Regression trees for longitudinal and multiresponse data

TL;DR

This paper introduces a new regression tree method for longitudinal and multiresponse data based on the GUIDE approach, addressing biases and computational issues of previous CART-based methods, and demonstrating its effectiveness through simulations and real data comparisons.

Contribution

It presents an unbiased, flexible regression tree algorithm for complex longitudinal data, applicable to various data structures and missing values, with theoretical consistency results.

Findings

Outperforms MVPART in mean squared prediction error

Effective with fixed, random, and missing data points

Shows comparable or improved results against linear mixed models

Abstract

Previous algorithms for constructing regression tree models for longitudinal and multiresponse data have mostly followed the CART approach. Consequently, they inherit the same selection biases and computational difficulties as CART. We propose an alternative, based on the GUIDE approach, that treats each longitudinal data series as a curve and uses chi-squared tests of the residual curve patterns to select a variable to split each node of the tree. Besides being unbiased, the method is applicable to data with fixed and random time points and with missing values in the response or predictor variables. Simulation results comparing its mean squared prediction error with that of MVPART are given, as well as examples comparing it with standard linear mixed effects and generalized estimating equation models. Conditions for asymptotic consistency of regression tree function estimates are also given.