• What is mediation?
• How are mediated effects calculated?
• Different tests of mediation
• Statistical power and mediation
• Frequency distributions
• Relevant projects and papers
• Downloadable papers
• Mediation Conference - March 1998
• Questions and answers about mediation
• Other papers about mediation

The mediational hypothesis reflects causal hypotheses about variables. In this approach, the relationship between an independent variable and a dependent variable is decomposed into direct and indirect (mediated) effects as shown below:

Mediation implies a causal hypothesis whereby an independent variable causes a mediator which causes a dependent variable (Holland, 1988; Sobel, 1990). 

The general model is described in terms of mediated effects. We assume multivariate normal distributions and normally distributed error terms throughout. The effect of adding a third variable can be calculated in two ways (MacKinnon, Warsi, & Dwyer, 1995) based on either the difference between two regression parameters (t - t') or the multiplication of two regression parameters (ab). The equivalence of the two methods was shown in MacKinnon et al. (1995). In the first method, the following two regression equations are estimated.  Model 1: Y = b₀₁ + t X + e₁  Model 2: Y = b₀₂ + t' X + bM + e₂ Y is the outcome variable, X is the program or independent variable, M is the mediator, t codes the relationship between the program to the outcome in the first equation, t' is the coefficient relating the program to the outcome adjusted for the effects of the mediator, e₁ and e₂ code unexplained variability, and the intercepts are b₀₁ and b₀₂. 

In the first regression, the outcome variable is regressed on the independent variable. In the second regression, the outcome is regressed on the independent variable and the mediator. The value of the mediated or indirect effect equals the difference in the program coefficients (t-t') in the two regression models (Judd & Kenny, l981). If the treatment coefficient (t') is zero when the mediator is included in the model, then the program effect is entirely mediated by the mediating variable. 

A second method also involves estimation of two regression equations. First, the coefficient in the model relating the mediator to the outcome is estimated (b) in Model 2 above. Second, the coefficient relating the program to the mediating variable is computed (a).  Model 3: M = b₀₃ + a X + e₃ Where M is the mediator outcome variable, b₀₃ is the intercept, X is the program variable and e₃ is the error term. The product of these two parameters (ab) is the mediated or indirect effect which is equivalent to (t - t'). The coefficient relating the treatment variable to the outcome adjusted for the mediator (t') is the nonmediated or direct effect. The rationale behind this method is that mediation depends on the extent to which the program changes the mediator (a) and the extent to which the mediator affects the outcome variable (b). 

Causal Steps 

These methods indicate a series of requirements which must be true for the mediation model to hold. As outlined by Baron and Kenny (1986) and Judd and Kenny (1981), the steps require that: (1) The total effect of the independent variable on the dependent variable must be significant (t in Model 1 above).(2) The path from the independent variable to the mediator must be significant (a in Model 3 above). (3) The path from the mediator to the dependent variable must be significant (b in Model 2 above). (4) The fourth step is required only for complete mediation. If the independent variable no longer has any effect on the dependent variable when the mediator has been controlled, the complete mediation has occurred (nonsignificant t'). 

A less stringent variation of the causal step method is to require simply that a and b both be significant.

Difference in Coefficient Methods 

Freedman (1992) and McGuigan and Langholtz (1988) each developed standard errors for the test of t-t'. Olkin and Finn (1995) developed a standard error for the difference between a correlation and the same correlation partialled for a third variable.

Product of Coefficient Methods 

Several standard errors have been developed to test the product ab.

From the following paper we have included these two PDF files (requires Adobe Acrobat to open) from footnote 1: Predicted and observed power, and footnote 2: Empirical M critical values.

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(1), 99-128.

Lockwood, C., & MacKinnon, D. P. (1998). Bootstrapping the standard error of the mediated effect. Presented at the 23^rd Annual Meeting of SAS Users Group International. 

MacKinnon, D. P. (1992). Statistical simulations in CALIS. Proceedings of the 17^th Annual SAS Users Group International Conference 1992, (pp.1199-1203).  Cary, NC: SAS Institute, Inc. 

Wang, E., Gong, A., & MacKinnon, D. P. (1991). A program to compute odds ratios and confidence intervals from LOGIST output. In Sugi 16. Proceedings of the 16^th Annual SAS Users Group International Conference 1991, 1228-1231. Reprinted in total in SAS Macro Facility Tips and Techniques, Version 6, First edition. 

