorly. At a more anecdotal level, 4 years ago there was a news article about a man who sued a police department for excluding him from employment based on their past negative experience with employees with 130+ IQs.

Posted by: micheal vassar at August 29, 2003 07:33 AM

Any suggestions as to why ability to attract a mate as a teenager is not considered a cognitive task?

Not considered by who?

These are all tasks at which people with substantially above average g do noticably poorly.

I can't agree or disagree. got a link?

Posted by: Jason Malloy at August 29, 2003 07:55 AM

Speaking of Gardner, and attracting the ladies in seventh grade, here's a post I remember liking from the evo psych discussion group by Timothy Miller (emph mine):

In my opinion, Gardner stubbornly refuses to distinguish between "Intelligence" one one hand and "talent" or "talents" on the other. We all know that some people with very modest IQs can possess one or more remarkable talents. I'm not talking about idiot savants. I'm just talking about ordinary people.

Intelligence is a kind of generalized talent, or an aptitude to acquire many different talents -- though not all, as I mentioned before. But people who have big vocabularies are MUCH more likely to have an aptitiude for mathematics, etc., etc., etc. If you want to choose a single measure that correlates best with g, it's vocabulary.

Another way to look at it: Gardner stubbornly refuses to distinguish between "intelligence" and personality traits. If someone is high on Extroversion, Gardner might call that "interpersonal intelligence" or something. If someone is low on extroversion he might call it "inanimate intelligence" or something.

Another problem with Gardner's theory is that no one has tried to factor analyze talents poorly correlated with IQ. Playing the saxaphone, dancing, basketball, whatever. Maybe they cluster in one way or another. Maybe they are purely idiosyncratic. I wish Gardner would shut up and find out. I'd like to know.

Gardner supports his theory not with evidence, but by trying to redefine the term "intelligence." The term has been around a long time, long before standardized intelligence tests.. He doesn't really have the authority to make it mean something different. He should make up his own words if he doesn't like the usual ones.
Posted by: Jason Malloy at August 29, 2003 08:11 AM

The g-task success conumdrum spoke of seems to be more an artifiact of personality than of g per se. There are signifignat correlations among personality traits (esp. the Eysenck PEN) and g, although I am not up to snuff on the literature here. H. Eysenck and Chris Brand have done much work here, though.

On the whole, g and task success seem to highly correlated. C. Benbow has done work here, specifically with the mathematically precocious.

It seems that g is plietropic (sp?), and certain underlying personality traits are among the things "co-inherited," but I can't cite anything off hand to give validity to the arguement.

Posted by: Alex B. at August 29, 2003 08:13 AM

It is a little hard to say what the narrow heritability of g is. a^2 cannot be differentiated from h^2 in many beh. gen. studies because of the samples used. Moreover, as tasks increase/decrease in complexity, so do the heritabilty coefficients.

I would say a general estimate would be around .3, but is moderated by task complexity and the sample.

Posted by: Alex B. at August 29, 2003 08:29 AM

The Devlin paper (PDF) puts it at around .35.

Posted by: Jason Malloy at August 29, 2003 08:35 AM

I built credit scoring models, and Gardiner's critique of G is based on a similar arguments in that literature. Basically, any single quantitative model can't explain everything, so supposedly it is not as good as a nebulous qualitative model, which can explain everything. These people see explanation and more important than prediction: g says that one test can explain much of other aptitude metrics, Gardiner says that we have a smorgasbord of talents, many uncorrelated with each other. But like a model with an R2=1, the 'explanation' approach only gives you the illusion of knowledge.

Posted by: eric f at August 29, 2003 09:26 AM

Anyone read Raymond B Cattell's book Beyondism, Religion from Science? Good book.

Posted by: Gordon Gekko at August 29, 2003 10:49 AM

past negative experience with employees with 130+ IQs

the negative experience was high turn-over i believe-training high IQ cops is less cost effective because they are more likely to move on to some other job, while a more average intelligence employee would be happy with $60,000 a year for that sort of work.... the small town (i believe in conneticut) couldn't afford to train new cops all the time, so they figured stupid cops would be less of a budget dent.

Posted by: razib at August 29, 2003 10:51 AM

G is strongly correlated with "Openness" from the 5-factor personality trait model (OCEAN) which is currently psychologically popular. In actuality, I think that when I use the word "intelligence" conversationally, what I mean is closer to "openness" than it is to g, which may be part of why I don't consider Vos Savant to be nearly as smart as Feinman. g correlates slighty negatively with neuroticism. Other traits (amiability, concienciousness, and extroversion) correlate negligably with g (though "genius" appears to usually require high g, high openness, and low concienciousness.) Military tests show that high g commanders perform poorly under pressure, though I don't have a link. Everyday observation shows that as teenagers high g "nerds" have difficulty getting laid, even with other "nerds".

Posted by: michael vassar at August 29, 2003 12:42 PM

"Military tests show that high g commanders perform poorly under pressure"

Norman Schwarzkopf's IQ was estimated to be at around 170.

Posted by: Peter Phillips at August 31, 2003 08:30 AM