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'''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.		 '''Mediation analysis''' is a decomposition of causal effects with [[Statistics/Mediator|mediation]].
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== Description == == Background ==
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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. [[Statistics/Mediator|Mediation]] looks like the following diagram.
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The effects pictured are: where the true causal effects are as follows:
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This can be estimated with the [[Statistics/SobelTest|Sobel test]], but best practice is to use a bootstrapping method.
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== Example == == Description ==
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The [[Statistics/SobelTest|Sobel test]] approach, using the [[R/Multilevel|multilevel package]]: === Sobel Test ===

The [[Statistics/SobelTest|Sobel test]] is a common approach for identifying and decomposing the mediated effects.

This example uses the [[R/Multilevel|multilevel package]]:
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The bootstrapping approach, using the [[R/Mediation|mediation package]]:

=== Bootstrapping ===

A bootstrapping approach is more accurate.

This example also uses the [[R/Mediation|mediation package]]:

Mediation Analysis

Mediation analysis is a decomposition of causal effects with mediation.

Contents

  1. Mediation Analysis
    1. Background
    2. Description
      1. Sobel Test
      2. Bootstrapping

Background

Mediation looks like the following diagram.

path.png

where the true causal effects are as follows:

  • 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)

Description

Sobel Test

The Sobel test is a common approach for identifying and decomposing the mediated effects.

This example uses 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

Bootstrapping

A bootstrapping approach is more accurate.

This example also uses 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

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Statistics/MediationAnalysis (last edited 2026-02-17 15:42:31 by DominicRicottone)