Inference for BART with Multinomial Outcomes

TL;DR

This paper introduces two new algorithms for fitting the MPBART model, improving convergence and predictive accuracy, especially in healthcare applications involving multinomial outcomes.

Contribution

The authors develop and analyze two novel algorithms for MPBART, demonstrating superior mixing rates and predictive performance over previous methods.

Findings

New algorithms show better MCMC convergence.

Enhanced posterior predictive accuracy.

Robustness to outcome imbalance and prior choices.

Abstract

The multinomial probit Bayesian additive regression trees (MPBART) framework was proposed by Kindo et al. (KD), approximating the latent utilities in the multinomial probit (MNP) model with BART (Chipman et al. 2010). Compared to multinomial logistic models, MNP does not assume independent alternatives and the correlation structure among alternatives can be specified through multivariate Gaussian distributed latent utilities. We introduce two new algorithms for fitting the MPBART and show that the theoretical mixing rates of our proposals are equal or superior to the existing algorithm in KD. Through simulations, we explore the robustness of the methods to the choice of reference level, imbalance in outcome frequencies, and the specifications of prior hyperparameters for the utility error term. The work is motivated by the application of generating posterior predictive distributions for mortality and engagement in care among HIV-positive patients based on electronic health records (EHRs) from the Academic Model Providing Access to Healthcare (AMPATH) in Kenya. In both the application and simulations, we observe better performance using our proposals as compared to KD in terms of MCMC convergence rate and posterior predictive accuracy.