Prevention Science

, Volume 1, Issue 4, pp 173–181 | Cite as

Equivalence of the Mediation, Confounding and Suppression Effect

  • David P. MacKinnon
  • Jennifer L. Krull
  • Chondra M. Lockwood
Article

Abstract

This paper describes the statistical similarities among mediation, confounding, and suppression. Each is quantified by measuring the change in the relationship between an independent and a dependent variable after adding a third variable to the analysis. Mediation and confounding are identical statistically and can be distinguished only on conceptual grounds. Methods to determine the confidence intervals for confounding and suppression effects are proposed based on methods developed for mediated effects. Although the statistical estimation of effects and standard errors is the same, there are important conceptual differences among the three types of effects.

mediation confounding suppression confidence intervals 

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REFERENCES

  1. Ajzen, I., & Fishbein, M. (1980). Understanding attitudes and predicting social behavior. Englewood Cliffs, NJ: Prentice Hall.Google Scholar
  2. Alwin, D. F., & Hauser, R. M. (1975). The decomposition of effects in path analysis. American Sociological Review, 40, 37–47.Google Scholar
  3. Aroian, L. A. (1944). The probability function of the product of two normally distributed variables. Annals of Mathematical Statistics, 18, 265–271.Google Scholar
  4. Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173–1182.Google Scholar
  5. Bobko, P., & Rieck, A. (1980). Large sample estimators for standard errors of functions of correlation coefficients. Applied Psychological Measurement, 4, 385–398.Google Scholar
  6. Breslow, N. E., & Day, N. E. (1980). Statistical methods in cancer research. Volume I–The Analysis of Case-Control Studies.Lyon: International Agency for Research on Cancer (IARC Scientific Publications No. 32).Google Scholar
  7. Cliff, N., & Earleywine, M. (1994). All predictors are ''mediators'' unless the other predictor is a ''suppressor.'' Unpublished manuscript.Google Scholar
  8. Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  9. Conger, A. J. (1974). A revised definition for suppressor variables: A guide to their identification and interpretation. Educational Psychological Measurement, 34, 35–46.Google Scholar
  10. Davis, M. D. (1985). The logic of causal order. In J. L. Sullivan and R. G. Niemi (Eds.), Sage university paper series on quantitative applications in the social sciences. Beverly Hills, CA: Sage Publications.Google Scholar
  11. Freedman, L. S., Graubard, B. I. & Schatzkin, A. (1992). Statistical validation of intermediate endpoints for chronic diseases. Statistics in Medicine, 11, 167–178.Google Scholar
  12. Goldberg, L., Elliot, D., Clarke, G. N., MacKinnon, D. P., Moe, E., Zoref, L., Green, C., Wolf, S. L., Greffrath, E., Miller, D. J., & Lapin, A. (1996). Effects of a multidimensional anabolic steroid prevention intervention: The adolescents training and learning to avoid steroids (ATLAS) program. Journal of the American Medical Association, 276, 1555–1562.Google Scholar
  13. Goodman, L. A. (1960). On the exact variance of products. Journal of the American Statistical Association, 55, 708–713.Google Scholar
  14. Hamilton, D. (1987). Sometimes R2 > ry12 + ry22. American Statistician, 41, 129–132.Google Scholar
  15. Hansen, W. B. (1992). School-based substance abuse prevention: A review of the state-of-the-art in curriculum, 1980–1990.Health Education Research: Theory and Practice, 7, 403–430.Google Scholar
  16. Harlow, L. L., Mulaik, S. A., & Steiger, J. H. (Eds.). (1997). What if there were no significance tests? Mahwah, NJ: Lawrence Erlbaum.Google Scholar
  17. Holland, P. W. (1988). Causal inference, path analysis, and recursive structural equations models Sociological Methodology, 18, 449–484.Google Scholar
  18. Horst, P. (1941). The role of predictor variables which are independent of the criterion. Social Science Research Council Bulletin, 48, 431–436.Google Scholar
  19. James, L. R., & Brett, J. M. (1984). Mediators, moderators and tests for mediation. Journal of Applied Psychology, 69(2), 307–321.Google Scholar
  20. Judd, C. M., & Kenny, D. A. (1981a). Process Analysis: Estimating mediation in treatment evaluations. Evaluation Review, 5(5), 602–619.Google Scholar
  21. Judd, C. M., & Kenny, D. A. (1981b). Estimating the effects of social interventions. New York: Cambridge University Press.Google Scholar
