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[ODP] The international general socioeconomic factor: Factor analyzing international

#51
In the newest revision, the discussion on the number of factors and variable reverse coding is quite satisfactory, although I would reorganize it so that the number of factors is discussed in section 3, but that's up to the author.

However, in section 12, it is still not made clear that the Johnson studies used CFA which will inherently lead to higher correlations than factor score comparisons, regardless of the number of variables. When this is corrected, I will approve publication.
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#52
Here's a new draft.

There are lots of changes in this one, including:
  • Many language changes for better cross-referencing and coherence.
  • A new subsection discussing Schmid-Leiman results.
  • A new section discussing other methods for measuring the strength of the general factor.
  • Rewritten Discussion section in light of comments.
  • New tables that show off data that was before mentioned merely in the text.
  • The inclusion of a new factor method in analyses that use all the available methods.
  • A new table in the Appendix with a list of S factor scores for all available countries, N=142. These are from unrotated PCA. When both sources have a value, they are averaged.
  • It is clearly indicated that it is a draft with a big fat grey DRAFT over the text.
  • Paper now runs for 21 PDF pages, with 45 references, 13 tables and 6 figures.


Attached Files
.pdf   international_socioeconomic_general.pdf (Size: 424.12 KB / Downloads: 535)
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#53
Perhaps your analysis would benefit from eliminating continental origin as a confound. I did a similar thing in my paper (http://dx.doi.org/10.1101/008011). This is to see if the correlation persists also within continent or is just mediated by them. It looks like East Asian countries have large positive residuals, because none of them is in the top 10 of the S rankings. This deserves further investigation and I think a continent-level analysis would provide it.
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#54
From the book "Intelligence, Genes, and Success: Scientists Respond to The Bell Curve", there is the following paragraph from Carroll's chapter (p143) :

Quote:It is necessary to reject two proposals that have sometimes been made to support the notion of a general intelligence factor: (1) The finding of uniformly positive intercorrelations ofcognitive variables as an indicator of the presence of a general factor. The mere fact that cognitive variables are positively correlated does not adequately validate the presence of a single general factor. It might indicate the presence of multiple general factors. (2) General factors identified as first principal components or principal factors in the factor analysis of a dataset. The first principal component, or eigenvector, is that vector that produces (under appropriate constraints) the maximal variance obtainable from a linear combination of the variables. The major problem with this proposal is that even if no general factor underlies the variables, the size of the first eigenroot is necessarily still relatively large, as compared with other eigenroots. The first principal component derived from a matrix of randomly generated correlations is necessarily larger than the remaining components. The first principal component is therefore not a valid indicator of the presence of a general factor. The same applies to the first principal factor (computed in such a way as to estimate the communalities of the variables).

In view of these considerations, only the complete factor analysis (either exploratory or confirmatory, or both) of a set of variables should be used to judge the presence of a general factor. We now give tentative conceptual and operational definitions of a general factor.

I thought he could be right. EFA as well as CFA should be used, as they are complementary. But you note that Revelle seems to disagree (this practice was apparently used to find a general factor of personality, by Rushton & Irwing, and others) and prefer the use of the hierarchical "Omega" which is the method you use in your section 12, to evaluate the strength of g. Honestly, the paper "The general factor of personality: A general critique." (Revelle & Wilt 2013) you linked was not easy to read. The authors do not specify clearly the advantage of Omega, unless it's just me.

I would say a more meaningful summary of the advantage of Omega is the paragraph here (from the pdf package psych) :

Quote:The omega function uses exploratory factor analysis to estimate the omega_h coefficient. It is important to remember that “A recommendation that should be heeded, regardless of the method chosen to estimate ω_h, is to always examine the pattern of the estimated general factor loadings prior to estimating ω_h. Such an examination constitutes an informal test of the assumption that there is a latent variable common to all of the scale's indicators that can be conducted even in the context of EFA. If the loadings were salient for only a relatively small subset of the indicators, this would suggest that there is no true general factor underlying the covariance matrix. Just such an informal assumption test would have afforded a great deal of protection against the possibility of misinterpreting the misleading ω_h estimates occasionally produced in the simulations reported here." (Zinbarg et al., 2006, p 137).

From Revelle & Wilt (2013) table 1, it is said that the sets S1 and S5 have a pattern consistent with the existence of g, but not the sets S4 and S8. For S4 and S8, this conclusion is explicited by the fact that a portion of the correlations are just zero while some others are strong. Do you agree with this interpretation of g/no g ?

Furthermore, I would like to know if you have found the cause of the problem with the Promax rotation and its low loadings.

Also, you can, if you want, talk a little bit about the consequences of finding such general socioeconomic factor. The mail you sent me was fine, for example.

