Combining LASSO-type Methods with a Smooth Transition Random Forest

In this work, we propose a novel hybrid method for the estimation of regression models, which is based on a combination of LASSO-type methods and smooth transition (STR) random forests. Tree-based regression models are known for their flexibility and skills to learn even very nonlinear patterns. The STR-Tree model introduces smoothness into traditional splitting nodes, leading to a non-binary labeling, which can be interpreted as a group membership degree for each observation. Our approach involves two steps. First, we fit a penalized linear regression using LASSO-type methods. Then, we estimate an STR random forest on the residuals from the first step, using the original covariates. This dual-step process allows us to capture any significant linear relationships in the data generating process through a parametric approach, and then addresses nonlinearities with a flexible model. We conducted numerical studies with both simulated and real data to demonstrate our method’s effectiveness. Our findings indicate that our proposal offers superior predictive power, particularly in datasets with both linear and nonlinear characteristics, when compared to traditional benchmarks.