Tree-Structured Mixed-Effects Regression Modeling for Longitudinal Data

Tree-structured models have been widely used because they function as interpretable prediction models that offer easy data visualization. A number of tree algorithms have been developed for univariate response data and can be extended to analyze multivariate response data. We propose a tree algorithm by combining the merits of a tree-based model and a mixed-effects model for longitudinal data. We alleviate variable selection bias through residual analysis, which is used to solve problems that exhaustive search approaches suffer from, such as undue preference to split variables with more possible splits, expensive computational cost, and end-cut preference. Most importantly, our tree algorithm discovers trends over time on each of the subspaces from recursive partitioning, while other tree algorithms predict responses. We investigate the performance of our algorithm with both simulation and real data studies. We also develop an R package melt that can be used conveniently and freely. Additional results are provided as online supplementary material.

树结构模型（Tree-structured models）因兼具可解释性强的预测特性与便捷的数据可视化能力，已得到广泛应用。目前已有多款面向单变量响应数据的树算法被提出，且均可扩展用于多变量响应数据的分析。针对纵向数据，本文提出一种融合树模型与混合效应模型（mixed-effects model）优势的树算法。本文通过残差分析（residual analysis）缓解变量选择偏差，以此解决穷举搜索方法存在的诸多问题：包括不当偏向可分裂选项更多的变量、计算成本过高，以及终端节点分裂偏好。尤为关键的是，本算法可通过递归划分（recursive partitioning）在各子空间中挖掘时序趋势，而现有多数树算法仅能完成响应变量预测。本文通过仿真实验与真实数据集实验，对所提算法的性能进行了验证。本文还开发了一款名为melt的R包（R package），可便捷免费地使用。额外的实验结果已作为在线补充材料予以提供。