Abstract
Mediation and moderation are two theories for refining and understanding a causal relationship. Empirical investigation of mediators and moderators requires an integrated research design rather than the data analyses driven approach often seen in the literature. This paper described the conceptual foundation, research design, data analysis, as well as inferences involved in a mediation and/or moderation investigation in both experimental and non-experimental (i.e., correlational) contexts. The essential distinctions between the investigation of mediators and moderators were summarized and juxtaposed in an example of a causal relationship between test difficulty and test anxiety. In addition, the more elaborate models, moderated mediation and mediated moderation, the use of structural equation models, and the problems with model misspecification were discussed conceptually.
Similar content being viewed by others
Notes
Path analysis and factor analysis are special cases of SEM. A path analysis is a type of SEM in which each variable has only one indicator and the relationship among the variables are specified. Hence, a path analysis approach to mediation and moderation does not deal with the problem of measurement errors, however, it, can deal with multiple univariate regression analyses in one model. A factor analysis is a type of SEM in which each latent variable has multiple indicators hence deals with the measurement error problem, but there are no relationship specified among the latent variables. A full SEM incorporates and integrates path analysis and factor analysis; the latent variables have multiple indicators and their relationships are modeled.
References
Aguinis, H., Boik, R. J., & Pierce, C. A. (2001). A generalized solution for approximating the power to detect effect of categorical moderator variables using multiple regression. Organizational Research Methods, 4, 291–323.
Algina, J., & Moulder, B. C. (2001). Note on estimating the Jöreskog-Yang model for latent variable interaction using LISREL 8.3. Structural Equation Modeling, 8, 40–52.
Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173–1182.
Bauer, D. J., Preacher, K. J., & Gil, K. M. (2006). Conceptualizing and testing random indirect effects and moderated mediation in multilevel models: new procedures and recommendations. Psychological Methods, 11, 142–163.
Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.
Bollen, K. A., & Paxton, P. (1998). Interactions of latent variables in structural equation models. Structural Equation Modeling, 5, 267–293.
Brown, R. L. (1997). Assessing specific mediational effect in complex theoretical models. Structural Equation Modeling, 4, 142–156.
Chaplin, W. F. (1991). The next generation in moderation research in personality psychology. Journal of Personality, 59, 143–178.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.
Cohen, J. P., Cohen, S. G., West, L. S., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
Cook, T., & Campbell, D. (1979). Quasi-experimentation: design and analysis issues for field settings. Boston: Houghton Mifflin.
Cole, D. A., & Maxwell, S. E. (2003). Testing mediational models with longitudinal data: questions and tips in the use of structural equation modeling. Journal of Abnormal Psychology, 4, 558–577.
Collins, L. M., Graham, J. W., & Flaherty, B. P. (1998). An alternative framework for defining mediation. Multivariate Behavioral Research, 33, 295–313.
Cronbach, L. J., & Meehl, P. E. (1955). Construct validity in psychological tests. Psychological Bulletin, 52, 281–302.
Frazier, P. A., Tix, A. P., & Baron, K. E. (2004). Testing moderator and mediator effects in counselling psychology. Journal of Counselling Psychology, 51, 115–134.
Hershberger, S. L. (2006). The problem of equivalent structural models. In G. R. Hancock & R. O. Muller (Eds.), Structural equation modeling: a second course (pp. 13–41). Greenwich, CT: Information Age Publishing.
Holbert, R. L., & Stephenson, M. T. (2003). The importance of indirect effects in media effects research: testing for mediation in structural equation modeling. Journal of Broadcasting and Electronic Media, 47, 556–572.
Holland, P. (1986). Statistics and causal inference. Journal of the American Statistical Association, 81, 945–960.
Holmbeck G. N. (1997). Toward terminological, conceptual, and statistical clarity in the study of mediators and moderators: examples from the child-clinical and pediatric psychology literatures. Journal of Consulting & Clinical Psychology, 65, 599–610.
Holmbeck, G. N. (2002). Post-hoc probing of significant moderational and mediational effects in studies of pediatric populations. Journal of Pediatric Psychology, 27, 87–96.
