Tree-structured models are a powerful alternative to parametric regression models if non-linear effects and interactions are present in the data. Yet, classical tree-structured models might not be appropriate if data comes in clusters of units, which requires taking the dependence of observations into account. This is, for example, the case in cross-national studies, as presented here, where country-specific effects should not be neglected. To address this issue, we present a flexible tree-structured approach that achieves a sparse modeling of unit-specific effects and identifies subgroups (based on individual-level covariates) that differ with regard to the outcome. The methodological advances were motivated by the analysis of quality of life in older adults using data from the survey of Health, Ageing and Retirement in Europe. Application of the proposed model yields promising results and illustrated the accessibility of the approach. A comparison to alternative methods with regard to variable selection and goodness-of-fit was performed in several simulation experiments.

翻译：当数据中存在非线性效应和交互作用时，树结构模型是参数回归模型的有力替代方案。然而，若数据以单元聚类形式呈现（需考虑观测值间的依赖性），经典树结构模型可能不再适用。本文展示的跨国研究案例正是如此，其中不应忽略国家特异性效应。为解决此问题，我们提出一种柔性树结构方法，该方法既能实现单元特异性效应的稀疏建模，又能识别在结果变量上存在差异的亚组（基于个体层面协变量）。本方法学进展源于对欧洲健康、老龄与退休调查数据的分析，旨在研究老年人生活质量问题。应用所提模型获得了具有前景的结果，并证明了该方法的可操作性。通过多组模拟实验，我们在变量选择与拟合优度方面与替代方法进行了比较。