Using this data:
I can do a PCA as thus:
plot(USArrests) otherPCA <- princomp(USArrests)
I can get the new components in
and the proportion of variance explained by components with
But what if I want to know which variables are mostly explained by which principal components? And vice versa: is e.g. PC1 or PC2 mostly explained by
murder? How can I do this?
Can I say for instance that PC1 is 80% explained by
I think the loadings help me here, but they show the directionality not the variance explained as i understand it, e.g.
otherPCA$loadings Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Murder 0.995 Assault -0.995 UrbanPop -0.977 -0.201 Rape -0.201 0.974
You are right, the loadings can help you here. They can be used to compute the correlation between the variables and the principal components. Moreover, the sum of the squared loadings of one variable over all principal components is equal to 1. Hence, the squared loadings tell you the proportion of variance of one variable explained by one principal component.
The problem with princomp is, it only shows the “very high” loadings. But since the loadings are just the eigenvectors of the covariance matrix, one can get all loadings using the
eigen command in R:
loadings <- eigen(cov(USArrests))$vectors explvar <- loadings^2
Now, you have the desired information in the matrix