Mediation Analysis

Mediation analysis is a decomposition of causal effects based on a mediator variable.

Note that there is a difference between mediation and moderation. The latter deals with how a causal link differs across levels of a moderating variable.

Description

In circumstances where a significant relationship has been found between an independent and dependent variable, but no causal mechanism has been identified, it is possible to propose hypotheses that a third mediator variable completes the causal model.

The effects pictured are:

• direct effect of X on Y = β₁

• direct effect of X on M = β₂

• direct effect of M on Y = β₃

• indirect effect of X on Y = β₂*β₃

• total effect of X on Y = β₁ + (β₂*β₃)

This can be estimated with the Sobel test, but best practice is to use a bootstrapping method.

Example

The Sobel test approach, using the multilevel package:

library(multilevel)

sorel(data$X, data$M, data$Y)

This displays:

• the component models, including the estimated coefficients and intercepts
• the indirect effect
• the pooled standard error
• the calculated Z statistic

The bootstrapping approach, using the mediation package:

XonY <- lm(Y ~ X, data = data)
XonM <- lm(M ~ X, data = data)
XMonY <- lm(Y ~ X + M, data = data)

library(mediation)

mediate(XonM, XMonY, treat='X', mediator='M', boot=TRUE, sims=500)

This displays:

• the average causal mediation effects (ACME), the key measure of this bootstrapping method

  • if significantly different than 0, then there is a significant mediation effect

• the average direct effects (ADE)

• the total effect

  • total effect = ACME + ADE

• the proportion of the total effect that was mediated

  • prop = ACME / total effect

CategoryRicottone