My scenario is this: I collected a bunch of vegetation data (% cover counts in a quadrant at different heights) in patches where birds were seen foraging and also in control patches where no foraging was known to occur. This habitat data all suffers (as expected) from multi-collinearity so I did a principal component analysis (PCA) which yielded 3 new habitat variables: PC1, PC2 and PC3.
I then decided to model patch type (1=forage patch, 0=control patch) via logistic regression:
patch type ~ pc1+pc2+pc3
to see how the probability that a bird used a patch for foraging was influenced by habitat variables. However since I collected this data in two different habitat types (grazed and ungrazed) I included this 2-level categorical habitat type variable as an interaction with each of the PC variables like this:
patch type ~ pc1*habitat type + pc2*habitat type + pc3*habitat type
My problem is that my PC variables themselves are correlated with my habitat type variable. Is there anything I can do to make this work with this approach?