Tree embedded linear mixed models

This work gives a contribution to the emerging literature on the use of regression trees for hierarchical data to increase the flexibility and the predictive ability of random effects models. The proposed procedure extends random effect re- gression trees considering a random effect model with both a tree component and a linear component. Moreover, it is suggested to decompose the effects of predictors within and between clusters. The performance of the proposed procedure is evaluated through a simulation study and an application to INVALSI data on students achieve- ment.