I am using regression tree to find the factors effecting food insecurity. I want to know how regression tree is better than OLS in terms of heterogeneity. Can anybody help?
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2$\begingroup$ This question is not clear. What do you mean by "how regression tree is better than OLS in terms of heterogeneity"? $\endgroup$– gung - Reinstate MonicaCommented May 5, 2014 at 1:27
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$\begingroup$ I mean to say that OLS smooth out all heterogeneity in the sample data but regression tree can make small groups of homogenous characteristics and then give results $\endgroup$– AlmazeaCommented May 5, 2014 at 1:38
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I am not sure exactly what you mean but 1) OLS regression with no interaction terms, splines or polynomial terms gives you one type of best fit to your data: The best fit that is a straight line combination of the p various independent variables in a p-dimensional space. This may be what you mean by "smooth out all heterogeneity". Regression trees do not do this: Continuous IVs can be split at any point, so the relation between an IV and the DV can be nonlinear or even non-monotonic. 2) With more than one IV, regression trees automatically consider interactions, but they do so in ways that OLS regression cannot (at least not easily).
answered May 5, 2014 at 10:10
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$\begingroup$ Thank you Peter Flom, Would you please help me to get some published reference for this? $\endgroup$– AlmazeaCommented May 8, 2014 at 2:24
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$\begingroup$ I don't know of a specific reference that says both of these things. Any book on regression will say the first and any book on trees will say the second. E.g. Breiman et al. $\endgroup$ Commented May 8, 2014 at 9:42