Mixed-effect models with trees

Tree-based regression models are a class of statistical models for predicting continuous response variables when the shape of the regression function is unknown. They naturally take into account both non-linearities and interactions. However, they struggle with linear and quasi-linear effects and assume iid data. This article proposes two new algorithms for jointly estimating an interpretable predictive mixed-effect model with two components: a linear part, capturing the main effects, and a non-parametric component consisting of three trees for capturing non-linearities and interactions among individual-level predictors, among cluster-level predictors or cross-level. The first proposed algorithm focuses on prediction. The second one is an extension which implements a post-selection inference strategy to provide valid inference. The performance of the two algorithms is validated via Monte Carlo studies. An application on INVALSI data illustrates the potentiality of the proposed approach.