I'm using the good old decision tree (CRT or CHAID algorithm, depending on the situation) in order to predict voting behavior and extract some profile (e.g: Women who live in the suburbs, who are not married and have a high income are a target group for Democrats).
I'd like to do the same exercise with the results of a random forest model, but I have no idea how I can extract such multivariate profiles (IF female, AND IF suburbs, AND IF not married, AND IF high income, odds are high that one votes Democratic). I do know that you can list the general importance of each variabele, but that's about it. This variable importance is not informative on how a combination of certain values results in a certain outcome. The whole reason I'm using decision trees here and not logistic regression is precisely because I'm interested in how the combination of certain values leads to a certain outcome. And since there are - let's say - 500 trees, with in each of them a subset of variables and a subset of cases, it's useless to look at these trees separately in order to formulate such profiles.
So, here's my question: is there any way to summarize the results of a random forest in order to extract profiles based on multiple variables?
Thanks!
PS: It's my first question on StackExchange, I hope I'm doing this right!