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The Regression Trunk Approach to Discover Treatment Covariate Interaction

Published online by Cambridge University Press:  01 January 2025

Elise Dusseldorp  and
Jacqueline J. Meulman
Elise Dusseldorp*
Affiliation:
Leiden University
Jacqueline J. Meulman
Affiliation:
Leiden University
*
Requests for reprints should be sent to Elise Dusseldorp, Data Theory Group, Faculty of Social and Behavioral Sciences, Leiden University, P.O. Box 9555, 2300 RB Leiden, The Netherlands (e-mail: dusseldorp@fsw.leidenuniv.nl)
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Abstract

The regression trunk approach (RTA) is an integration of regression trees and multiple linear regression analysis. In this paper RTA is used to discover treatment covariate interactions, in the regression of one continuous variable on a treatment variable withmultiple covariates. The performance of RTA is compared to the classical method of forward stepwise regression. The results of two simulation studies, in which the true interactions are modeled as threshold interactions, show that RTA detects the interactions in a higher number of cases (82.3% in the first simulation study, and 52.3% in the second) than stepwise regression (56.5% and 20.5%). In a real data example the final RTA model has a higher cross-validated variance-accounted-for (29.8%) than the stepwise regression model (12.5%). All of these results indicate that RTA is a promising alternative method for demonstrating differential effectiveness of treatments.

Keywords

classification and regression treesmultiple linear regressiontreatment covariate interactiondifferential effectivenessaptitude treatment interaction
Type
Theory and Methods
Information
Psychometrika , Volume 69 , Issue 3 , September 2004 , pp. 355 - 374
Copyright
Copyright © 2004 The Psychometric Society

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Footnotes

Supported by The Netherlands Organization for Scientific Research (NWO), grant 030-56403 to Jacqueline Meulman for the Pioneer project “Subject-Oriented Multivariate Analysis,” and grant 451-02-058 to Elise Dusseldorp for the Veni project “Modeling interaction effects as small trees in regression and classification.” We thank Bram Bakker for making the data of his doctoral dissertation available, and David Hand, Jerome Friedman, Bart Jan van Os, Philip Spinhoven, and the anonymous reviewers for their helpful suggestions. Special thanks are due to Lawrence Hubert.

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