Mixed Effects Trees and Random Forests for Clustered Data

• Activity Number: 544
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Ahlem Hajjem*+ and François Bellavance and Denis Larocque
• Companies: ESG UQAM and HEC Montréal and HEC Montréal
• Keywords: Clustered data ; Mixed effects ; Regression tree ; Random forest ; EM algorithm

Abstract

We present the mixed effects regression tree and random forest methods. These are extensions of tree-based methods for clustered data, where the correlated observations are viewed as nested within clusters rather than as vectors of multivariate repeated responses. The mixed effects approach allows for unbalanced clusters and observations within clusters to be splitted, and can incorporate random effects and observation-level covariates. These extensions are implemented using standard tree and forest algorithms within the framework of the EM algorithm. Simulation results show that the proposed methods provide substantial improvements over standard tree and forest when the random effects are non negligible. We illustrate these methods using a real dataset on first-week box office revenues of movies.