Moving one step up, one of us showed that among 71 Danish immigrant groups ranked on 4 different measures of socioeconomic variables (crime, use of social benefits, income, education attainment) there was a large (40% of variance explained) general socioeconomic factor[2].

I have problem with that. When you say "one of us" you refer to [2] a study by Kirkegaard and Fuerst. That seems confusing to me.

The general mental ability factor at the individual level has been termed "g" (often italicized "g"[3]), while the national-level group equivalent has been termed "G" ("big g factor").[4] Keeping in line with this terminology, one might refer to the general socioeconomic factor at the individual level as "s factor" and the group level version "S factor" (or "big s").

In that case shouldn't it be "national-level" instead of "group" level ?

He mentions that in 26% of a sample of studies using principal components in PsychINFO, the case-to-var ratio was between 2 and 5 as it is with our two datasets.

Do you know what is the recommended ratio ? I think you should say it explicitly, as it would help some people lost here (like me).

Since you use KMO, why not add a little sentence about what it is ? See Andy Field book "Discovering statistics using spss: Introducing statistical method" (p647).

*Another alternative is to use the Kaiser–Meyer–Olkin measure of sampling adequacy (KMO) (Kaiser, 1970). The KMO can be calculated for individual and multiple variables and represents the ratio of the squared correlation between variables to the squared partial correlation between variables. The KMO statistic varies between 0 and 1. A value of 0 indicates that the sum of partial correlations is large relative to the sum of correlations, indicating diffusion in the pattern of correlations (hence, factor analysis is likely to be inappropriate). A value close to 1 indicates that patterns of correlations are relatively compact and so factor analysis should yield distinct and reliable factors. Kaiser (1974) recommends accepting values greater than 0.5 as barely acceptable (values below this should lead you to either collect more data or rethink which variables to include). Furthermore, values between 0.5 and 0.7 are mediocre, values between 0.7 and 0.8 are good, values between 0.8 and 0.9 are great and values above 0.9 are superb (Hutcheson & Sofroniou, 1999).*

Since I found that regardless of method and dataset used, the first factor was a general factor accounting for about 40-47% of the variance, it was interesting to know how many components one needed to measure it well. To find out, I sampled subsets of components at random from the datasets, extracted the first factor, and then correlated this with the first factor using all the components. Irepeated the sampling 1000 timesto reduce sampling error to almost zero.

I do not understand what's in bold.

Often authors will also argue for a causal connection from national IQ/G to country-level variables. The typical example of this is wealth (e.g. [17, 18, 19, 20, 21]). Since I know that g causes greater wealth at the individual level, and that nations can generally be considered a large group of individuals, it would be very surprising, though not impossible, if there was no causation at the group level as well.

The word "causation" is too strong. Given the annoted references, only 20 and 21 talk a little bit about causation, but that's not even clear there is strong evidence for this pattern of causation. Instead, there is evidence that the causation wealth->IQ is not well established. Perhaps my best conclusion is that it would be best to argue, at least for now, that we don't have strong evidence for either of these two pattern of causation (i.e., wealth cause IQ or the reverse). You can argue there is probably some very indirect suggestion that IQ causes wealth more than the reverse, as your articles on immigrations, notably with John, seems to show this, but as i said, it's very indirect proof.

If population differences in G is a main cause of national differences in many socioeconomic areas, then aggregating measures should increase the correlation with G, since measurement specificity averages out.

Even if G is not causal here, aggregation would also improve the correlation, no ?

I think table 2 should better be made as the table 1.

Not related, but can you tell me how you manage to generate the nice graph at figures 2-5 ? Concerning the figures 2-5, again, have you contacted Major and his co-authors to ask for opinion ? I bet he (they) will be very interested.