Hoyle, R. H., & Kenny, D. A. (1999). Statistical power and tests of mediation. In R. H. Hoyle (Ed.), Statistical strategies for small sample research. Newbury Park: Sage.
Hoyle, R. H., & Robinson, J. I. (2003). Mediated and moderated effects in social psychological research: measurement, design, analysis issues. In C. Sansone, C. Morf, & A. T. Panter (Eds.), Handbook of methods in social psychology (pp. 213–233). Thousand Oaks, CA: Sage.
Hoyle, R. H., & Smith, G. T. (1994). Formulating clinical research hypothesis as structural models: a conceptual overview. Journal of Consulting and Clinical Psychology, 62, 429–440.
Jaccard, J., Turrisi, R., & Wan, C. K. (1990). Interaction effects in multiple regression. Newbury Park, CA: Sage.
Jaccard, J., & Wan, C. K. (1995). Measurement error in the analysis of interaction effects between continuous predictors using multiple regression: multiple indicator and structural equation approaches. Psychological Bulletin, 117, 348–357.
Jaccard, J., & Wan, C. K. (1996). LISREL approaches to interaction effects in multiple regression. Thousand Oaks, CA: Sage.
James, L. R., & Brett, J. M. (1984). Mediators, moderators, and test for mediation. Journal of Applied Psychology, 69, 307–321.
Judd, C. M., & Kenny, D. A. (1981). Process analysis: estimating mediation in treatment evaluation. Evaluation Review, 5, 602–619.
Kenny, D. A. (1979). Correlation and causality. New York: Wiley.
Kenny, D. A., & Judd, C. M. (1984). Estimating the linear and interative effects of latent variable. Psychological Bulletin, 105, 361–373.
Kenny, D. A., Kashy, D. A., & Bolger, N. (1998). Data analysis in social psychology. In D. Gilbert, S. Fiske, & G. Lindzey (Eds.), The handbook of social psychology (Vol. 1, 4th ed., pp. 233–265). Boston, MA: McGraw-Hill.
Kenny, D. A., Korchmaros, J. D., & Bolger, N. (2003). Lower level mediation in multilevel models, Psychological Methods, 8, 115–128.
Kraemer, H. C., Stice, E., Kazdin, A, Offord, D., & Kupfer, D. (2001). How do risk factors work together? Mediators, moderators, and independent, overlapping, and proxy risk factors. American Journal of Psychiatry, 158, 848–856.
Kraemer, H. C., Wilson, G T., Fairburn, C. G., & Agras, W. S. (2002). Mediators and moderators of treatment effects in randomized clinical trials. Archives of General Psychiatry, 59, 877–883.
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.
MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7, 19–40.
MacCorquodale, K., & Meehl, P. E. (1948). On a distinction between hypothetical constructs and intervening variables. Psychological Review, 55, 95–107.
MacKinnon, D. P., Krull, J. L., & Lockwood, C. M. (2000). Equivalence of mediation, confounding, and suppression effect. Prevention Sciences, 1, 173–181.
MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparisons of methods to test mediation and other intervening variable effects. Psychological Methods, 7, 83–104.
MacKinnon, D. P., Warsi, G., & Dwyer, J. H. (1995). A simulation study of mediated effect measures. Multivariate Behavioral Research, 30, 41–62.
Mallinckrodt, B., Abraham, W. T., Wei, M., & Russell, D. W. (2006). Advances in testing the statistical significance of mediation effects. Journal of Counselling Psychology, 53, 372–378.
Marsh, H. W., Wen, Z., & Hau, K. T. (2004). Structural equation models of latent interactions: evaluation of alternative estimation strategies and indicator construction. Psychological Methods, 9, 275–299.
Messick, S. (1989). Validity. In R. L. Linn (Ed.), Educational measurement (3rd ed., pp. 13–103). New York: American Council of Education & Macmillan.
Mogan-Lopes, A. A., & MacKinnon, D. P. (2006). Demonstration and evaluation of methods for assessing mediated moderation. Behavior Research Methods, 38, 77–87.
Moulder, B. B., & Algina, J. (2002). Comparison of methods for estimating and testing latent variable interactions. Structural Equation Modeling, 9, 1–19.
