The regression trunk approach to discover treatment covariate interaction |
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Authors: | Email author" target="_blank">Elise?DusseldorpEmail author Jacqueline?J?Meulman |
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Institution: | (1) Data Theory Group, Faculty of Social and Behavioral Sciences, Leiden University, P.O. Box 9555, 2300 RB Leiden, The Netherlands |
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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.
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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Keywords: | classification and regression trees multiple linear regression treatment covariate interaction differential effectiveness aptitude treatment interaction |
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