Friday, May 12, 2006

Insight into the nature of g? Some recent brain-imaging results   posted by Darth Quixote @ 5/12/2006 05:09:00 PM
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In an earlier post, I suggested that g as a construct may not prove amenable to the rage for localization in cognitive neuroscience. This is essentially because, unlike most of the constructs that interest brain imagers, g is not describable in terms of domain content or cognitive processes. As this particular distinction is rather abstract, I thought it would be helpful to use some slick figures from recent brain-imaging studies to illustrate the point.


In the first study a team of Korean scientists and Jeremy Gray (known to longtime GNXP readers as the second half of the Thompson and Gray (2004) dynamic duo) put two groups of Korean subjects, divided by superior and average performance on Raven's Progressive Matrices (RPM), through fMRI measurements as they worked successively on an easy RPM-type problem and a difficult one. Their results are summarized well in the following figure:

In both groups the more difficult and highly g-loaded problem elicited more change in blood oxygenation (which presumably indexes neural activity) in lateral prefrontal, posterior parietal, and anterior cingulate. Moreover, the higher-g subjects showed more diffuse activation and a larger contrast between conditions. These results led the authors to suggest that "superior g may ... be due to ... the functional facilitation of the fronto-parietal network particularly driven by the posterior parietal activation."

First, some words about the RPM. Each item of the RPM consists of a 3-by-3 matrix of figural elements where the bottom-right element is missing and must be selected from a multiple-choice array. In order to solve a given item, the subject must figure out the rule or rules that govern the arrangement of the elements in the matrix. The RPM is a favorite of researchers because it is nonverbal and thus "culture reduced" and also because it appears to be a pure measure of g. That is, in a factor analysis of a diverse battery of mental tests, not only does g make up a large portion of the RPM variance, but it is the only latent factor on which the RPM shows a salient loading. That is somewhat mysterious when you think about it. Most tests elicit g through the activity of what we might call "modules," that is, ability domains corresponding to language, number, space, short-term memory, and so on. How is it possible to measure g without tapping any module of this kind? Apparently the extremely abstract reasoning called for by the RPM does not fall within the domain of any adapted module and instead is executed by ad hoc circuits put together and recruited on the fly.

A high g loading and the failure to show salient loadings on any non-g factors does not mean the RPM captures the "essence" of g. Take vocabulary tests. Although vocabulary shows a strong loading on a verbal factor, it also shows a g loading that often exceeds that of the RPM. The point is that there are many indicators of g, some even more sensitive than the RPM although not as specific. So, the question: how do we know that the brain regions revealed by subtracting the fMRI signal for an easy RPM-type item from the signal for a hard one have a privileged relationship to g? Are the same regions preferentially activated in learning the meanings of words, mentally rotating shapes, memorizing random strings of digits, or figuring out what "statue" and "poem" have in common? The study by Lee, Gray, and their colleagues does not answer this question. In the end we can have learned some phrenology relating to the RPM, but cannot be sure that we have found out much about g.

A study in press by Colom, Jung, and Haier takes a different approach. We know that brain volume is correlated with IQ, so why not keep following this up? They reanalyze the results of an earlier study finding individual-difference correlations between IQ and volumes of specific brain regions, trying to see which of these regions are specifically related to g. They use what Professor Jensen calls the method of correlated vectors: essentially, taking a column vector of test g loadings and a column vector of test correlations with some external variable (here, the amount of gray or white matter in a specific brain region) and seeing if element pairs are correlated. Now, already we have a methodological ambiguity. Although the method of correlated vectors has become widely accepted, more sophisticated psychometricians have objected vociferously to its use (e.g., Dolan & Hamaker, 2001). The problem is that doing the simple thing and seeing whether the g loading of a test predicts the magnitude of its correlation with brain size (or its power to discriminate whites and blacks, or whatever) is that it glides over a lot of potential pitfalls in the implicit model. For example, what if the verbal tests in a given battery just happen to tend toward larger g loadings than the spatial or memory tests? (This is in fact the case in the Wechsler intelligence scales.) For reasons of this kind, the critics of the method of correlated vectors claim that the most appropriate methodology for this type of question is structural equation modeling.

Please note that this dispute is not over some trivial, peripheral issue. The method of correlated vectors is a crucial plank in Professor Jensen's research program attempting to link the black-white IQ gap to the genetic and neural substrate underlying the surface behaviors recorded by IQ tests. Thus, all students of the subject of racial differences in mental abilities would do well to await the settlement of this methodological point. Now, I admit that the merits of the arguments by Dolan and colleagues are beyond my current competence to adjudicate (I'll have to overcome the headaches I get looking at pages and pages of matrix notation ... man, are those squiggly things letters?) ... but I will offer an opinion anyway! I think that no matter what methodology is ultimately adopted for determining the factorial structure of the relationship between IQ and external variables, those variables that have shown consistent and substantial "Jensen effects" (covariation with g loadings according to the method of correlated vectors) across studies (the black-white gap, reaction time, overall head/brain size, heritability) will prove to be related to g while those that have not (the Flynn Effect) will prove to be primarily non-g. Of course, it may be the case that we will have to move beyond black-box, purely statistical approaches to make any real progress. Note also that Professor Jensen has brought lines of evidence to the black-white issue other than purely psychometric ones (e.g., mental chronometry).

