Abstract
Third-variable effects, such as mediation and confounding, are core concepts in prevention science, providing the theoretical basis for investigating how risk factors affect behavior and how interventions change behavior. Another third variable, the collider, is not commonly considered but is also important for prevention science. This paper describes the importance of the collider effect as well as the similarities and differences between these three third-variable effects. The single mediator model in which the third variable (T) is a mediator of the independent variable (X) to dependent variable (Y) effect is used to demonstrate how to estimate each third-variable effect. We provide difference in coefficients and product of coefficients estimators of the effects and demonstrate how to calculate these values with real data. Suppression effects are defined for each type of third-variable effect. Future directions and implications of these results are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Change history
12 July 2021
Springer Nature’s version of this paper was updated to reflect the removal of the redundant sentence: "The correct causal model is an exacting qualification,requiring a program of research with precise definition of causal effects, specification of assumptions, and sensitivity analysis for how violatingassumptions affects results.", which was inadvertently added in the last paragraph of Discussion section.
Notes
This paper describes adjustment as including an additional predictor in a regression model. Adjustment comes in other forms and names including conditioning on a variable, controlling for a variable, stratifying by a variable, and selection into a study by a variable (see Elwert & Winship, 2014 and Morgan & Winship, 2015 for more on these topics).
References
Asendorpf, J. B. (2012). Bias due to controlling a collider: A potentially important issue for personality research. European Journal of Personality, 26, 391–392.
Banack, H. R., & Kaufman, J. S. (2014). The obesity paradox: Understanding the effect of obesity on mortality among individuals with cardiovascular disease. Preventive Medicine, 62, 96–102. https://doi.org/10.1016/j.ypmed.2014.02.003
Berkson, J. (1946). Limitations of the application of fourfold table analysis to hospital data. Biometrics Bulletin, 2, 47–53. https://doi.org/10.2307/3002000
Botvin, G. J., Griffin, K. W., Diaz, T., Miller, N., & Ifill-Williams, M. (1999). Smoking initiation and escalation in early adolescent girls: One-year follow-up of a school-based prevention intervention for minority youth. Journal of the American Medical Women’s Association., 54, 139–143.
Breslow, N. E., Day, N. E., & Heseltine, E. (1980). Statistical methods in cancer research (Vol. 1, pp. 248–279). Lyon: International Agency for Research on Cancer.
Bureau of Labor Statistics (2019). National Longitudinal Survey of Youth 1979 cohort, 1979–2014 . Retrieved from https://www.nlsinfo.org/content/cohorts/nlsy79
Clogg, C. C., Petkova, E., & Haritou, A. (1995). Statistical methods for comparing regression coefficients between models. American Journal of Sociology, 100, 1261–1293. https://doi.org/10.1086/230638
Cole, S. R., Platt, R. W., Schisterman, E. F., Chu, H., Westreich, D., Richardson, D., & Poole, C. (2010). Illustrating bias due to conditioning on a collider. International Journal of Epidemiology, 39, 417–420. https://doi.org/10.1093/ije/dyp334
Conger, A. J. (1974). A revised definition for suppressor variables: A guide to their identification and interpretation. Educational and Psychological Measurement, 34, 35–46.
Cresswell, J. W., & Clark, V. L. P. (2017). Designing and conducting mixed methods research. Sage.
Cuijpers, P. (2002). Effective ingredients of school-based drug prevention programs: A systematic review. Addictive Behaviors, 27, 1009–1023. https://doi.org/10.1016/s0306-4603(02)00295-2
Elwert, F., & Winship, C. (2014). Endogenous selection bias: The problem of conditioning on a collider variable. Annual Review of Sociology, 40, 31–53. https://doi.org/10.1146/annurev-soc-071913-043455
Fairchild, A. J., & MacKinnon, D. P. (2009). A general model for testing mediation and moderation effects. Prevention Science, 10, 87–99. https://doi.org/10.1007/s11121-008-0109-6
Glymour, M. M., & Hamad, R. (2018). Causal thinking as a critical tool for eliminating social inequalities in health. American Journal of Public Health, 108, 623. https://doi.org/10.2105/AJPH.2018.304383
Goldberg, L., Elliot, D., Clarke, G. N., MacKinnon, D. P., Moe, E., Zoref, L., & Lapin, A. (1996). Effects of a multidimensional anabolic steroid prevention intervention: The Adolescents Training and Learning to Avoid Steroids (ATLAS) program. JAMA, 276, 1555–1562. https://doi.org/10.1001/jama.1996.03540190027025
Greenland, S., & Morgenstern, H. (2001). Confounding in health research. Annual Review of Public Health, 22, 189–212. https://doi.org/10.1146/annurev.publhealth.22.1.189
Hernán, M. (2018). The C-word: Scientific euphemisms do not improve causal inference from observational data. American Journal of Public Health, 108, 616–619. https://doi.org/10.2105/AJPH.2018.304337
Hernández-Díaz, S., Schisterman, E. F., & Hernán, M. A. (2006). The birth weight “paradox” uncovered? American Journal of Epidemiology, 164, 1115–1120. https://doi.org/10.1093/aje/kwj275
Imai, K., Keele, L., & Tingley, D. (2010). A general approach to causal mediation analysis. Psychological Methods, 15, 309–334. https://doi.org/10.1037/a0020761
James, L. R. (1980). The unmeasured variables problem in path analysis. Journal of Applied Psychology, 65, 415–421. https://doi.org/10.1037/0021-9010.65.4.415
King, G. (2015). Cover endorsement in Morgan, S. L., & Winship, C. (2015). Counterfactuals and Causal Inference. University Press.