MacKinnon, D. P., & Wang, E. (1989). INDIRECT: A program to calculate indirect effects and their standard errors. 

MacKinnon, D. P., & Wang, E. (1989). A SAS/IML matrix program to estimate indirect effects and their standard errors. SUGI 14: Proceedings of the Statistical Analysis System Conference (pp. 1151-1156). Cary, NC: SAS Institute, Inc. 

MANUSCRIPTS IN PREPARATION 

Merrill, R., MacKinnon, D. P., & Mayer, L. (2005). Estimating mediated moderator effects in treatment studies . Manuscript in preparation.

MacKinnon, D. P., & Tein, J. -Y. (2005). Standard error of the three-path mediated effect . Manuscript in preparation .

Morgan-Lopez, A. A., MacKinnon, D. P., & Tein, J.-Y (2005). Balancing computational ease, statistical power and type I error rates in mediated baseline by treatment interaction models. Manuscript in preparation.

MacKinnon, D. P., Fairchild, A. J., Fritz, M. S. (2006). Mediation analysis. Manuscript in preparation.

Fairchild, A. J., MacKinnon, D. P., & Taborga, M. P. (2006). R 2 effect-size measures for the mediated effect. Manuscript in preparation.

Fritz, M. S., & MacKinnon, D. P. (2006). Plotting the mediated effect: A graphical method of examining mediation. Manuscript in preparation.

MANUSCRIPTS SUBMITTED 

MacKinnon, D. P., Lockwood, C. M., Brown, C.H., & Hoffman, J. M. (2007). The intermediate endpoint effect in logistic and probit regression . Submitted to Clinical Trials.

MacKinnon, D.P., Yoon, M., Lockwood, C.M., & Taylor, A. (2005). A comparison of methods to test mediation and other intervening variable effects in logistic regression. Submitted to Psychological Methods.

MacKinnon, D.P., Yoon, M., Ryu, E., & Fairchild, A. (2005). Evaluation of the proportion mediated measure of mediation . Submitted to the British Journal of Mathematical and Statistical Psychology.

Fairchild, A. J., & MacKinnon, D. P. (2005) Tests of significance for a person-centered approach to mediation. Submitted to Multivariate Behavioral Research.

Taylor, A. B., & MacKinnnon, D. P. (2005). Permutation tests for mediation Submitted to Multivariate Behavioral Research.

Tofighi, D., MacKinnon, D. P., & Yoon, M. (2006). Covariance among regression coefficients in a single mediator model. Submitted to the British Journal of Mathematical and Statistical Psychology.

PUBLICATIONS 

MacKinnon, D. P., Fritz, M. S., Williams, J. & Lockwood, C. M. (in press). Distribution of the product confidence limits for the indirect effect: Program PRODCLIN. Behavior Research Methods.

Fritz, M. S., & MacKinnon, D. P. (in press). A graphical representation of the mediated effect. Behavior Research Methods.

Taylor, A. B., MacKinnon, D. P., & Tein, J.-Y. (in press). Tests of the three-path mediated effect. Organizational Research Methods.

Williams, J., & MacKinnon, D. P. (in press). Resampling and distribution of the product methods for testing indirect effects in complex models. Structural Equation Modeling.

MacKinnon, D. P. (in press). Mediating variable. In D. Matsumoto (Ed.) The Cambridge Dictionary of Psychology. Cambridge University Press.

MacKinnon, D.P. (in press) Introduction to statistical mediation analysis. Mahwah, NJ: Erlbaum.

MacKinnon, D. P., Fairchild, A. J., Fritz, M. S. (2007). Mediation analysis. Annual Review of Psychology, 58, 593 -614.

Fritz, M. S., & MacKinnon, D. P. (2007). Required sample size to detect the mediated effect. Psychological Science, 18(3), 233-239.

Morgan-Lopez, A. A., & MacKinnon, D. P. (2006). Demonstration and evaluation of a method to assess mediated moderation. Behavior Research Methods, 38 (1), 77-87 .

Tein, J.-Y., Sandler, I. N., MacKinnon, D. P., & Wolchik, S. A. (2004).  How did it work? Who did it work for? Mediation in the context of a moderated prevention effect for children of divorce. Journal of Consulting and Clinical Psychology, 72(4), 617-624.

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(1), 99-128.

Cheong, J., MacKinnon, D. P., & Khoo, S.-T. (2003). Investigation of mediational processes using parallel process latent growth curve modeling. Structural Equation Modeling, 10(2), 238-262.

