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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: [email protected])
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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.

References

Bakker, A., van Dyck, R., Spinhoven, P., & van Balkom, A.J.L.M. (1999). Paroxetine, clomipramine and cognitive therapy in the treatment of panic disorder. Journal of Clinical Psychiatry, 60, 831–838CrossRefGoogle ScholarPubMed
Bakker, A., Spinhoven, P., van Balkom, A.J.L.M., Vleugel, L., & van Dyck, R. (2000). Cognitive therapy by allocation versus cognitive therapy by preference in the treatment of panic disorder. Psychotherapy and Psychosomatics, 69, 240–243CrossRefGoogle ScholarPubMed
Bakker, A., Spinhoven, P., van der Does, A.J.W., van Balkom, A.J.L.M., & van Dyck, R. (2002). Locus of control orientation in panic disorder and the differential effects of treatment. Psychotherapy and Psychosomatics, 71, 85–89CrossRefGoogle ScholarPubMed
Barber, J.P., & Muenz, L.R. (1996). The role of avoidance and obsessiveness in matching patients to cognitive and interpersonal psychotherapy: Empirical findings from the treatmetn for depression collaborative research program. Journal of Consulting and Clinical Psychology, 64, 951–958CrossRefGoogle Scholar
Breiman, L., Friedman, J.H., Olshen, R.A., & Stone, C.J. (1984). Classification and regression trees. Belmont, CA: WadsworthGoogle Scholar
Chaudhuri, P., Lo, W.-D., Loh, W.-Y., & Yang, C.-C. (1995). Generalized regression trees. Statistica Sinica, 5, 641–666Google Scholar
Ciampi, A. (1991). Generalized regression trees. Computational Statistics and Data Analysis, 12, 57–78CrossRefGoogle Scholar
Clark, L.A., & Pregibon, D. (1993). Tree-based models. In Chambers, J.M., Hastie, T.J. (Eds.), Statistical models in S (pp. 377–419). London: Chapman & HallGoogle Scholar
Cohen, J. (1988). Statistical power analysis for the behavioral sciences 2nd ed., Hillsdale, NJ: Lawrence ErlbaumGoogle Scholar
Cronbach, L.J., & Snow, R.E. (1977). Aptitudes and instructional methods: A handbook for research on interactions. New York: IrvingtonGoogle Scholar
Dance, K.A., & Neufield, R.W.J. (1988). Aptitude-treatment interaction in the clinical setting: A review of attempts to dispel the “patient uniformity” myth. Psychological Bulletin, 104, 192–213CrossRefGoogle ScholarPubMed
Digiusto, E., & Bird, K.D. (1995). Matching smokers to treatment: Self-control versus social support. Journal of Consulting and Clinical Psychology, 63, 290–295CrossRefGoogle ScholarPubMed
Dusseldorp, E., & Meulman, J.J. (2001). Prediction in medicine by integrating regression trees into regression analysis with optimal scaling. Methods of Information in Medicine, 40, 403–409Google Scholar
Efron, B., & Tibshirani, R.J. (1993). An introduction to the bootstrap. New York: Chapman & HallCrossRefGoogle Scholar
Gaul, W., & Säuberlich, F. (1999). Classification and positioning of data mining tools. In Gaul, W. & Locarek-Junge, H. (Eds.), Classification in the information age. Studies in classification, data analysis, and knowledge organization (pp. 145–154). Heidelberg: SpringerGoogle Scholar
Glidden-Tracey, C.E., & Wagner, L. (1995). Gender salient attribute × treatment interaction effects on ratings of two analogue counselors. Journal of Counseling Psychology, 42, 223–231CrossRefGoogle Scholar
Goska, R.E., & Ackerman, Ph. L. (1996). An aptitude-treatment interaction approach to transfer within training. Journal of Educational Psychology, 88, 249–259CrossRefGoogle Scholar
Hand, D.J. (1997). Construction and assessment of classification rules. Chichester: WileyGoogle Scholar
Harrell, F.E. (2001). Regression modeling strategies: With applications to linear models, logistic regression, and survival analysis. New York: SpringerCrossRefGoogle Scholar
Humphreys, L.G., & Fleishman, A. (1974). Pseudo-orthogonal and other analysis of variance designs involving individual-differences variables. Journal of Educational Psychology, 66, 464–472CrossRefGoogle Scholar
Koziol, J.A., & Wu, S.C.H. (1996). Changepoint statistics for assessing a treatment-covariate interaction. Biometrics, 52, 1147–1152CrossRefGoogle ScholarPubMed
Loh, W.-Y. (2002). Regression trees with unbiased variable selection and interaction detection. Statistica Sinica, 12, 361–386Google Scholar
Loh, W.-Y., & Shih, Y.-S. (1997). Split selection methods for classification trees. Statistica Sinica, 7, 815–840Google Scholar
Mallows, C.L. (1973). Some comments onC p. Technometrics, 15, 661–675Google Scholar
McInerney, V., McInerney, D.M., & Marsh, H.W. (1997). Effects of metacognitive strategy training within a cooperative group learning context on computer achievement and anxiety: An aptitude-treatment study. Journal of Educational Psychology, 89, 686–695CrossRefGoogle Scholar
Meulman, J.J., Heiser, W.J., & SPSS, (1999). SPSS Categories 10.0. Chicago, IL: SPSS Inc.Google Scholar
Morgan, J.N., & Sonquist, J.A. (1963). Problems in the analysis of survey data, and a proposal. Journal of the American Statistical Association, 58, 415–434CrossRefGoogle Scholar
Piper, W.E., McCallum, M., Joyce, A.S., Azim, H.F., & Ogrodniczuk, J.S. (1999). Follow-up findings for interpretive and supportive forms of psychotherapy and patient personality variables. Journal of Consulting and Clinical Psychology, 67, 267–273CrossRefGoogle ScholarPubMed
Quinlan, J.R. (1993). C4.5: Programs for machine learning. San Mateo, CA: Morgan KaufmannGoogle Scholar
Rice, J.A. (1995). Mathematical statistics and data analysis 2nd ed., Belmont, CA: Duxbury PressGoogle Scholar
Rueter, M.A., Conger, R.D., & Ramisetty-Mikler, S. (1999). Assessing the benefits of a parenting skills training program: A theoretical approach to predicting direct and moderating effects. Family Relations, 48, 67–77CrossRefGoogle Scholar
Shomon-Salomon, V., & Hannah, M.T. (1991). Client-treatment interaction in the study of differential change processes. Journal of Consulting and Clinical Psychology, 59, 217–225CrossRefGoogle Scholar
Snow, R.E. (1991). Aptitude-treatment-interaction as a framework for research on individual differences in psychotherapy. Journal of Consulting and Clinical Psychology, 59, 205–216CrossRefGoogle ScholarPubMed
Stevens, J. (1992). Applied multivariate statistics for the social sciences 2nd ed., Hillsdale, NJ: ErlbaumGoogle Scholar
Thompson, S.C., & Wierson, M. (2000). Enhancing perceived control in psychotherapy. In Snyder, C.R. & Ingram, R.E. (Eds.), Handbook of psychological change: Psychotherapy processes & practices for the 21st Century (pp. 177–197). New York: WileyGoogle Scholar
Van der Linden, W.J. (1981). Using aptitude measurements for the optimal assignment of subjects to treatments with and without mastery scores. Psychometrika, 46, 257–274CrossRefGoogle Scholar