Joint Models for Handling Non-Ignorable Missing Data using Bayesian Additive Regression Trees: Application to Leaf Photosynthetic Traits Data

TL;DR

This paper introduces two novel Bayesian additive regression tree (BART) based methods for handling non-ignorable missing data, especially MNAR, with applications to leaf photosynthetic traits, demonstrating improved performance over existing approaches.

Contribution

The paper develops two BART-based models for joint modeling of data and missingness mechanisms under MNAR, extending flexible non-parametric modeling to missing data problems.

Findings

Both models outperform existing methods in simulations.

The methods effectively recover missing data mechanisms in real leaf trait data.

The second approach captures complex, non-linear missingness relationships.

Abstract

Dealing with missing data poses significant challenges in predictive analysis, often leading to biased conclusions when oversimplified assumptions about the missing data process are made. In cases where the data are missing not at random (MNAR), jointly modeling the data and missing data indicators is essential. Motivated by a real data application with partially missing multivariate outcomes related to leaf photosynthetic traits and several environmental covariates, we propose two methods under a selection model framework for handling data with missingness in the response variables suitable for recovering various missingness mechanisms. Both approaches use a multivariate extension of Bayesian additive regression trees (BART) to flexibly model the outcomes. The first approach simultaneously uses a probit regression model to jointly model the missingness. In scenarios where the relationship between the missingness and the data is more complex or non-linear, we propose a second approach using a probit BART model to characterize the missing data process, thereby employing two BART models simultaneously. Both models also effectively handle ignorable covariate missingness. The efficacy of both models compared to existing missing data approaches is demonstrated through extensive simulations, in both univariate and multivariate settings, and through the aforementioned application to the leaf photosynthetic trait data.