Bayesian additive regression trees for multivariate skewed responses

This paper introduces a nonparametric regression approach for univariate and multivariate skewed responses using Bayesian additive regression trees (BART). Existing BART methods use ensembles of decision trees to model a mean function, and have become popular recently due to their high prediction accuracy and ease of use. The usual assumption of a univariate Gaussian error distribution, however, is restrictive in many biomedical applications. Motivated by an oral health study, we provide a useful extension of BART, the skewBART model, to address this problem. We then extend skewBART to allow for multivariate responses, with information shared across the decision trees associated with different responses within the same subject. The methodology accommodates within-subject association, and allows varying skewness parameters for the varying multivariate responses. We illustrate the benefits of our multivariate skewBART proposal over existing alternatives via simulation studies and application to the oral health dataset with bivariate highly skewed responses. Our methodology is implementable via the R package skewBART, available on GitHub.