Let us take the method of correlated vectors for granted. So what did its application to the structural MRI data gathered by Haier and colleagues show?


The two sides of this figure represent the findings from independent samples. Brain regions in red indicate voxels where quantity of gray matter was significantly correlated to Full Scale IQ in the earlier analysis. The specific Brodmann areas labeled by number and circled in green indicate vowels where the correlations of the subtests with gray matter quantity were significantly predicted by their g loadings. Now, this is surely a bigtime exercise in data mining. Keep in mind also that the degrees of freedom for the method of correlated vectors is the number of subtests (not subjects) minus two, so even if valid the method has very weak power.

But even if we put those kinds of issue aside, what can we make of these data? There is noticeable heterogeneity between samples; different voxels are found to be related to g in the two groups. What about the claim by Lee and colleagues about a frontal-parietal network? Well, looking at both samples we see g voxels in frontal, temporal and occipital. No parietal. Moreover, in the UNM sample the lobe with the most g vowels is temporal, and in the UCI sample it is occipital. Thus, contrary to the suggestions made by Lee and colleagues from their functional data, these structual data do not reveal anything particular about the frontal and parietal lobes. To me it looks like IQ is associated with gray matter volume everywhere in the cortex.

This is a key point. What I would like to see from Haier and colleagues are the intercorrelations of gray matter volume among voxels. We know from previous studies that brain volume is in fact interrcorrelated across regions. Pennington et al. (2000) found that a subcortical factor (of which white matter was an indicator) was more highly correlated with IQ than a cortical factor. MacLullich et al. (2002) produced results in the same line. Administering the RPM and tests of reading comprehension, memory, visual and auditory recall, verbal fluency, and coding speed to a sample of 97 healthy elderly men and then using structural MRI to measure the volumes of their frontal lobes, temporal lobes, and hippocampi, they found that the best-fitting structual equation model was a correlation between overall brain size and a general mental ability factor. That is, there was no reason to believe that specific tests had narrow relationships to specific brain regions, and also no reason to think that any brain region had a privileged relationship to the extracted g.

I think that these results are consistent with my hunch that g arises from individual differences in extremely diffuse and global aspects of the central nervous system that modify the efficency of information processing in a manner independent of whatever local region or specific cognitive process is called upon. As Willerman and Bailey (1987) put it,

Correlations between phenotypically different mental tests may arise, not because of any causal connection among the mental elements required for correct solutions or because of the physical sharing of neural tissue, but because each test in part requires the same "qualities" of brain for successful performance. For example, the efficiency of neural conduction or the extent of neuronal arborization may be correlated in different parts of the brain because of a similar epigenetic matrix, not because of concurrent functional overlap.

In this thread GC pointed out a genetic mechanism for intercorrelations among anthropometric measurements to refute the notion that mechanistic hypothesis regarding factor-analytic constructs are idle exercises in "reification." In the same vein suppose that a gene (e.g., MCPH1?) tends to increase the number of neurons everywhere across the cortex because of a widespread pattern of expression or diffuse downstream effects cascading through development. And suppose that having more neurons somehow increases the processing power of a brain region. On pages 99 and 100 of How the Mind Works, Steven Pinker presents a clear example of how an extra layer of toy neurons allows a neural net to perform more powerful computations. The end result will be a g factor arising from mental tests that tap distinguishable neural circuits.

As I said before, I've seen preliminary MEG results with the Hick choice reaction-time task consistent with my hunch. Because of its extraordinary temporal acuity, MEG is the ideal tool to use in conjunction with mental chronometry, and I hope that reseachers will eagerly adopt it. I predict that differences in psychometric ability tests will prove to be associated with differences in processing speed/consistenty along disjoint pathways of neural signal propagation across different g-loaded reaction-time tasks. [Importantly, Wickett, Vernon, and Lee (2000) have shown that brain volume substantially mediates the relationship between IQ and reaction time.] But what if I'm right? What then? We will know a lot about what g isn't but not all that much about how exactly it is that more neurons or interneuronal connections (or whatever) allow you to learn more words, rotate shapes in your head more accurately, and so on. At that point I suspect that even more powerful brain-probing technologies than are currently available, in conjunction with novel analytic, theoretical advances, will be necessary to attain the holy grail of reductionistically understanding the as-yet casually murky g factor.