I have a dataset with 500+ variables and have done PCA.

There is a particular Principal Component that is correlated more than the others with an Event of Interest -- a binary variable -- but still is one of the least important Principal Components ranking at the 425 position.

I scaled the loadings of these Principal Component to be able to discern more clearly which Variables contribute significantly more --either in a positive or negative way-- to the formation of this Principal Component.

There is a Variable measuring the number of Mobile Transactions and there is a variable that is the Square of the Former (say X and X^2).

Variable X has a scaled loading value of 2.33 (2.33 standard deviations from the mean which is zero) and the Variable X^2 has a scaled loading value of -1.4.

Since the loadings have been scaled and these numbers represent std. deviations, the information they convey is by how much the loadings of X and X^2 respectively are larger or smaller from the average loadings of all the Variables in this Principal Component. So the specific values 2.3 and -1.4 tells us that on the one hand X contributes much more to the Principal Component compared to the other Variables of the Dataset and on the other hand conversely X^2 contributes much less. But how can this be possible? If X is important should not also X^2 be important --and actually more so?

• How do you define "loading"? According to PCA terminology loading is the covariance (or correlation) between a component (unit scaled) and a variable. You might want to search pca loadings eigenvectors on the site, to read. – ttnphns Sep 6 '17 at 20:47