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

翻译：线性变系数模型假设结果变量与协变量之间存在线性关系，其中协变量效应被建模为额外效应修正因子的函数。尽管该模型在统计学和计量经济学中已有长期的研究与应用历史，但现有最先进的变系数建模方法无法在不对函数形式施加限制性假设或涉及计算密集型超参数调优的情况下，处理多元效应修正因子。为此，我们提出了VCBART方法，该方法利用贝叶斯加性回归树灵活估计变系数模型中的协变量效应。在简单的默认设置下，VCBART在协变量效应估计、不确定性量化和结果预测方面均优于现有变系数方法。我们通过两个案例研究说明了VCBART的实用性：一是考察晚年认知能力与社会经济地位指标之间的关联如何随年龄和社会人口学特征变化；二是估计城市犯罪的时间趋势如何在邻里层面发生变化。实现VCBART的R包可从https://github.com/skdeshpande91/VCBART 获取。