set.seed(10311993)
library(mediation)
library(psych)
library(tidyverse)
# Created Toy Data Set
# Variance Covariance
sigma <- rbind(c(1,-0.4,-0.3), c(-0.4,1, 0.7), c(-0.3,0.7,1))
# Variable Mean
mu <- c(7, 50, 7)
# Generate the Multivariate Normal Distribution
df <- as.data.frame(mvrnorm(n=100, mu=mu, Sigma=sigma))
df <- round(df,0)
colnames(df) <- c("mediator1","outcome","predictor")
df$condition <- rep(1:2,50)R Workshop: Mediation and Moderation
Running a Moderation Analysis in R
moderation <- lm(outcome ~ condition*predictor, data = df)
summary(moderation)- 1
-
Create a mediation object using the
lm()function. The condition*predictor syntax gets you both the main effects of condition and predictor as well as the interaction effect between the two - 2
-
Show a summary of the moderation using the
summary()function.
Call:
lm(formula = outcome ~ condition * predictor, data = df)
Residuals:
Min 1Q Median 3Q Max
-1.79555 -0.56073 -0.05061 0.55043 1.71457
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 44.85018 1.68125 26.677 < 2e-16 ***
condition -0.01414 1.06533 -0.013 0.98943
predictor 0.76026 0.23452 3.242 0.00163 **
condition:predictor -0.01533 0.14964 -0.102 0.91864
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.8027 on 96 degrees of freedom
Multiple R-squared: 0.5089, Adjusted R-squared: 0.4936
F-statistic: 33.16 on 3 and 96 DF, p-value: 8.49e-15Running a Mediation Analysis in R
#Regress M on X
outcomeM_fit <- lm(mediator1 ~ condition, data = df)
summary(outcomeM_fit)
#Regress Y on M and X
outcomeY_fit <- lm(outcome ~ mediator1 + condition, data = df)
summary(outcomeY_fit)
#Run Mediation with Bootstrap
outcome_fit <- mediation::mediate(outcomeM_fit,
outcomeY_fit,
treat = "condition",
mediator = "mediator1",
boot = TRUE,
sims = 5000)
#Summary of Mediation
summary(outcome_fit)
#Path Coefficients
plot(outcome_fit)- 1
-
Run a regression of the M (mediator) on X using the
lm()function - 2
-
Show output of the M on X regression using the
summary()function - 3
-
Run a regression of Y on M and X using the
lm()function - 4
-
Show output of the Y on M and X regression using the
summary()function - 5
-
Run a mediation using the two regressions above.
treatis the name of your X condition.mediatoris the name of your mediating variable. SettingboottoTRUEwill ensure that your mediation is bootstrapped. Lastly, thesimsargument tells R how many samples you wish to bootstrap from. Typically you want ~ 5000 or more. - 6
-
For a summary of your mediation, use the
summary()function. The indirect effect is labeled ACME - 7
-
The
plot()function here will give you a graphical representation of the output above with respect to the range of the confidence interval for each metric. Please note by default this is the 95% confidence interval
Call:
lm(formula = mediator1 ~ condition, data = df)
Residuals:
Min 1Q Median 3Q Max
-2.860 -0.755 0.140 1.140 2.280
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.0000 0.3412 20.515 <2e-16 ***
condition -0.1400 0.2158 -0.649 0.518
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.079 on 98 degrees of freedom
Multiple R-squared: 0.004276, Adjusted R-squared: -0.005884
F-statistic: 0.4209 on 1 and 98 DF, p-value: 0.518
Call:
lm(formula = outcome ~ mediator1 + condition, data = df)
Residuals:
Min 1Q Median 3Q Max
-2.2245 -0.5522 -0.0769 0.4724 3.4724
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 53.53460 0.74376 71.979 < 2e-16 ***
mediator1 -0.45066 0.09569 -4.709 8.28e-06 ***
condition -0.30309 0.20487 -1.479 0.142
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.022 on 97 degrees of freedom
Multiple R-squared: 0.1954, Adjusted R-squared: 0.1788
F-statistic: 11.78 on 2 and 97 DF, p-value: 2.634e-05
Causal Mediation Analysis
Nonparametric Bootstrap Confidence Intervals with the Percentile Method
Estimate 95% CI Lower 95% CI Upper p-value
ACME 0.0631 -0.1217 0.29 0.52
ADE -0.3031 -0.7098 0.08 0.12
Total Effect -0.2400 -0.6849 0.19 0.28
Prop. Mediated -0.2629 -6.0955 4.66 0.76
Sample Size Used: 100
Simulations: 5000 Assumptions of Moderation Analyses
# Residual Normality
shapiro.test(residuals(moderation))
# Multicollinearity
car::vif(moderation, type = c("predictor"))
# Independence of Errors
car::durbinWatsonTest(moderation)- 1
-
Test of the residual normality of the moderation using the
shapiro.test()function - 2
-
Test of the multicollinearity of the moderation analyses using the
vif()function in thecarpackage. Because there is an interaction, you must specify an additional argument oftype = c("predictor")to properly account for the interaction effect. - 3
-
To test the independence of errors assumption, you can do so using the
durbinWatsonTest()function from thecarpackage.
