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A replication of the S factor among US states

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  • Ulster Institute for Social Research

Abstract and Figures

A dataset of 127 variables concerning socioeconomic outcomes for US states was analyzed. Of these, 81 were used in a factor analysis. The analysis revealed a general socioeconomic factor. This factor correlated .961 with one from a previous analysis of socioeconomic data for US states.
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IQ and socioeconomic development across Regions of the UK: a reanalysis
Abstract
A reanalysis of (Carl, 2015) revealed that the inclusion of London had a strong effect on the S loading
of crime and poverty variables. S factor scores from a dataset without London and redundant variables
was strongly related to IQ scores, r = .87. The Jensen coefficient for this relationship was .86.
Introduction
Carl (2015) analyzed socioeconomic inequality across 12 regions of the UK. In my reading of his
paper, I thought of several analyses that Carl had not done. I therefore asked him for the data and he
shared it with me. For a fuller description of the data sources, refer back to his article.
Redundant variables and London
Including (nearly) perfectly correlated variables can skew an extracted factor. For this reason, I created
an alternative dataset where variables that correlated above |.90| were removed. The following pairs of
strongly correlated variables were found:
1. median.weekly.earnings and log.weekly.earnings r=0.999
2. GVA.per.capita and log.GVA.per.capita r=0.997
3. R.D.workers.per.capita and log.weekly.earnings r=0.955
4. log.GVA.per.capita and log.weekly.earnings r=0.925
5. economic.inactivity and children.workless.households r=0.914
In each case, the first of the pair was removed from the dataset. However, this resulted in a dataset with
11 cases and 11 variables, which is impossible to factor analyze. For this reason, I left in the last pair.
Furthermore, because capitals are known to sometimes strongly affect results (Kirkegaard, 2015a,
2015b, 2015d), I also created two further datasets without London. One with the redundant variables,
one without. Thus, there were 4 datasets:
1. A dataset with London and redundant variables.
2. A dataset with redundant variables but without London.
3. A dataset with London but without redundant variables.
4. A dataset without London and redundant variables.
Factor analysis
Each of the four datasets was factor analyzed. Figure 1 shows the loadings.
Removing London strongly affected the loading of the crime variable which changed from moderately
positive to moderately negative. The poverty variable also saw a strong change, from slightly negative
to strongly negative. Both changes go towards a purer S factor (desirable outcomes with positive
loadings, undesirable outcomes with negative loadings). Removing the redundant variables did not
have much effect.
As a check, I checked that these results were stable across 30 different factor analytic methods.1 They
were, all loadings and scores correlated near 1.00. For my analysis, I used those extracted with the
combination of minimum residuals and regression.
Mixedness
Due to London's strong effect on the loadings, one should check that the two methods developed for
finding such cases can identity it (Kirkegaard, 2015c). Figure 2 shows the results from these two
methods (mean absolute residual and change in factor size):
1 There are 6 different extraction and 5 scoring methods supported by the fa() function from the psych package (Revelle,
2015). Thus, there are 6*5 combinations.
Figure 1: S factor loadings in four analyses.
As can be seen, London was identified as a far outlier using both methods.
S scores and IQ
Carl's dataset also contains IQ scores for the regions. These correlate .87 with the S factor scores from
the dataset without London and redundant variables. Figure 3 shows the scatter plot.
However, it is possible that IQ is not really related to the latent S factor, but just the other variance of
the extracted S scores. For this reason I used Jensen's method (method of correlated vectors) (Jensen,
1998). Figure 4 shows the results.
Figure 2: Mixedness metrics for the complete dataset.
Figure 3: Scatter plot of S and IQ scores for regions of the UK.
Jensen's method thus supported the claim that IQ scores and the latent S factor are related.
Discussion and conclusion
My reanalysis revealed some interesting results regarding the effect of London on the loadings. This
was made possible by data sharing and shows why sharing data is very important (Wicherts & Bakker,
2012).
Supplementary material
R source code and datasets are available at the OSF.
References
Carl, N. (2015). IQ and socioeconomic development across Regions of the UK. Journal of Biosocial
Science, 1–12. http://doi.org/10.1017/S002193201500019X
Jensen, A. R. (1998). The g factor: the science of mental ability. Westport, Conn.: Praeger.
Kirkegaard, E. O. W. (2015a). Examining the S factor in Mexican states. The Winnower. Retrieved from
https://thewinnower.com/papers/examining-the-s-factor-in-mexican-states
Kirkegaard, E. O. W. (2015b). Examining the S factor in US states. The Winnower. Retrieved from
https://thewinnower.com/papers/examining-the-s-factor-in-us-states
Kirkegaard, E. O. W. (2015c). Finding mixed cases in exploratory factor analysis. The Winnower.
Retrieved from https://thewinnower.com/papers/finding-mixed-cases-in-exploratory-factor-
analysis
Figure 4: Jensen's method for the S factor's relationship to IQ scores.
Kirkegaard, E. O. W. (2015d). The S factor in Brazilian states. The Winnower. Retrieved from
https://thewinnower.com/papers/the-s-factor-in-brazilian-states
Revelle, W. (2015). psych: Procedures for Psychological, Psychometric, and Personality Research
(Version 1.5.4). Retrieved from http://cran.r-project.org/web/packages/psych/index.html
Wicherts, J. M., & Bakker, M. (2012). Publish (your data) or (let the data) perish! Why not publish
your data too? Intelligence, 40(2), 73–76. http://doi.org/10.1016/j.intell.2012.01.004
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analysis Figure 4: Jensen's method for the S factor's relationship to IQ scores
  • E O W Kirkegaard
Kirkegaard, E. O. W. (2015c). Finding mixed cases in exploratory factor analysis. The Winnower. Retrieved from https://thewinnower.com/papers/finding-mixed-cases-in-exploratory-factoranalysis Figure 4: Jensen's method for the S factor's relationship to IQ scores.