MacKinnon, D. P., & Dwyer, J. H. (2003). Major data analysis issues in drug abuse prevention research. In Z. Sloboda & W. J. Bukoski (Eds.), Handbook for drug abuse prevention: theory, science, and practice (pp. 541-556). Kluwer Academic/ Plenum Publishing: New York.

MacKinnon, D. P., & Lockwood, C. M. (2003). Advances in statistical methods for substance abuse prevention research. Prevention Science, 4(3), 155-171.

Morgan-Lopez, A. A., Castro, F. G., Chassin, L., & MacKinnon, D. P. (2003). A mediated moderation model of cigarette use among Mexican-American youth. Addictive Behaviors, 28 (3), 583-589.

Tein, J.-Y., & MacKinnon, D. P. (2003). Estimating mediated effects with survival data. H. Yanai, A. O. Rikkyo, K. Shigemasu, Y. Kano, J. J. Meulman (Eds.) New Developments on Psychometrics (pp. 405-412). Tokyo, Japan: Springer-Verlag Tokyo Inc.

MacKinnon, D. P., Taborga, M. P., & Morgan-Lopez, A. A. (2002). Mediation designs for tobacco prevention research. Drug and Alcohol Dependence, 68, S69-S83.

MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test the significance of the mediated effect. Psychological Methods, 7(1), 83-104.

MacKinnon, D. P. (2002). Mediating variable. In N. J. Smelser & P. B. Baltes (Eds.), International encyclopedia of the social and behavioral sciences (pp. 9503-9507). New York: Elsevier.

Cheong, J., MacKinnon, D. P., & Khoo, S. T. (2001). A latent growth modeling approach to mediation analysis. In L. M. Collins & A. Sayer (Eds.), New methods for the analysis of change (pp. 390-392). Washington, DC: American Psychological Association. 

MacKinnon, D. P. (2001). Commentary on Donaldson, Mediator and moderator analysis in program development. In S. Sussman (Ed.), Handbook of program development for health behavior research and practice (pp. 497-500). Thousand Oaks, CA: Sage. 

Krull, J. L., & MacKinnon, D. P. (2001). Multilevel modeling of individual and group level mediated effects. Multivariate Behavioral Research, 36, 249-277. 

MacKinnon, D. P. (2000). Contrasts in multiple mediator models. In J. Rose, L. Chassin, C. C. Presson, & S. J. Sherman (Eds.), Multivariate applications in substance use research: New methods for new questions (pp. 141-160). Mahwah, NJ:  Erlbaum.   

MacKinnon, D. P., Goldberg, L., Clarke, G. N., Elliot, D. L., Cheong, J., Lapin, A., Moe, E. L., & Krull, J. L. (2001). Mediating mechanisms in a program to reduce intentions to use anabolic steroids and improve exercise self-efficacy and dietary behavior. Prevention Science, 2, 15-28. 

MacKinnon, D. P., Krull, J. L., & Lockwood, C. M. (2000). Equivalence of the mediation, confounding, and suppression effect. Prevention Science, 1, 173-181. 

Sandler, I. N., Kim-Bae, L. S., & MacKinnon, D. P. (2000). Coping and negative appraisal as mediators between control beliefs and psychological symptoms in children of divorce. Journal of Clinical Child Psychology, 29, 336-347. 

Krull, J. L. & MacKinnon, D. P. (1999) Multilevel mediation modeling in group-based intervention studies.Evaluation Review, 23, 418-444. 

Lockwood, C., & MacKinnon, D. P. (1998). Bootstrapping the standard error of the mediated effect. Proceedings of the 23^rd Annual Meeting of SAS Users Group International. (pp. 997-1002). Cary, NC: SAS Institute, Inc. 

Finch, J., West, S., & MacKinnon, D. P. (1997) Effects on non-normality on mediated effect estimates. Structural Equation Modeling, 4, 87-107. 

Sandler, I. N., Wolchik, S.A., MacKinnon, D.P., Ayers, T.S., & Roosa, M.W. (1997). Developing linkages between theory and intervention in stress and coping processes in Handbook of children's coping: Linking theory and intervention. Plenum Press: New York. 

West, S., & Aiken, L. (1996). Toward understanding individual effects in multiple component prevention programs: Design and analysis strategies. In K. Bryant, M. Windle, & S. G. West (Eds.), New methodological approaches to prevention research (pp. 167-209). Washington, DC: American Psychological Association. 

