Unbiased Regression Trees for Longitudinal Data

• Activity Number: 343
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Wei Fu*+ and Jeffrey Simonoff
• Companies: New York University and New York University
• Keywords: Longitudinal data ; Mixed effect model ; Tree based method ; Bias correction

Abstract

This paper presents a new version of the RE-EM regression tree method proposed by Sela and Simonoff (2012). In their work, Sela and Simonoff present a methodology that combines the structure of mixed effects models for longitudinal and clustered data with the flexibility of tree-based estimation methods. They show that the RE-EM tree is less sensitive to parametric assumptions and provides improved predictive power compared to linear models with random effects and regression trees without random effects. However, they used the CART tree algorithm proposed by Breiman et al. (1984) for tree building, and therefore the RE-EM regression tree method inherits the tendency of CART to split on variables with more possible splits. We propose a revised version of the RE-EM regression tree that corrects for this bias by using the conditional inference tree proposed by Hothorn et al. (2006) as the underlying tree algorithm instead of CART. Simulation studies show that the new version is indeed unbiased, and has several improvements over the original RE-EM regression tree in terms of prediction accuracy and the ability to recover the correct true structure.