I think Shalizi isn't too far off the mark in writing "as if Thomson's theory had been ignored". Although a few psychologists & psychometricians have acknowledged Thomson's sampling model, in everyday practice it's generally ignored. There are far more papers out there that fit g-oriented factor models as a matter of course than those that try to fit a Thomson-style model. Admittedly, there is a very good reason for that — Thomson-style models would be massively underspecified on the datasets available to psychologists, so it's not practical to fit them — but that doesn't change the fact that a g-based model is the go-to choice for the everyday psychologist.
There's an interesting analogy here to Shalizi's post about IQ's heritability, now I think about it. Shalizi writes it as if psychologists and behaviour geneticists don't care about gene-environment correlation, gene-environment interaction, nonlinearities, there not really being such a thing as "the" heritability of IQ, and so on. One could object that this isn't true — there are plenty of papers out there concerned with these complexities — but on the other hand, although the textbooks pay lip service to them, researchers often resort to fitting models that ignore these speedbumps. The reason for this is the same as in the case of Thomson's model: given the data available to scientists, models that accounted for these effects would usually be ruinously underspecified. So they make do.
However, it seems to me that the fatal problem of the sampling theory is that nobody has ever managed to figure out a way to sample disjoint sets of these hypothetical uncorrelated modules. If all practically useful mental abilities and all the tests successfully predicting them always sample some particular subset of these modules, then we might as well look at that subset as a unified entity that represents the causal factor behind g, since its elements operate together as a group in all relevant cases.
Or is there some additional issue here that I'm not taking into account?
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Part 2