I have a model with 5 basic predictors and all interactions between the predictors themselves. Something like (I'm simplifying here, in reality I have many more variables):
lm(Y ~ poly(X1, 3)*X2*X3*X4*X5)
I want to determine which variables and/or interactions have the largest impact on the model $R^2$ and one way to do this is to extract the principal components.
However, I don't think PCA can tell me if there are some linear combinations of predictors and interactions that significantly contribute to the model $R^2$, especially in presence of polynomial terms and interactions, where the basic predictors can not be interpreted in isolation.
poly(X1, 3) + X2*X3 could have a large explanatory power, but not
poly(X1, 3) and
X2*X3 in isolation, or
X1^2 by itself. See this thread for some background.
How can I identify the predictors, interactions and combinations of terms with the largest explanatory power?