MacKinnon, D. P., Warsi, G., & Dwyer, J. H. (1995). A simulation study of mediated effect measures. Multivariate Behavioral Research, 30, 41-62. 

MacKinnon, D. P. (1994). Analysis of mediating variables in prevention intervention studies. In A. Cazares and L. A. Beatty (Eds.), Scientific methods for prevention intervention research (pp.127-153). Washington, DC: NIDA Research Monograph 139, DHHS Pub. 94-3631. 

MacKinnon, D. P., & Dwyer, J. H. (1993). Estimating mediated effects in prevention studies. Evaluation Review, 17, 144-158. 

MacKinnon, D. P., Johnson, C. A., Pentz, M. A., Dwyer, J. H., Hansen, W. B., Flay, B. R., & Wang, E. (1991). Mediating mechanisms in a school-based drug prevention program: One year effects of the Midwestern Prevention Project. Health Psychology, 10, 164-172. 

MacKinnon, D. P., Weber, M. D., & Pentz, M. A. (1989). How do school-based drug prevention programs work and for whom? Drugs and Society, 3, 125-143.

MEDIATION CONFERENCE 

Mediation Conference was held Monday, March 23 and Tuesday, March 24, 1998 at Arizona State University. To learn more about this conference, see the Mediation Conference page. 

PRESENTATIONS 

Fairchild, A. J., MacKinnon, D. P. (2007, May). Joint analysis of moderation and mediation effects in single sample designs. Paper submitted to the 15th annual meeting of the Society for Prevention Research, Washington, DC.

Fairchild, A. J., MacKinnon, D. P. (2007, May). Causal inference in mediation models. Paper submitted to the 15th annual meeting of the Society for Prevention Research, Washington, DC.

MacKinnon, D. P. (2007, May). Dual process models. Paper submitted to the 15th annual meeting of the Society for Prevention Research, Washington, DC.

Wang, W. & MacKinnon, D. P. (2007, May). Moderation and mediation with a binary dependent variable. Paper submitted to the 15th annual meeting of the Society for Prevention Research, Washington, DC.

Taylor, A. B., MacKinnon, D. P., Fritz, M. S. (2007, May). Joint analysis of moderation and mediation effects in single sample designs. Poster submitted to the 15th annual meeting of the Society for Prevention Research, Washington, DC.

MacKinnon, D. P. (2007, March). Moderators and mediators. Invited presentation at National Cancer Institute, Washington, DC.

MacKinnon, D. P. (2007, March). Methods to assess how interventions change behavior. Invited presentation at Health Maintenance Consortium, Washington, DC.

MacKinnon, D. P. (2006, November). Mediation for physical activity interventions. Invited presentation at the National Institutes for Health Grantee Meeting for Mechanisms of Physical Activity, Denver, CO.

MacKinnon, D. P. (2006, November). Mediation. Invited presentation at the University of Southern California, Los Angeles.

MacKinnon, D. P. (2006, November). Designs for investigating mediation variables. Invited presentation at Stanford University, Palo Alto, CA.

Fritz, M. S., & MacKinnon, D. P. (2006, May). Plots of the XM interaction in models of the mediated effect. Poster presented to the 14th annual meeting of the Society for Prevention Research, San Antonio, TX.

Feaster, D. J., McCabe, B., & MacKinnon, D. P. (2006, May). Using repeated observations to estimate person-specific models of mediation. Paper presented to the 14th annual meeting of the Society for Prevention Research, San Antonio, TX.

Taylor, A. B., & MacKinnon, D. P. (2006, May). A permutation test for mediation. Poster presented to the 14th annual meeting of the Society for Prevention Research, San Antonio, TX.

MacKinnon, D.P. (2006, April). New methods for mediation analysis . Invited presentation at the 86th annual Convention of the Western Psychological Association.

MacKinnon, D.P. (2005, October). Issues in mediation modeling in prevention effectiveness trials. Workshop presentation to the New Directions for Mental Health and Drug Abuse Effectiveness and Dissemination Trial Research and Methodology. Baltimore, MD.

Fairchild, A. J., & MacKinnon, D. P. (2005, August). Developing significance tests for a person-centered approach to mediation. Poster presented at the 113 th annual convention of the American Psychological Association, Washington, D.C.

