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.<\/p>\n
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:<\/p>\n
- \n
- A dataset with London and redundant variables.<\/li>\n
- A dataset with redundant variables but without London.<\/li>\n
- A dataset with London but without redundant variables.<\/li>\n
- A dataset without London and redundant variables.<\/li>\n<\/ol>\n
Factor analysis<\/b><\/p>\n
Each of the four datasets was factor analyzed. Figure 1 shows the loadings.<\/p>\n
![\"loadings\"](\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/loadings2-1024x657.png\")
<\/a><\/p>\nFigure 1: S factor loadings in four analyses.<\/i><\/span><\/p>\n
Removing London strongly affected the loading of the crime variable, which changed from moderately positive to moderately negative. The poverty variable also saw a large change, from slightly negative to strongly negative. Both changes are in the direction towards a purer S factor (desirable outcomes with positive loadings, undesirable outcomes with negative loadings). Removing the redundant variables did not have much effect.<\/p>\n
As a check, I investigated whether these results were stable across 30 different factor analytic methods.1<\/sup><\/a> 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.<\/p>\n
Mixedness<\/b><\/p>\n
Due to London’s strong effect on the loadings, one should check that the two methods developed for finding such cases can identify it (Kirkegaard, 2015c). Figure 2 shows the results from these two methods (mean absolute residual and change in factor size):<\/p>\n
![\"mixedness\"](\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/mixedness1-1024x657.png\")
<\/a>
Figure 2: Mixedness metrics for the complete dataset.<\/i><\/span><\/p>\nAs can be seen, London was identified as a far outlier using both methods.<\/p>\n
S scores and IQ<\/b><\/p>\n
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.<\/p>\n
![\"IQ_S\"](\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/IQ_S-1024x657.png\")
<\/a>
Figure 3: Scatter plot of S and IQ scores for regions of the UK.<\/i><\/span><\/p>\nHowever, it is possible that IQ is not really related to the latent S factor, 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.<\/p>\n
![\"loadings\"](\"http:\/\/emilkirkegaard.dk\/en\/wp-content\/uploads\/loadings2.png\")
<\/a><\/p>\n