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变量的函数。尽管在统计学和计量经济学中具有悠久的研究和应用历史，但现有的先进变系数建模方法无法在不施加严格函数形式假设或进行计算密集型超参数调优的情况下处理多元效应修正变量。为此，我们提出了VCBART，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展示了VCBART的实用性：第一个案例探究晚年认知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；第二个案例估计城市犯罪的时间趋势在社区层面如何变化。实现VCBART的R软件包可在https://github.com/skdeshpande91/VCBART获取。