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领域有着悠久的研究与应用历史，但现有顶尖的变系数建模方法难以处理多元效应修正因子，且需借助限制性函数形式假设或涉及计算密集型的超参数调优。为此，我们提出VCBART方法，通过贝叶斯加性回归树灵活估计变系数模型中的协变量效应。在简单默认参数设置下，VCBART在协变量效应估计、不确定性量化及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VCBART的实用性：其一探究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；其二估计城市犯罪的时间趋势如何在社区层面呈现差异。实现VCBART的R语言工具包可在https://github.com/skdeshpande91/VCBART获取。