Four-way interaction in linear regression

#1
Dear all,

I have 4 independent variables, and I want to check their combined and interrelated effects on 1 dependent variable (thus 1 y and 4 -xs).

(My study is into the effects of certain portfolio configurations, thus involving a lot of interactions)

I understand that this can be done via the creation of a 4-way interaction variable. However, this has the disadvantage of having to implement a whole lot of other terms aswell (for possible interaction, one term), or am I wrong?

The (second) question is, can this be done in a linear regression model?

Thanks in advance

Paul de Boer
 
#2
I've done 3 way interactions and you have to put it into hierarchical regression as...

Block 1:
IV1
IV2
IV3

Block 2:
IV1 x IV2
IV1 x IV3
IV2 x IV3

Block 3:

IV1 x IV2 x IV3

So I would imagine that a four-way interaction would be similar, but you'd have to provide more blocks - with more two and three-way interactions. HOWEVER, I have been told that to actually interpret what is going on, this may be too complicated for a linear regression and you may be better off with structural equational modelling, unless you looked at each relationship separately i.e. with 16 separate regressions or something.