Mediation Analysis

by

David P. MacKinnon, Matthew Valente

• LAST REVIEWED: 26 June 2019
• LAST MODIFIED: 26 June 2019
• DOI: 10.1093/obo/9780199828340-0245

Introduction

Mediation analysis is a statistical method used to quantify the causal sequence by which an antecedent variable causes a mediating variable that causes a dependent variable. Although mediation analysis is useful for observational studies, it is perhaps most compelling for answering questions of cause and effect in randomized treatment and prevention programs. Information about mediating mechanisms improves programs by providing information about the critical ingredients of successful programs. Sewall Wright’s work in the 1920s first applied the notion of mediated or indirect effects in path models for the inheritance of skin color in guinea pigs. Methodological developments and applications of mediation analysis have dramatically increased since ideas about mediation in the social sciences were first formalized by Herbert Hyman and Paul Lazarsfeld in 1955. Innovations in mediation analyses have been rapid in the last forty years, and recently progress in understanding the causal basis of mediation analysis has been a major breakthrough.

Early History of Mediation

Wright 1920 was the first work to describe effects on variables that are indirect through other variables in the study of heritability of guinea pigs. Hyman 1955 and Lazarsfeld 1955 provide the original descriptions of how a third variable affects the relation between two variables through a series of statistical tests that were later translated into decomposition of effects by Alwin and Hauser 1975, mediation in psychology by James and Brett 1984 and Baron and Kenny 1986, and in evaluation by Judd and Kenny 1981. Sobel 1982 and Sobel 1986 describe matrix formulas for the calculation of indirect effects and their standard errors that can be used to form confidence intervals and significance testing for the indirect effect. MacKinnon, et al. 1991 applies tests of mediation in the analysis of an intervention study. Robins and Greenland 1992 describes a counterfactual-based approach to mediated effects that form the basis of subsequent causal mediation analysis. MacKinnon and Dwyer 1993 formalizes these developments for regression models and applies them to prevention and treatment research.

• Alwin, D. F., and R. M. Hauser. 1975. The decomposition of effects in path analysis. American Sociological Review 40:37–47.

  DOI: 10.2307/2094445

  Mathematical description of how total effects are decomposed into direct and indirect effects based on prior research. Includes a clear description of the many types of indirect effects and how they are calculated.

• Baron, R. M., and D. A. Kenny. 1986. The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology 51.6: 1173–1182.

  DOI: 10.1037/0022-3514.51.6.1173

  Clarifies the difference between mediation and moderation with an overview of how to conduct analyses with regression.

• Hyman, H. H. 1955. Survey design and analysis: Principles, cases and procedures. Glencoe, IL: Free Press.

  First to present a list of steps for testing mediation elaborated in later mediation publications.

• James, L. R., and J. M. Brett. 1984. Mediators, moderators, and tests for mediation. Journal of Applied Psychology 69.2: 307–321.

  DOI: 10.1037/0021-9010.69.2.307

  Describes mediation and moderation as functional relations between variables and their conceptualization in psychology.

• Judd, C. M., and D. A. Kenny. 1981. Process analysis: Estimating mediation in treatment evaluations. Evaluation Review 5.5: 602–619.

  DOI: 10.1177/0193841X8100500502

  The classic mediation paper. Contains the first description of causal steps to assess mediation and the importance of the interaction of the moderator and the mediator and longitudinal mediation models data.

• Lazarsfeld, P. F. 1955. Interpretation of statistical relations as a research operation. In The language of social research: A reader in the methodology of social research. Edited by P. F. Lazarsfeld and M. Rosenberg, 115–125. Glencoe, IL: Free Press.

  Original description of how including a third variable in analysis affects the relation between two variables, including how an intervening variable would affect the relation between two variables.

• MacKinnon, D. P., and J. H. Dwyer. 1993. Estimating mediated effects in prevention studies. Evaluation Review 17.2: 144–158.

  DOI: 10.1177/0193841X9301700202

  Includes equations for mediation estimation, standard error formulas, and evaluates methods with a statistical simulation study. Describes how mediation analysis with logistic regression leads to different values for product of coefficient and difference in coefficient methods for mediation analysis.

• MacKinnon, D. P., C. A. Johnson, M. A. Pentz, et al. 1991. Mediating mechanisms in a school-based drug prevention program: First-year effects of the Midwestern Prevention Project. Health Psychology 10.3: 164–172.

  DOI: 10.1037/0278-6133.10.3.164

  First paper to estimate mediated effects and standard errors in the evaluation of an intervention.

• Robins, J. M., and S. Greenland. 1992. Identifiability and exchangeability for direct and indirect effects. Epidemiology 3.2: 143–155.

  DOI: 10.1097/00001648-199203000-00013

  Outlines all the possible actual and counterfactual conditions for mediation analysis as a function of assumptions. Introduces what later became the counterfactual mediation model. Groundbreaking paper on a counterfactual approach to causal mediation.

• Sobel, M. E. 1982. Asymptotic confidence intervals for indirect effects in structural equation models. Sociological Methodology 13:290–312.

  DOI: 10.2307/270723

  Derives the standard error of the indirect effect for confidence intervals based on the multivariate delta method. Also derives the multivariate standard error for the effect size measures, the proportion mediated, and the ratio of the mediated effect to the direct effect.

• Sobel, M. E. 1986. Some new results on indirect effects and their standard errors in covariance structure models. Sociological Methodology 16:159–186.

  DOI: 10.2307/270922

  General matrix formulation for multivariate delta method standard errors for indirect effects for general structural equation models. Matrix equations in this paper are used in modern software to compute mediated effects and standard errors.

• Wright, S. 1920. The relative importance of heredity and environment in determining the piebald pattern of guinea pigs. Proceedings of the National Academy of Sciences 6:320–332.

  DOI: 10.1073/pnas.6.6.320

  Classic, original, description of path analysis with direct and indirect effects applied to the skin color of guinea pigs. Mention of indirect effects as the product of path coefficients.