Thursday, November 22, 2007

IQ G

The dread IQ debate is back due to the arrogant ignorance of William Salaten.

One of many excellent debunkings is was written by Daniel Koffler at Jewcy.

Key points is that the time trend of measured IQ is huge and positive (on the order of 3 points per decade) demonstrating the importance of environmental factors and that, according to (different) scientific racists, the brain size of Asians used to be lower than that of Whites and is now larger. You know all that economic success gave them swollen heads.

I disagree with one claim made by Koffler. It is very commonly made by critics of the genes to IQ to everything crowd. It is also clearly false.

It concerns g

g, the general intelligence factor, which in its initial formulation by Spearman is the quality that all tests of mental ability measure in addition to any specific qualities, and is still supposed today to be responsible for a significant proportion of observable correlations in performance among standardized tests, and between tests and academic performance. If g does not exist, then there is no one quality that even a perfectly designed intelligence test would measure,


Koffler argues

Cosma Shalizi, a statistician at Carnegie Mellon, offers an exhaustive exploration of the mythical existence of g, the bottom line of which is that factor analysis, without which we would have no concept of g, while useful for descriptive statistics, is virtually useless for doing explanatory statistics. That is, if you already know that some given abilities are interdependent, a factor-analytic examination of them could greatly simplify the explanatory picture. If, on the other hand, you are seeking to explain correlations among variables, all that factor analysis can do is confirm your pre-theoretical biases. In other words, when Spearman, or Rushton and Jensen, or Herrnstein and Murray, or Saletan look at IQ test data and infer a general factor behind the results, they are doing nothing but gazing in the mirror.


Hmmm what is Shalizi saying ? Is he* saying that the statistical analysis that yields g has no empirical content, because estimation of principle components analysis must yield a principle factor ? This is certainly not what he means as he is a statistician and knows better. If you have multiple variables, you can find a principle component which is correlated with each of them. However, nothing implies that such correlations are positive. It is an empirical fact that the scores on many different tests of cognitive ability are positively correlated. It is thus an empirical fact that when one calculated principle components, the first component is positively correlated with scores on tests of verbal, spatial and mathematical ability.

This doesn't mean that all mental abilities are positively correlated with verbal, spatial and mathematical ability. It has nothing to do with the question of heritability as far as I can tell. It is an empirical observation. It is not the necessary result of applying the statistical technique.

* I'm not sexist I checked that he is a he and discovered he looks even more like Trotsky than I do.

update: That is actually a photograph of Trotsky. I hope people believe that gullibility is not negatively correlated with g.

update: from comments Cosma Shalizi himself writes

I uses that picture of Trotsky because I do, in fact, look him; people have recognized me at conferences from it...

The empirical fact is simply that the test scores are positively correlated with each other. Given that, factor analysis (which is not quite the same thing as principal component analysis) is guaranteed to find a common factor on to which the observables load positively. (This follows from the Frobenius-Perron theorem on the leading eigenvectors of positive matrices.) Moreover, the fraction of variance "explained" by the leading factor will typically be quite sizeable, even when the correlation matrix is basically random.

All-positive correlations can arise in many ways, including (but not limited to) ones in which the actual abilities are completely uncorrelated, but all your observables are very crude measurements which sum many abilities. So discovering that factor analysis gives us positively-loaded a common factor in no way explains the positive correlations; if anything the explanation runs the other way. Hence factor analysis is (in this way, at least) unable to tell us about the causal structure. For that matter, such artifacts of bad measurement procedures can have arbitrarily high heritabilities.


I should note that Cosma Shalizi's web page clearly states that the photo was chosen to make him look "older and more important" than he is. I think I look slightly like Trotsky, although it might be mainly just grooming. Face recognition is a particular mental ability and I am bad at it. It develops extraordinarily late. Kids are fooled by fake beards and such. I can remember when I was about 10 watching some dumb cop show on TV when the police note that a photograph of a man with long hair glasses and a beard is of a bald suspect wearing a wig and non-prescription glasses. I did not recognize the face although it was obvious to my father.

Tell me if my belief that I look sortof like Trotsky demonstrates lack of face recognition ability (comments on my nose will not be appreciated)

Photo Sharing and Video Hosting at Photobucket
Photo Sharing and Video Hosting at Photobucket

As Cosma Shalizi notes a one dimensional common factor from principle components analysis does not at all imply that causal common factors are one dimensional. To interpret the analysis that way is, indeed, the mistake of mistaking a choice of technique for a discovery. For example I would have a very low score on all parts of a written IQ test used in Japan, because I don't understand the questions.

Now I speculated that there are forms of cognitive ability which are not correlated with verbal, mathematical or spatial ability. I don't know what I am talking about, but I think that one might be "social intelligence" as in getting hints and not irritating people. A huge fraction of our mental effort is devoted to winning friends and influencing people. Everyone seems to think that social intelligence is negatively correlated with the sort of cognitive abilities measured by IQ tests and, in particular, mathematical ability. I'm sure serious research has been done on the topic.

1 comment:

Cosma said...

I uses that picture of Trotsky because I do, in fact, look him; people have recognized me at conferences from it...

The empirical fact is simply that the test scores are positively correlated with each other. Given that, factor analysis (which is not quite the same thing as principal component analysis) is guaranteed to find a common factor on to which the observables load positively. (This follows from the Frobenius-Perron theorem on the leading eigenvectors of positive matrices.) Moreover, the fraction of variance "explained" by the leading factor will typically be quite sizeable, even when the correlation matrix is basically random.

All-positive correlations can arise in many ways, including (but not limited to) ones in which the actual abilities are completely uncorrelated, but all your observables are very crude measurements which sum many abilities. So discovering that factor analysis gives us positively-loaded a common factor in no way explains the positive correlations; if anything the explanation runs the other way. Hence factor analysis is (in this way, at least) unable to tell us about the causal structure. For that matter, such artifacts of bad measurement procedures can have arbitrarily high heritabilities.