[R] Generating Interaction Factors (combinations of Data Frame columns)

[Thomas Hopper]

I'm starting to do a fair amount of DOE in my day job and need to 
generate full- and fractional-factorial designs.

One of the things I'd like to do is generate all possible interaction 
effects, given the main effects. I've been searching through the 
documentation, packages and mail list archives, but the closest I can 
find are combin() in package combinat and combine() and combinations() 
in gregsmisc, none of which actually produces the results I want.

Given a data frame with columns labeled A, B, C and D, I would like to 
generate a data frame with columns that are the combination of each of 
the columns in the original data frame. The output columns would be 
A*B, A*C, A*D, A*E, A*B*C, A*B*D,..., A*B*C*D.

Alternatively, I'd want to generate the interactions for a given level 
(2-factor or 3-factor).

If such a function already exists, I'd be more than happy to use it.

If it doesn't, I can write it, but I would appreciate a little help 
with the algorithm for generating the combinations...how do I loop 
through the given factors to generate all possible combinations?

Thanks,

Tom