  This paper presents a new approach for trees-based regression, such as simple
regression tree, random forest and gradient boosting, in settings involving
correlated data. We show the problems that arise when implementing standard
trees-based regression models, which ignore the correlation structure. Our new
approach explicitly takes the correlation structure into account in the
splitting criterion, stopping rules and fitted values in the leaves, which
induces some major modifications of standard methodology. The superiority of
our new approach over trees-based models that do not account for the
correlation is supported by simulation experiments and real data analyses.
