VCBART: Bayesian Trees for Varying Coefficients

Abstract

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