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I would like to investigate interactions between my explanatory variables prior to building a statsitical model.

Apparently it is possible to do it in R using a regression tree (library: tree). This method is based on binary recursive partitioning. The algorithm predicts a response variable by partitioning the data into subgroups based on the predictor variables.

I do not understand, however, how this algorithm investigates interactions between predictors. I would be very grateful for an easy to understand explanation for non-expert.

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  • $\begingroup$ I've been meaning to look into this as well. Never really understood this claim. Though my interest lies more with the use of random forests and boosted regression trees in identifying interactions. $\endgroup$ – charles Nov 26 '13 at 14:35
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(1) In the tree below BUN is the most significant predictor, but for both levels of BUN, Systolic Blood pressure is an important predictor. There is no interaction. Serum Creatinine appears to be important in patients with high BUN and Low Blood Pressure, and thus interacts with one or both these variables.

Risk Factors for Poor Outcomes in Patients with AHF

(2) Another explanation of using a regression tree to explore interactions can be seen at:
http://www.dmstat1.com/res/OriginalCHAIDintent.html

(3) Another example on page 30. They do not explicitly use the term "interaction", but instead talk of differing effects of a variable given a level of another variable.
http://www3.imperial.ac.uk/pls/portallive/docs/1/1171924.PDF

(4) Still not sure about a number of things:
(a) how to you determine three-way or higher level interactions. Looks like you have one in (1) above but not quite sure.
(b) With more than 3 variables this is going to be a mess.

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