Should I include interactions in ridge regression? I'm running the a ridge regression broadly analogous to the one at http://www.mathworks.com.au/help/stats/ridge.html. 
However, I have a lot more predictors (12) than the example (which only has 3). Thus when I include the interactions the number of parameters blows out. 
What should I do? I don't have any particular reason for thinking there would/would not be interactions.
 A: The ols function in the R rms package allows differential penalization.  For example you can penalize interactions more than you penalize main effects.  When you allow for nonlinearity (which is usually necessary) you can have increasing penalization for linear main effects, nonlinear main effects, linear interaction effects, nonlinear interaction effects.
A: You have a lot of options, and we can't really tell you what will work best given the limited information you've provided. That said, here are some ideas to explore:


*

*Try the regression with just your 12 predictors and see if that doesn't give you a good enough result.

*Including just two-way interactions will add ${{12}\choose{2}} = 66$ terms, giving a total of 78 terms. That's not so bad: just give it a shot and see what happens.

*If you want to try to elucidate more specifically where there might be interactions, train a decision tree model and look at variable interactions along different branches.

*You could add a variable selection element to your regression by using lasso or elastic-net instead of ridge regression.
