We are used to Multivariate Regression and Experimental Design (Factorial Designs, Response Surface, etc) to model data and understand predictor/response correlations and interactions. Recently, we started to look into CART and TreeNET learning models. The latter approaches seem to have better predictive ability, primarily through improved pattern recognition. With the presence of these newer machine learning models, is there any justification for continued use of conventional regression approaches? Any thoughts would be greatly appreciated. Thanks.
All of them are machine learning models. The difference is how each algorithm builds the regression models. Some are more robust against overfitting, others are more interpretable, others handle non-linearity, others need less samples for training... I wouldn't dare to say that any of them is better than the rest without stating specifically in which context and for which data.
Surely yes, especially if the classical approaches ae used in a sensible way (i.e. avoiding collinearity of regressors by using principal componenrs as regressors or other methods). The basic point is not only 'obtaining the best prediction' but to have an explainable soution and for this last task classical methods are much more explainbale than machine learning (mainly black box) approaches.
See : https://doi.org/10.1016/j.patter.2020.100025
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