Groupe d’études et de recherche en analyse des décisions

# Mixed-Effects Regression Trees for Clustered Data

## Ahlem Hajjem, François Bellavance et Denis Larocque

Tree based methods have not yet been adapted to handle mixed effects. Previous works extending them to accommodate correlated data are based on the multivariate repeated-measures approach and not on the mixed effects approach. We propose a mixed effects regression tree" method which is more flexible in terms of data requirements because the observations are viewed as nested within clusters rather than as multivariate vectors. The new method can handle unbalanced clusters, allows clusters to be splitted and can incorporate random effects. This new tree method is implemented using a standard tree algorithm within the framework of the expectation-maximization (EM) algorithm. Simulation results show that the new method can provide substantial improvements over standard trees and a real data example illustrates its application.

, 23 pages

Ce cahier a été révisé en décembre 2008