Paradox with the loadings of a Principal Component

pca
2017-09-06 20:42:42

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 fro