MacKinnon, D. P. (2008). Introduction to statistical mediation analysis. Lawrence Erlbaum.
MacKinnon, D. P., & Dwyer, J. H. (1993). Estimating mediated effects in prevention studies. Evaluation Review, 17, 144–158. https://doi.org/10.1177/0193841X9301700202
MacKinnon, D. P., Johnson, C. A., Pentz, M. A., Dwyer, J. H., Hansen, W. B., Flay, B. R., & Wang, E.Y.I. (1991). Mediating mechanisms in a school-based drug prevention program: First-year effects of the Midwestern Prevention Project. Health Psychology, 10, 164–172.
MacKinnon, D. P., Krull, J. L., & Lockwood, C. M. (2000). Equivalence of the mediation, confounding, and suppression effect. Prevention Science, 1, 173–181. https://doi.org/10.1023/A:1026595011371
MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7, 83–104. https://doi.org/10.1037/1082-989X.7.1.83
MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39, 99–128. https://doi.org/10.1207/s15327906mbr3901_4
MacKinnon, D. P., Valente, M. J., & Gonzalez, O. J. (2020). The correspondence between causal and traditional mediation analysis: The link is the mediator by treatment interaction. Prevention Science, 21, 147–157. https://doi.org/10.1007/s11121-019-01076-4
MacKinnon, D. P., Valente, M. J., & Wurpts, I. C. (2018). Benchmark validation of statistical mediation analysis: Application to imagery and memory theory. Psychological Methods, 23, 654–671. https://doi.org/10.1037/met0000174
MacKinnon, D. P., Warsi, G., & Dwyer, J. H. (1995). A simulation study of mediated effect measures. Multivariate Behavioral Research, 30, 41–62. https://doi.org/10.1207/s15327906mbr3001_3
Miočević, M., O’Rourke, H. P., MacKinnon, D. P., & Brown, H. C. (2018). Statistical properties of four effect size measures for mediation models. Behavior Research Methods, 50, 285–301. https://doi.org/10.3758/s13428-017-0870-1
Moldonado, G., & Greenland, S. (1993) Simulation study of confounder-selection strategies. American Journal of Epidemiology, 138, 923–936. https://doi.org/10.1093/oxfordjournals.aje.a116813
Morgan, S. L., & Winship, C. (2015). Counterfactuals and causal inference (2nd Edition). New York: NY: Cambridge, MA.
Muniz, F. B., & MacKinnon, D. P. (2021). Four tests for statistical suppression. Manuscript submitted for publication.
Murray, A. L., Johnson, W., McGue, M., & Iacono, W. G. (2014). How are conscientiousness and cognitive ability related to one another? A re-examination of the intelligence compensation hypothesis. Personality and Individual Differences, 70, 17–22. https://doi.org/10.1016/j.paid.2014.06.014
Musci, R. J., & Stuart, E. (2020). Ensuring causal, not casual inference. Prevention Science, 3, 452–456.
Pearl, J. (2009). Causal inference in statistics: An overview. Statistics Surveys, 3, 96–146. https://doi.org/10.1214/09-SS057
Richardson, T. G., Davey Smith, G., & Munafo, M. R. (2019). Conditioning on a collider may induce spurious associations: Do the results of Gale et al., (2017) support a health-protective effect of neuroticism in population subgroups? Psychological Science, 1–4. https://doi.org/10.1177/0956797618774532
Selvin, S. (2004). Statistical analysis of epidemiological data. Oxford.
Stelzl, I. (1986). Changing a causal hypothesis without changing the fit. Some rules for generating equivalent path models. Multivariate Behavioral Research, 21, 309–331. https://doi.org/10.1207/s15327906mbr2103_3
Stuart, E. A., Bradshaw, C. P., & Leaf, P. J. (2015). Assessing the generalizability of randomized trial results to target populations. Prevention Science, 16, 475–485. https://doi.org/10.1007/s11121-014-0513-z
Valeri, L., & VanderWeele, T. J. (2013). Mediation analysis allowing for exposure–mediator interactions and causal interpretation: Theoretical assumptions and implementation with SAS and SPSS macros. Psychological Methods, 18, 137–150. https://doi.org/10.1037/a0031034
VanderWeele, T. (2015). Explanation in causal inference: Methods for mediation and interaction. Oxford University Press.
Whitcomb, B. W., Schisterman, E. F., Perkins, N. J., & Platt, R. W. (2009). Quantification of collider-stratification bias and the birthweight paradox. Pediatric and Perinatal Epidemiology, 23, 394–402. https://doi.org/10.1111/j.1365-3016.2009.01053.x.
Acknowledgements
We thank Adam Cohen, Matthew Fritz, Linda Luecken, June Tangney, Jenn Tein, Matthew Valente, members of the Research in Prevention Laboratory, and reviewers for helpful comments.
Funding
A grant from the National Institute on Drug Abuse (R37DA09757) supported this research in part. Some of this research was presented at the 2019 conference of the American Psychological Association.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethics Approval
All analyses in the article were secondary data analyses. All procedures, including the informed consent process, were conducted in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2000 and the Arizona State University Human Subjects Internal Review Board.
Informed Consent
Data were collected via Informed Consent in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2000.
Conflict of Interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
MacKinnon, D.P., Lamp, S.J. A Unification of Mediator, Confounder, and Collider Effects. Prev Sci 22, 1185–1193 (2021). https://doi.org/10.1007/s11121-021-01268-x
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11121-021-01268-x