The regression trunk approach to discover treatment covariate interaction

Psychometrika volume 69, pages355–374(2004)Cite this article

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.

This is a preview of subscription content, log in to check access.

References

  1. 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, 831–838.

    PubMed  Google Scholar 

  2. 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, 240–243.

    Article  PubMed  Google Scholar 

  3. 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, 85–89.

    PubMed  Google Scholar 

  4. 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, 951–958.

    PubMed  Google Scholar 

  5. Breiman, L., Friedman, J.H., Olshen, R.A., & Stone, C.J. (1984).Classification and regression trees. Belmont, CA: Wadsworth.

    Google Scholar 

  6. Chaudhuri, P., Lo, W.-D., Loh, W.-Y., & Yang, C.-C. (1995). Generalized regression trees.Statistica Sinica, 5, 641–666.

    Google Scholar 

  7. Ciampi, A. (1991). Generalized regression trees.Computational Statistics and Data Analysis, 12, 57–78.

    Article  Google Scholar 

  8. Clark, L.A., & Pregibon, D. (1993). Tree-based models. In J.M. Chambers & T.J. Hastie (Eds.), Statistical models in S (pp. 377–419). London: Chapman & Hall.

    Google Scholar 

  9. Cohen, J. (1988).Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  10. Cronbach, L.J., & Snow, R.E. (1977).Aptitudes and instructional methods: A handbook for research on interactions. New York: Irvington.

    Google Scholar 

  11. 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, 192–213.

    Article  PubMed  Google Scholar 

  12. Digiusto, E., & Bird, K.D. (1995). Matching smokers to treatment: Self-control versus social support.Journal of Consulting and Clinical Psychology, 63, 290–295.

    Article  PubMed  Google Scholar 

  13. 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, 403–409.

    PubMed  Google Scholar 

  14. Efron, B., & Tibshirani, R.J. (1993).An introduction to the bootstrap. New York: Chapman & Hall.

    Google Scholar 

  15. Gaul, W., & Säuberlich, F. (1999). Classification and positioning of data mining tools. In W. Gaul & H. Locarek-Junge (Eds.),Classification in the information age. Studies in classification, data analysis, and knowledge organization (pp. 145–154). Heidelberg: Springer.

    Google Scholar 

  16. Glidden-Tracey, C.E., & Wagner, L. (1995). Gender salient attribute × treatment interaction effects on ratings of two analogue counselors.Journal of Counseling Psychology, 42, 223–231.

    Article  Google Scholar 

  17. Goska, R.E., & Ackerman, Ph. L. (1996). An aptitude-treatment interaction approach to transfer within training.Journal of Educational Psychology, 88, 249–259.

    Article  Google Scholar 

  18. Hand, D.J. (1997).Construction and assessment of classification rules. Chichester: Wiley.

    Google Scholar 

  19. Harrell, F.E. (2001).Regression modeling strategies: With applications to linear models, logistic regression, and survival analysis. New York: Springer.

    Google Scholar 

  20. Humphreys, L.G., & Fleishman, A. (1974). Pseudo-orthogonal and other analysis of variance designs involving individual-differences variables.Journal of Educational Psychology, 66, 464–472.

    Google Scholar 

  21. Koziol, J.A., & Wu, S.C.H. (1996). Changepoint statistics for assessing a treatment-covariate interaction.Biometrics, 52, 1147–1152.

    PubMed  Google Scholar 

  22. Loh, W.-Y. (2002). Regression trees with unbiased variable selection and interaction detection.Statistica Sinica, 12, 361–386.

    Google Scholar 

  23. Loh, W.-Y., & Shih, Y.-S. (1997). Split selection methods for classification trees,Statistica Sinica, 7, 815–840.

    Google Scholar 

  24. Mallows, C.L. (1973). Some comments onC p.Technometrics, 15, 661–675.

    Google Scholar 

  25. 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, 686–695.

    Article  Google Scholar 

  26. Meulman, J.J., Heiser, W.J., & SPSS (1999).SPSS Categories 10.0. Chicago, IL: SPSS Inc.

    Google Scholar 

  27. Morgan, J.N., & Sonquist, J.A. (1963). Problems in the analysis of survey data, and a proposal.Journal of the American Statistical Association, 58, 415–434.

    Google Scholar 

  28. 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, 267–273.

    Article  PubMed  Google Scholar 

  29. Quinlan, J.R. (1993).C4.5: Programs for machine learning. San Mateo, CA: Morgan Kaufmann.

    Google Scholar 

  30. Rice, J.A. (1995).Mathematical statistics and data analysis (2nd ed.). Belmont, CA: Duxbury Press.

    Google Scholar 

  31. 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, 67–77.

    Google Scholar 

  32. Shomon-Salomon, V., & Hannah, M.T. (1991). Client-treatment interaction in the study of differential change processes.Journal of Consulting and Clinical Psychology, 59, 217–225.

    Google Scholar 

  33. Snow, R.E. (1991). Aptitude-treatment-interaction as a framework for research on individual differences in psychotherapy.Journal of Consulting and Clinical Psychology, 59, 205–216.

    Article  PubMed  Google Scholar 

  34. Stevens, J. (1992).Applied multivariate statistics for the social sciences (2nd ed.). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  35. Thompson, S.C., & Wierson, M. (2000). Enhancing perceived control in psychotherapy. In C.R. Snyder & R.E. Ingram (Eds.),Handbook of psychological change: Psychotherapy processes & practices for the 21st Century (pp. 177–197). New York: Wiley.

    Google Scholar 

  36. Van der Linden, W.J. (1981). Using aptitude measurements for the optimal assignment of subjects to treatments with and without mastery scores.Psychometrika, 46, 257–274.

    Article  Google Scholar 

Download references

Author information

Affiliations

  1. Data Theory Group, Faculty of Social and Behavioral Sciences, Leiden University, P.O. Box 9555, 2300 RB, Leiden, The Netherlands

    Elise Dusseldorp & Jacqueline J. Meulman

Authors
  1. Elise Dusseldorp
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacqueline J. Meulman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elise Dusseldorp.

Additional information

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.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dusseldorp, E., Meulman, J.J. The regression trunk approach to discover treatment covariate interaction. Psychometrika 69, 355–374 (2004). https://doi.org/10.1007/BF02295641

Download citation

Key words

  • classification and regression trees
  • multiple linear regression
  • treatment covariate interaction
  • differential effectiveness
  • aptitude treatment interaction