Muller, D., Judd, C. M., & Yzerbyt, V. Y. (2005). When moderation is mediated mediation is moderated. Journal of Personality and Social Psychology, 89, 852–863.
Pearl, J. (2000). Causality: models reasoning, and inference. Cambridge, UK: Cambridge University Press.
Ping, R. A. Jr. (1996). Latent variable interaction and quadratic effect estimation: a two-step technique using structural equation analysis. Psychological Bulletin, 119, 166–175.
Preacher, K. J., & Hayes, A. F. (2004). SPSS and SAS procedures for estimating indirect effects in simple mediation models. Behavior Research Methods, Instruments, and Computers, 36, 717–731.
Preacher, K. J., Rucker, D. D., & Hayes, A. F. (in press). Addressing moderated mediation hypothesis: theory, methods, and prescriptions. Multivariate Behavioral Research.
Rogosa, D. (1987). Causal models do not support scientific conclusions: a comment in support of Freedman. Journal of Educational Statistics, 12, 185–195.
Rose, B. M., Holmbeck, G. N., Coakley, R. M., & Franks, E. A. (2004). Mediator and moderator effects in developmental and behavioral pediatric research. Developmental and Behavioral Pediatrics, 25, 58–67.
Rosenbaum, P. R. (1984). From association to causation on observational studies: the role of tests of strongly ignorable treatment assignment. Journal of the American Statistical Association, 79, 41–48.
Rozeboom, W. W. (1956). Mediation variable in scientific theory. Psychological Review, 63, 249–264.
Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and non-randomized studies. Journal of Educational Psychology, 66, 688–701.
Rubin, D. (1986). “Comment: which ifs have causal answers?” Journal of the American Statistical Association, 81, 961–962.
Saunders, D. R. (1956). Moderator variables in prediction. Educational and Psychological Measurement, 16, 209–222.
Schermelleh-Engel, K., Klein, A., & Moosbrugger, H. (1998). Estimating nonlinear effects using a Latent Moderated Structural Equations Approach. In R. E. Schumacker & G. A. Marcoulides (Eds.), Interaction and nonlinear effects in structural equation modeling (pp. 203–238). Mahwah, NJ: Erlbaum.
Schumacker, R. E. (2002). Latent variable interaction modeling. Structural Equation Modelling, 9, 40–54.
Schumacker, R., & Marcoulides, G. (Eds.) (1998). Interaction and nonlinear effects in structural equation modeling. Mahwah, NJ: Erlbaum.
Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference. Boston: Houghton-Mifflin.
Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: new procedures and recommendations. Psychological Methods, 4, 422–445.
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.
Sobel, M. E. (1988) Direct and indirect effects in structural equation models. In J. S. Long (Ed.), Common problems/proper solutions: avoiding error in quantitative research (pp. 46–64). Beverly Hill, CA: Sage.
Sobel, M. E. (1990). Effect analysis and causation in linear structural equation models. Psychometrika, 55, 495–515.
Sobel, M. E. (1995). Causal inference in social and behavioral sciences. In G. Arminger, C. C. Clog, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (pp. 1–32). New York: Plenum Press.
Sobel, M. E. (2005) Discussion: the scientific model of causality. Sociological Methodology, 35, 99–133.
Spencer, S. J., Zanna, M. P., & Fong, G. T. (2005). Establishing a causal chain: why experiments are often more effective than mediational analysis in examining psychological processes. Journal of Personality and Social Psychology, 89, 845–851.
Wegener, D., & Fabrigar, L. (2000). Analysis and design for nonexperimental data addressing causal and noncausal hypothesis. In H. T. Reis & C. M. Judd (Eds.), Handbook of research methods in social and personality psychology (pp. 412–450). New York: Cambridge University Press.
West, S. G., Aiken, L. S., & Krull, J. L. (1996). Experimental personality design: analyzing categorical by continuous variable interactions. Journal of Personality, 64, 1–49.
Woodworth, R. S. (1928). Dynamic psychology. In C. Murchison (Ed.), Psychology of 1925. Worcester, MA: Clark University Press.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, A.D., Zumbo, B.D. Understanding and Using Mediators and Moderators. Soc Indic Res 87, 367–392 (2008). https://doi.org/10.1007/s11205-007-9143-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11205-007-9143-1