Cheong, J., MacKinnon, D., Williams, J., & Fritz, M. (2005, May). Evaluation of longitudinal mediating mechanisms of a drug prevention program for adolescent athletes. A paper to be presented at the annual convention of the Society for Prevention Research. [Submitted for consideration of presentation] Washington, DC.

Fritz, M.S., & MacKinnon, D.P. (2005, May). Sample size and statistical power in tests of mediation. A paper presented at the annual meeting of the Society for Prevention Research, Washington, D.C.

Lockwood, C. M., MacKinnon, D. P., Brown, C. H., & Hoffman, J. M. (2005, May). Mediation analysis with binary outcomes. A paper presented at the 13 th annual meeting of the Society for Prevention Research, Washington, D.C.

MacKinnon, D. P. (2005, May). Statistical mediation analysis . Invited Presentation Center for Disease Control AIDS/HIV Prevention Quantitative group.

Tein, J.-Y., MacKinnon, D. P., & Kwok, O.-M. (2005, May). Method of probing simple mediation effects for models with combined mediated and moderated effects. A paper presented at the 13 th annual meeting of the Society for Prevention Research, Washington, D.C.

MacKinnon, D. P. (2005, April). Mediation and moderation in alcohol and tobacco research . Workshop presentation for the Second East-West Conference on Tobacco and Alcohol Use m eeting at the, Pasadena, CA.

MacKinnon, D. P. (2005, March). Mediation models for longitudinal data. Invited presentation at the Psychology Department, University of Arizona, Tucson, AZ.

MacKinnon, D. P. (2005, March). Mediation analysis in drug prevention studies. Invited presentation at the Family Studies Department, University of Arizona, Tucson, AZ.

MacKinnon, D. P. (2005, February). Longitudinal mediation models. Invited presentation at Vanderbilt University, Nashville, TN.

MacKinnon, D.P. (2004, November) Mediation models for longitudinal data. Presentation given at the Arizona State University Prevention in Research Center Postdoc seminar, Tempe, AZ.

MacKinnon, D.P., Yoon, M., & Ryu, E. (2004, July). Evaluation of the proportion mediated effect size measure. Abstract presented at the 112 th annual convention of the American Psychological Association, Honolulu, HI.

MacKinnon, D.P., Williams, J., Lockwood, C., & Fritz, M. (2004, July). Empirical power of 20 mediation tests. Abstract presented at the 112 th annual convention of the American Psychological Association, Honolulu, HI.

MacKinnon, D.P. (2004, June ). Introduction to statistical mediation analysis . Presentation given at the Research Foundation of SUNY, Buffalo,NY.

MacKinnon, D.P., Jo, B., Brown, C. H., Kellam, S. G., & Sobel, M. (2004, May). Mediation and moderation in prevention research. Abstract presented at the 12 th annual meeting of the Society for Prevention Research, Québec City, Québec.

MacKinnon, D.P., Williams, J., & Yoon, M. (2004, May). Evaluation of mediation tests from surrogate endpoints research. Abstract presented at the 12 th annual meeting of the Society for Prevention Research, Québec City, Québec.

Weaver, S., Cheong, J., & MacKinnon, D. P. (2004, May). Ethnic differences in alcohol use and peer norms: Investigation of a mediation model. Abstract presented at the 12 th annual meeting of the Society for Prevention Research, Québec City, Québec.

MacKinnon, D. P. (2004, May). New designs and methods for trials research. Poster chair session at the 12 th annual meeting of the Society for Prevention Research, Québec City, Québec.

MacKinnon, D.P. (2004, April). Statistical mediation analysis . Workshop presentation at the 84th annual convention of the Western Psychological Association, Phoenix, AZ.

MacKinnon, D.P., & Alwin, D. (2004, March). Led a breakout discussion section at the Merrill Advanced Studies Center conference on Modeling Developmental Processes in Ecological Context, Tempe, AZ.

MacKinnon, D.P. (2004, March). Methodology for MH/drug prevention & early intervention mediation analysis. Presentation to the University of South Florida Prevention Science & Methodology Group. Tampa, FL.

MacKinnon, D. P. (2004, February). National Institute on Drug Abuse Meeting on the Mechanisms of Action of Behavioral Treatments, Washington, DC.

MacKinnon, D.P. (2003, December). Mediators, moderators, & more. University of Southern Florida, Tampa, FL.

