I'm (very) new to PCA and confused about how to use the output of a PCA analysis to construct new variables that will be used as predictors in a regression analysis. I've looked at previous questions (e.g. Creating a new PC variable based on PCA loadings) but I'm still not sure I'm doing the right thing, as my intent is that the PCA loadings will be used to weight a new variable, rather than one that currently exists (as is the case in the existing question).
I've conducted a PCA analysis using the principal function in the R psych package. A Scree plot suggested 2 components was sensible.
twopca <- principal(facto, nfactors=2, rotate="varimax")
The loadings output looks like this:
Loadings: RC1 RC2 articulate 0.826 ambitious 0.557 competent 0.872 hardworking 0.316 intelligent 0.848 reliable 0.734 cheerful 0.831 downtoearth 0.448 fun 0.709 friendly 0.863 pleasant 0.845 warm 0.873 RC1 RC2 SS loadings 3.735 3.127 Proportion Var 0.311 0.261 Cumulative Var 0.311 0.572
I have two questions. First, what exactly are these loadings? Second, if I wanted to create two new variables based on these loading weights, is it possible do something like:
newvar1 = (cheerful * 0.831) + (downtoearth * 0.448) .... + (warm * 0.873) newvar2 = (articulate * 0.826) + ... (reliable * 0.734)
This has been suggested to me, but I want to make sure it's legit (and part of that comes from understanding what these loadings mean in the first place). Thankyou for any help !