  22. Kirk, R. E. (1995). Experimental design: Procedures for the behavioral sciences. Pacific Grove, CA: Brooks/Cole Publishing Company.Google Scholar
  23. Krantz, D. H. (1999). The null hypothesis testing controversy in psychology. Journal of the American Statistical Association, 44, 1372–1381.Google Scholar
  24. Last, J. M. (1988).Adictionary of epidemiology. NewYork: Oxford Unversity Press.Google Scholar
  25. Lazarsfeld, P. F. (1955). Interpretation of statistical relations as a research operation. In P. F. Lazardsfeld, & M. Rosenberg (Eds.), The language of social research:Areader in the methodology of social research (pp. 115–125). Glencoe, IL: Free Press.Google Scholar
  26. Lord, F. M., & Novick, R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.Google Scholar
  27. MacCallum, R. C., Wegener, D. T., Uchino, B. N., & Fabrigar, L.R. (1993). The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin, 114, 185–199.Google Scholar
  28. MacKinnon, D. P., & Dwyer, J. H. (1993). Estimating mediated effects in prevention studies. Evaluation Review, 17(2), 144–158.Google Scholar
  29. MacKinnon, D. P., Warsi, G., & Dwyer, J. H. (1995). A simulation study of mediated effect measures. Multivariate Behavioral Research, 30(1), 41–62.Google Scholar
  30. Mayer, L. (1996 Spring). Confounding, mediation, and intermediate outcomes in prevention research. Paper presented at the 1996 Prevention Science and Methodology Meeting, Tempe, AZ.Google Scholar
  31. McFatter, R. M. (1979). The use of structural equation models in interpreting regression equations including suppressor and enhancer variables. Applied Psychological Measurement, 3, 123–135.Google Scholar
  32. McGuigan, K., & Langholtz, B. (1988). A note on testing mediation paths using ordinary least squares regression. Unpublished note.Google Scholar
  33. Meinert, C. L. (1986). Clinical trials: Design, conduct, and analysis.New York: Oxford University Press.Google Scholar
  34. Olkin, I. & Finn, J. D. (1995). Correlations redux. Psychological Bulletin, 118, 155–164.Google Scholar
  35. Robins, J. M. (1989). The control of confounding by intermediate variables. Statistics in Medicine, 8, 679–701.Google Scholar
  36. Robins, J. M. & Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology, 3, 143–155.Google Scholar
  37. Rubin, D. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66, 688–701.Google Scholar
  38. Selvin, S. (1991). Statistical analysis of epidemiologic data. New York: Oxford University Press.Google Scholar
  39. Sharpe, N. R., & Roberts, R. A. (1997). The relationship among sums of squares, correlation coefficients, and suppression. The American Statistician, 51, 46–48.Google Scholar
  40. Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. In S. Leinhardt (Ed.), Sociological methodology, (pp. 290–312). Washington, DC: American Sociological Association.Google Scholar
  41. Sobel, M. E. (1986). Some new results on indirect effects and their standard errors in covariance structure models. In N. Tuma (Ed.), Sociological methodology, (pp. 159–186). Washington, DC: American Sociological Association.Google Scholar
  42. Sobel, M. E. (1990). Effect analysis and causation in linear structural equation models. Psychometrika, 55(3), 495–515.Google Scholar
  43. Spirtes, P., Glymour, C., & Scheines, R. (1993). Causality, prediction and search. Berlin: Springer-Verlag.Google Scholar
  44. Stelzl, I. (1986). Changing a causal hypothesis without changing the fit. Some rules for generating equivalent path models.Multivariate Behavioral Research, 21, 309–331.Google Scholar
  45. Susser, M. (1973). Causal thinking in the health sciences: Concepts and strategies of epidemiology. New York: Oxford University Press.Google Scholar
  46. Tzelgov, J., & Henik, A. (1991). Suppression situations in psychological research: Definitions, implications, and applications.Psychological Bulletin, 109, 524–536.Google Scholar
  47. Velicer, W. F. (1978). Suppressor variables and the semipartial correlation coefficient. Educational and Psychological Measurement, 38, 953–958.Google Scholar
  48. Winer, B. J., Brown, D. R., & Michels, K. M. (1991). Statistical principles in experimental design. New York: McGraw-Hill.Google Scholar

Copyright information

© Society for Prevention Research 2000

Authors and Affiliations

  • David P. MacKinnon
    • 1
  • Jennifer L. Krull
    • 2
  • Chondra M. Lockwood
    • 2
  1. 1.Arizona State UniversityUSA
  2. 2.Arizona State UniversityUSA

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