Enhancing Statistical Inference in Mixed-Effect Three-Tree Model: A Data-Carving Estimation Strategy with an Application on Amyotrophic Lateral Sclerosis Data

In the framework of mixed-effects models, this paper explores the Three-Tree Mixed-Effects Model for longitudinal data. This model is a semi-parametric extension of the linear mixed-effects model, comprising a linear component and three tree-based components. This approach results in a model capable of handling interactions and nonlinearities while ensuring interpretability. Moreover, we propose an algorithm for estimating model parameters based on the data-carving post-selection inference procedure. The performance of the proposed algorithm is evaluated through a Monte Carlo study. The proposed methodology is applied to a real case study on Amyotrophic Lateral Sclerosis (ALS).