MacKinnon, D.P. (2003, November). Finding structural needles in statistical haystacks: Methods for identifying mediators and moderators. Mediators & Moderators Workshop, Western Psychiatric Institute & Clinic at the University of Pittsburgh School of Medicine, Pittsburgh, PA.

MacKinnon, D.P. (2003, November). Moderators and mediators of treatments in randomized controlled trials. Association for Advancement of Behavior Therapy, Boston, MA.

MacKinnon, D.P. (2003, July). Mediation analysis in social psychology , workshop on mediation. Society of Personality and Social Psychology Summer Institute in Social Psychology, Boulder, CO.

MacKinnon, D.P., Yoon, M., Lockwood, C. (June 2003). Comparison of methods to assess mediation in logistic regression. Abstract submitted for presentation at the 11th annual Society for Prevention Research, Washington, D.C.

MacKinnon, D.P. (2003, March). Comparison of single sample and resampling tests for mediation. Society for Prevention Research, Washington, DC.

Morgan-Lopez, A. A. (2002). Bias-corrected bootstrap estimation of mediated baseline by treatment interaction effects in intervention trials. Invited colloquium presented at Quantitative Methodology in Prevention Seminar Series, The Methodology Center, The Pennsylvania State University, University Park, PA, November 8, 2002.

Morgan-Lopez, A. A., MacKinnon, D. P., Goldberg, L., & Moe, E. L. (2002, May-June). The influence of participation in athletics on adolescent intoxication and DUI: A multi-level, multiple-mediator model of sport-specific risk and protection. Abstract submitted for presentation at the Society for Prevention Research annual meeting, Seattle, WA.

Cheong, J., MacKinnon, D. P., & Pentz, M. A. (2002: June). Evaluation of the mediating mechanisms of a drug prevention program to reduce adolescent DUI. Poster presented at the annual meeting of the Research Society on Alcoholism, San Francisco, CA.

Cheong, J., & MacKinnon, D. P. (2002, May-June). A simulation study on latent growth model to test mediation. Paper presented at the 10^th annual meeting of the Society for Prevention Research, Seattle, WA.

Williams, J., MacKinnon, D. P., & Cheong, J. (2002, May). The effect of missing data techniques on mediated program estimates. Poster presented at the 10^th annual meeting of the Society for Prevention Research, Seattle, WA.

MacKinnon, D. P., Lockwood, C. M., Williams, J., & Anderson, G. (2002, May). A comparison of single sample and resampling tests for the mediated effect. Paper presented at the 10^th annual meeting of the Society for Prevention Research, Seattle, WA.

MacKinnon, D. P., Cheong, J., Goldberg, L., Williams, J., & Moe, E. (2002, May). Mediating mechanisms in the second cohort of a program to prevent anabolic steroid use. Paper presented at the 10^th annual meeting of the Society for Prevention Research, Seattle, WA.  

Williams, J., & MacKinnon, D.P. (2002). Selection bias and the estimation of the mediated effect. Poster presented at the 10^th annual meeting of the Western Psychological Association, Irvine, CA.

Yoon, M., MacKinnon, D. P., & Lockwood, C. M. (2002, April). The difference in coefficient test for mediation in logistic regression. Poser presented at the annual meeting of the Western Psychological Association, Irvine, CA. 

Tein, J. -Y., & MacKinnon, D. P. (2001, July). Estimating mediated effects with survival data. Presented at the International Meeting of the Psychometric Society, Osaka, Japan. 

MacKinnon, D. P., Taborga, M. P., & Morgan-Lopez, A. A. (2001, June). Mediation designs for tobacco prevention research. Presented at the 9^th annual meeting of the Society for Prevention Research, Washington, DC. 

Morgan-Lopez, A. A., & MacKinnon, D. P. (2001, June). A mediated moderation model simulation: Mediational processes that vary as a function of second predictors. [Abstract]. Presented at the 9^th annual meeting of the Society for Prevention Research, Washington, DC. 

MacKinnon, D. P., & Lockwood, C. M. (2001, May). An approximate randomization test for the mediated effect. Abstract presented at the annual meeting of the Western Psychological Association, Maui, HI. 

Tein, J. -Y., Sandler, I. N., MacKinnon, D. P., & Wolchik, S. A. (2000, June). Testing of mediation when program effects interact with pretest mediator of outcome variables. Paper presented at the 8^th annual meeting of the Society for Prevention Research Conference, Montreal, Quebec. 

