VCBART: Bayesian trees for varying coefficients

TL;DR

VCBART introduces a Bayesian tree-based approach for flexible, multivariate varying coefficient modeling that outperforms existing methods in estimation, uncertainty quantification, and prediction, with practical case studies demonstrating its utility.

Contribution

The paper presents VCBART, a novel Bayesian additive regression tree method for multivariate varying coefficient models, overcoming limitations of existing approaches.

Findings

VCBART outperforms existing methods in covariate effect estimation.

VCBART provides better uncertainty quantification.

VCBART improves outcome prediction accuracy.

Abstract

The linear varying coefficient models posits a linear relationship between an outcome and covariates in which the covariate effects are modeled as functions of additional effect modifiers. Despite a long history of study and use in statistics and econometrics, state-of-the-art varying coefficient modeling methods cannot accommodate multivariate effect modifiers without imposing restrictive functional form assumptions or involving computationally intensive hyperparameter tuning. In response, we introduce VCBART, which flexibly estimates the covariate effect in a varying coefficient model using Bayesian Additive Regression Trees. With simple default settings, VCBART outperforms existing varying coefficient methods in terms of covariate effect estimation, uncertainty quantification, and outcome prediction. We illustrate the utility of VCBART with two case studies: one examining how the association between later-life cognition and measures of socioeconomic position vary with respect to age and socio-demographics and another estimating how temporal trends in urban crime vary at the neighborhood level. An R package implementing VCBART is available at https://github.com/skdeshpande91/VCBART