  This paper proposes FREEtree, a tree-based method for high dimensional
longitudinal data with correlated features. Popular machine learning
approaches, like Random Forests, commonly used for variable selection do not
perform well when there are correlated features and do not account for data
observed over time. FREEtree deals with longitudinal data by using a piecewise
random effects model. It also exploits the network structure of the features by
first clustering them using weighted correlation network analysis, namely
WGCNA. It then conducts a screening step within each cluster of features and a
selection step among the surviving features, that provides a relatively
unbiased way to select features. By using dominant principle components as
regression variables at each leaf and the original features as splitting
variables at splitting nodes, FREEtree maintains its interpretability and
improves its computational efficiency. The simulation results show that
FREEtree outperforms other tree-based methods in terms of prediction accuracy,
feature selection accuracy, as well as the ability to recover the underlying
structure.
