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I have a dataset with only a few features (about 5 or 6) that I am interested in using to make predictions related to an outcome, and the context in which I am making the predictions is outside of my feature space. I have good a priori reasons to think that the relationship between my features and the outcome is fairly monotonic and maybe even linear, which would lend itself to well to some kind of linear model. However, I also have a priori reasons to believe there are strong interactions between my features, which would lend itself to some kind of decision-tree model. So what I am wondering is, what kind of model could pick up on trends in my features to extrapolate outside of the feature space, but also pick up on interactions between the features? In case it matters, my outcome variable could be framed as either a continuous/numeric outcome or a dichotomous/categorical outcome, but all of the features are continuous/numeric.

Here's some more detail about my project, since people have requested context in previous questions that I've posted: I am interested in predicting some global health outcomes based on a couple of features related to demographics, wealth, and climate through the 21st century. I'm using historic observations health outcomes, and I'd like make predictions based on other models that have predicted climate, gdp, demographics, etc for the next several decades. These predictions of climate and GDP are outside of my feature space (i.e., I'm making predictions based both higher GDP levels and higher temperatures than have been observed in my training data). In the historic data, higher temperatures hurt health outcomes and higher GDP improves health outcomes, and it is reasonable to assume these trends continue as temperatures rise and GDP increases. Similarly, we'd expect that there is an interaction between GDP and temperature - higher temperatures dont affect health outcomes as much in high GDP contexts (this historical data shows this and the model should be able to describe this). Its a bit more complicated than just GDP and temperature, though, so I'd like to have a model that can account for more complex interactions with other factors like demographics, land use, etc.

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    $\begingroup$ Based on your question, it seems you are trying to extrapolate? If that is true, please look at the following link: stats.stackexchange.com/questions/219579/… $\endgroup$
    – M Waz
    Jul 17, 2019 at 18:03
  • $\begingroup$ Thanks for the comment. There is some interesting discussion at that question. However, if what I am doing is making appropriate or inappropriate "extrapolations," that is an issue for the topic experts in my field and outside the scope of this particular question. I'd mostly just like some help with a machine learning question. $\endgroup$ Jul 17, 2019 at 18:29
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    $\begingroup$ Is your question then what type of model can handle interactions? IMO, you should start with the simplest type of model (multiple regression) and see how it works for you. Regression models are easy to interpret and explain. $\endgroup$
    – M Waz
    Jul 17, 2019 at 19:50

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