When moderation is mediated and mediation is moderated.

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Abstract

Procedures for examining whether treatment effects on an outcome are mediated and/or moderated have been well developed and are routinely applied. The mediation question focuses on the intervening mechanism that produces the treatment effect. The moderation question focuses on factors that affect the magnitude of the treatment effect. It is important to note that these two processes may be combined in informative ways, such that moderation is mediated or mediation is moderated. Although some prior literature has discussed these possibilities, their exact definitions and analytic procedures have not been completely articulated. The purpose of this article is to define precisely both mediated moderation and moderated mediation and provide analytic strategies for assessing each.

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Process Analysis: Estimating Mediation in Treatment Evaluations

C. M. Judd, D A Kenny (1981)

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A Simulation Study of Mediated Effect Measures.

David P. MacKinnon, Ghulam Warsi, James Dwyer (1995)

Analytical solutions for point and variance estimators of the mediated effect, the ratio of the mediated to the direct effect, and the proportion of the total effect that is mediated were studied with statistical simulations. We compared several approximate solutions based on the multivariate delta method and second order Taylor series expansions to the empirical standard deviation of each estimator and theoretical standard error when available. The simulations consisted of 500 replications of three normally distributed variables for eight sample sizes (N = 10, 25, 50, 100, 500, 1000, and 5000) and 64 parameter value combinations. The different solutions for the standard error of the indirect effect were very similar for sample sizes of at least 50, except when the independent variable was dichotomized. A sample size of at least 500 was needed for accurate point and variance estimates of the proportion mediated. The point and variance estimates of the ratio of the mediated to nonmediated effect did not stabilize until the sample size was 2,000 for the all continuous variable case. Implications for the estimation of mediated effects in experimental and nonexperimental studies are discussed.