And finally :

Quote:in the Schmid-Leiman transformation and divide it by the number of variables (Λg(Λ/N)). This is the amount of variance accounted

Shouldn't it be Λg/N instead ? (see Revelle & Wilt 2013 p 496)

Quote:The strength of the S factor in the international data is quite similar to, perhaps a little stronger than, the g factor in the classic datasets, while the general factor of personality is clearly weaker.

You don't need to put a comma after "stronger than".

P.S. there is a problem with reference 23. The length of the link goes out of bound. I think you already know it, but is there is no possibility to correct for this ?
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#55
Hi Meng Hu.

Thank you for reviewing my paper.

Quote: I thought he could be right. EFA as well as CFA should be used, as they are complementary. But you note that Revelle seems to disagree (this practice was apparently used to find a general factor of personality, by Rushton & Irwing, and others) and prefer the use of the hierarchical "Omega" which is the method you use in your section 12, to evaluate the strength of g. Honestly, the paper "The general factor of personality: A general critique." (Revelle & Wilt 2013) you linked was not easy to read. The authors do not specify clearly the advantage of Omega, unless it's just me.

As I wrote before, it is an exploratory study. I didn't have a ready made model or alternative model to use CFA on to begin with.

Well, as you can see in the RW paper, they use many different methods. I used all the same methods, except the cluster one which I don't know how they used.

It is a hard paper yes, their methods aren't quite clear, which is why I wasn't more clear. I am simply following their lead and showing that their methods too confirm the strength of the general factor.

Quote: From Revelle & Wilt (2013) table 1, it is said that the sets S1 and S5 have a pattern consistent with the existence of g, but not the sets S4 and S8. For S4 and S8, this conclusion is explicited by the fact that a portion of the correlations are just zero while some others are strong. Do you agree with this interpretation of g/no g ?

Yes.

Quote: Shouldn't it be Λg/N instead ? (see Revelle & Wilt 2013 p 496)

The parentheses shows the eigenvalue and variable numbers from which the value was calculated. It is somewhat unclear, but how else to write it? It is common to put e.g. SD's in parentheses too.

Quote: You don't need to put a comma after "stronger than".

It seems right to me. http://en.wikipedia.org/wiki/Subordinate...unctuation

Quote: P.S. there is a problem with reference 23. The length of the link goes out of bound. I think you already know it, but is there is no possibility to correct for this ?

I see. However, I don't think I can fix it. It is a bug in bibtex apparently. However, I note that if you click the link, it works fine. It is only visually broken thus only a minor problem.

--

I will add a new version shortly with some more stuff in the discussion.
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#56
I think I'm fine with the last version, it's just that I don't know why you have such low correlation for promax when you compute schmid transformation by hand. Have you contacted others and see what they could think of it ?
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#57
Revelle told me I was incompetent.

However, I noted that the schmid() function only uses the 1st order factors to get the general factor. When I did it manually, I extracted 2/3 2nd order factors to extract a general factor from. Perhaps this extra level causes some factor instability.

I searched for reasons to prefer promax over oblimin or reversely, but didn't find much. Most seemed to say that promax was developed because it was a more computationally effective method that gave similar results to oblimin. This effectiveness criteria has no relevance with today's computer for these analyses.

A friend is currently proofreading my next draft. I will attach it once it is done. The major change besides language fixes is that I added two more paragraphs to the conclusion. One about the nascent field of psychoinformatics, and one about whether we should care about the existence of an S factor.
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#58
Whatever the case, I will prefer obviously the schmid function incorporated in R. That's common sense. I just wanted to know why it behaves like this when you do it manually. Concerning promax/oblimin, my question was that some people did say they slightly prefer promax and I see promax more often in use than oblimin, although the latter is also very widely used. As you say, there is no logical reason that we should dismiss one or the other.

I will wait your final version.
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#59
This version has:
- Small language fixes
- Two new sections in the Discussion


Attached Files
.pdf   international_socioeconomic_general.pdf (Size: 425.75 KB / Downloads: 521)
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#60
So, the only modification is on the discussion section. I don't have anything to add, or to complain.

I, of course, will give my acceptance for its publication.

By the way, it's funny when I look at the last version, I am redirected to page 2, not page 1, as is usually the case. It's rare but sometimes this happens, when I open pdf articles. I never understood why.

One last remark (or request). Don't forget to publish the updated syntax for R. I am interested in everything related to R. I'm trying to move, from SPSS to R. But that's not easy. Recoding variable in R is impossible for me, even after spending hours on the web and finding examples. They are all inapplicable for my General Social Survey data. Then, I have to do the data preparation on SPSS, and the analysis on R. Ridiculous, indeed, but I don't have a better option yet.
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