# Type 2 Tobit Sample Selection Models with Bayesian Additive Regression Trees

arXiv: https://arxiv.org/abs/2502.03600 · HTML: https://mlsanity.com/paper/2502.03600/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2025.

## Built on by (most cited first, 1 of 1)

- [Heckman-Corrected Epistemic Uncertainty: Selection on Unobservables Defeats Importance Weighting](https://mlsanity.com/paper/2607.05806/) (2026)

## Abstract (arXiv)

This paper introduces Type 2 Tobit Bayesian Additive Regression Trees (TOBART-2). BART can produce accurate individual-specific treatment effect estimates. However, in practice estimates are often biased by sample selection. We extend the Type 2 Tobit sample selection model to account for nonlinearities and model uncertainty by including sums of trees in both the selection and outcome equations. A Dirichlet Process Mixture distribution for the error terms allows for departure from the assumption of bivariate normally distributed errors. Soft trees and a Dirichlet prior on splitting probabilities improve modeling of smooth and sparse data generating processes. We include a simulation study and an application to the RAND Health Insurance Experiment dataset.