Inference for BART with multinomial outcomes

Abstract

The multinomial probit Bayesian additive regression trees (MP- BART) framework was proposed by [9] (KD), approximating the latent util- ities in the multinomial probit (MNP) model with BART [4]. Compared to multinomial logistic models, MNP does not assume independent alternatives and the correlation structure among alternatives can be specified through mul- tivariate Gaussian distributed latent utilities. We introduce two new algo- rithms 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 ref- erence 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 bet- ter performance using our proposals as compared to KD in terms of MCMC convergence rate and posterior predictive accuracy. The package for imple- mentation is publicly available at https://github.com/yizhenxu/ GcompBART.