  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.
