RE-EM tree is a tree-based method that combines the regression tree and the linear mixed effects model for modeling univariate response longitudinal or clustered data. In this paper, we generalize the RE-EM tree method to multivariate response data, by adopting the Multivariate Regression Tree method proposed by De'Ath [2002]. The Multivariate RE-EM tree method estimates a population-level single tree structure that is driven by the multiple responses simultaneously and object-level random effects for each response variable, where correlation between the response variables and between the associated random effects are each allowed. Through simulation studies, we verify the advantage of the Multivariate RE-EM tree over the use of multiple univariate RE-EM trees and the Multivariate Regression Tree. We apply the Multivariate RE-EM tree to analyze a real data set that contains multidimensional nonfinancial characteristics of poverty of different countries as responses, and various potential causes of poverty as predictors.

翻译：RE-EM树是一种结合回归树与线性混合效应模型的基于树的方法，用于对单变量响应的纵向或聚类数据建模。本文通过采纳De'Ath [2002]提出的多元回归树方法，将RE-EM树方法推广至多元响应数据。多元RE-EM树方法估计出一个由多个响应共同驱动的总体单树结构，以及每个响应变量的对象级随机效应，其中响应变量之间的相关性及其相关随机效应之间的相关性均被允许。通过模拟研究，我们验证了多元RE-EM树相比使用多个单变量RE-EM树和多元回归树的优势。我们将多元RE-EM树应用于分析一个真实数据集，该数据集包含不同国家贫困的多维非财务特征作为响应变量，以及各种潜在贫困成因作为预测变量。