  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.

Methodology