Morgan-Lopez, A. A., Castro, F. G., Chassin, L. A. & MacKinnon, D. P. (2000, June). A mediated moderation model of tobacco use in Mexican-American youth. Paper presented at the 8^th annual meeting of the Society for Prevention Research, Montreal, Quebec. 

Taborga, M. P., MacKinnon, D. P., & Krull, J. L. (1999, June). A simulation study of effect size measures in mediation models. Poster presented at the 7^th Annual Meeting of the Society for Prevention Research, New Orleans, LA. 

Cheong, J., MacKinnon, D. P., & Khoo, S. T.  (1998, October).  A latent growth modeling approach to mediation analysis.  Poster session presented at the Conference on New Methods for the Analysis of Change, State College, PA. 

Krull, J. (1998). Mediation in multilevel models. Presented at the Mediation Conference, ASU, Tempe, AZ on March 14, 1998. 

MacKinnon, D. P. (1998). Distribution of products approaches to testing the significance of mediation effects. Presented at the Mediation Conference, ASU, Tempe, AZ on March 23, 1998. 

MacKinnon, D. P., Lockwood, C., & Hoffman, J. (1998). A new method to test for mediation. Presented at the Society for Prevention Research Annual Meeting in Park City, Utah on June 5, 1998. 

Tein, J-Y. (1998). Testing of mediation effect with two mediators in the causal chain. Presented at the Mediation Conference, ASU, Tempe, AZ on March 23, 1998. 

West, S., & Aiken, L. (1998). Toward understanding effects of individual components in multicomponent interventions. Presented at the 1998 Mediation Conference, ASU, Tempe, AZ on March 24, 1998. 

Lockwood, C., & MacKinnon, D. P. (1997). Power to detect mediated effects. Meeting of the Western Psychological Association, Seattle, WA. 

MacKinnon, D. P., & Tein, J-Y. (1997). Mediation models for implementation data. Prevention Research Methodology Group, Seattle, WA. 

MacKinnon, D. P., & Krull, J. (1997). Inconsistent mediation models. Presented at the 1997 meeting of the American Psychological Association, Chicago, IL. 

MacKinnon, D. P. (1997). Mediation effects in prevention studies. Invited paper for the 1997 meeting of the American Psychological Association, Chicago, IL. 

Tien, J-Y., & MacKinnon, D. P. (1997). Multiple path mediation models. Presented at the 1997 meeting of the American Psychological Association, Chicago, IL. 

Supplemental Tables

Supplemental tables for MacKinnon, D.P., Taylor, A.B., Yoon, M., & Lockwood, C.M. (2007). A comparison of methods to test mediation and other intervening variable effects in logistic regression. Submitted to Psychological Methods.

Programs for Estimating Empirical Power:

SAS: Baron and Kenny, Joint, Sobel, Prodclin

R: Percentile and Bias-Corrected Bootstrap

Fritz, M.S., & MacKinnon, D.P. (In press). Required sample size to detect the mediated effect.  Psychological Science.

Programs for Estimating Three-Path Mediated Effects

SAS program for estimating three-path mediated effects when all variables are manifest

SAS program for finding bias-corrected bootstrap confidence interval from a set of bootstrapped estimates

Taylor, A. B., MacKinnon, D. P., & Tein, J. -Y. (in press). Tests of the three-path mediated effect. Organizational Research Methods.

PowerPoint Presentation software required to view these documents:

Association for Advancement of Behavior Therapy presentation (Boston - Nov '03)

National Institute on Drug Abuse Meeting on the Mechanisms of Action of Behavioral Treatments (Washington, DC - Feb '04)

Adobe Acrobat Reader is required to view these documents:

Technical Assistance Report: Mediation Analysis 
An overview of mediation analysis with SAS and SPSS code. 

Cumulative Frequency Distributions of the Mediated Effect 
MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test the significance of the mediated effect. Psychological Methods, 7(1), 83-104.

A Simulation Study of Mediation, Suppression and Confounding 
Addendum to MacKinnon, D. P., Krull, J. L., & Lockwood, C. M. (2000). Equivalence of the mediation, confounding, and suppression effect. Prevention Science, 1, 173-181. 

A Detailed Description of the Discrepancy in Formulas for the Standard Error of the Difference Between
a Raw and Partial Correlation: A Typographical Error in Olkin and Finn (1995). Technical Report. Lockwood, C. M., & MacKinnon, David P. (2000).

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