Abstract
Variable selection is an important statistical problem. This problem becomes more challenging when the candidate predictors are of mixed type (e.g., continuous and binary) and impact the response variable in nonlinear and/or nonadditive ways. In this paper, we review existing variable selection approaches for the Bayesian additive regression trees (BART) model, a nonparametric regression model, which is flexible enough to capture the interactions between predictors and nonlinear relationships with the response. An emphasis of this review is on the ability to identify relevant predictors. We also propose two variable importance measures, which can be used in a permutation-based variable selection approach, and a backward variable selection procedure for BART. We introduce these variations as a way of illustrating limitations and opportunities for improving current approaches and assess these via simulations.
Funding Statement
Luo and Daniels were partially supported by NIH R01 CA183854. Daniels was also partially supported by NIH R01 HL166324.
Acknowledgments
The authors thank the Editor, Associate Editor and three referees whose comments greatly improved the manuscript.
Citation
Chuji Luo. Michael J. Daniels. "Variable Selection Using Bayesian Additive Regression Trees." Statist. Sci. 39 (2) 286 - 304, May 2024. https://doi.org/10.1214/23-STS900
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