A regression tree method for longitudinal and clustered data with multivariate responses

In this paper, we propose a tree-based method called Multivariate RE-EM tree, which combines the regression tree and the linear mixed effects model for modeling multivariate response longitudinal or clustered data. 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.