Shapiro-Wilk normality test
data: residuals(moderation)
W = 0.98684, p-value = 0.4272
GVIF Df GVIF^(1/(2*Df)) Interacts With Other Predictors
condition 1 3 1 predictor --
predictor 1 3 1 condition --
lag Autocorrelation D-W Statistic p-value
1 -0.02268275 2.029087 0.756
Alternative hypothesis: rho != 0Assumptions of Mediation Analyses
# Linearity
plot(lm(outcome ~ predictor, data = df),2)- 2
-
To assess multicollinearity, the best course of action is a simple correlation matrix. You can achieve this using the
cor()function for a correlation matrix
plot(lm(outcome ~ mediator1, data = df),2)
plot(lm(mediator1 ~ predictor, data = df),2)
# Multicollinearity
cor(df) mediator1 outcome predictor condition
mediator1 1.00000000 -0.4210068 -0.38328907 -0.06539201
outcome -0.42100683 1.0000000 0.71129322 -0.10692147
predictor -0.38328907 0.7112932 1.00000000 -0.07432941
condition -0.06539201 -0.1069215 -0.07432941 1.00000000Using Moderation and Mediation Usings Hayes PROCESS Macro (for R)
Click on the following link to download the R script for the PROCESS macro for R.
source("process.R")
********************* PROCESS for R Version 4.3.1 *********************
Written by Andrew F. Hayes, Ph.D. www.afhayes.com
Documentation available in Hayes (2022). www.guilford.com/p/hayes3
***********************************************************************
PROCESS is now ready for use.
Copyright 2020-2023 by Andrew F. Hayes ALL RIGHTS RESERVED
Workshop schedule at http://haskayne.ucalgary.ca/CCRAM
A Moderation Example Using Hayes PROCESS Macro
process(data = df,
y = "outcome",
x = "predictor",
w = "mediator1",
model = 1,
stand = 1)- 1
-
Assign your data to the
dataargument - 2
-
Assign your outcome variable to the
yargument - 3
-
Assign your predictor variable to the
xargument - 4
-
Assign your moderator to the
wargument - 5
-
Set your
modelargument to1for simple moderation - 6
-
The
stand = 1argument standardizes your output
********************* PROCESS for R Version 4.3.1 *********************
Written by Andrew F. Hayes, Ph.D. www.afhayes.com
Documentation available in Hayes (2022). www.guilford.com/p/hayes3
***********************************************************************
Model : 1
Y : outcome
X : predictor
W : mediator1
Sample size: 100
***********************************************************************
Outcome Variable: outcome
Model Summary:
R R-sq MSE F df1 df2 p
0.7294 0.5320 0.6141 36.3739 3.0000 96.0000 0.0000
Model:
coeff se t p LLCI ULCI
constant 47.3198 3.6872 12.8336 0.0000 40.0008 54.6389
predictor 0.5567 0.5256 1.0592 0.2922 -0.4866 1.6001
mediator1 -0.2975 0.5240 -0.5676 0.5716 -1.3377 0.7427
Int_1 0.0169 0.0761 0.2222 0.8246 -0.1341 0.1679
Product terms key:
Int_1 : predictor x mediator1
Test(s) of highest order unconditional interaction(s):
R2-chng F df1 df2 p
X*W 0.0002 0.0494 1.0000 96.0000 0.8246
******************** ANALYSIS NOTES AND ERRORS ************************
Level of confidence for all confidence intervals in output: 95
NOTE: Standardized coefficients not available for models with moderators.
Tip
The Hayes PROCESS for R requires that all data is numeric in nature. As such, ensure that any potential factor variables are numeric prior to running the analyses. A failure to do so will result in PROCESS not running.
A Mediation Example Using Hayes PROCESS Macro
process(data = df,
y = "outcome",
x = "predictor",
m = "mediator1",
model = 4,
stand = 1,
boot = 5000)- 1
-
Assign your data to the
dataargument - 2
-
Assign your outcome variable to the
yargument - 3
-
Assign your predictor variable to the
xargument - 4
-
Assign your mediator to the
margument - 5
-
Set your
modelargument to4for simple mediation - 6
-
The
stand = 1argument standardizes your output - 7
-
The
bootargument specifies the number of samples you wish to bootstrap
********************* PROCESS for R Version 4.3.1 *********************
Written by Andrew F. Hayes, Ph.D. www.afhayes.com
Documentation available in Hayes (2022). www.guilford.com/p/hayes3
***********************************************************************
Model : 4
Y : outcome
X : predictor
M : mediator1
Sample size: 100
Random seed: 818206
***********************************************************************
Outcome Variable: mediator1
Model Summary:
R R-sq MSE F df1 df2 p
0.3833 0.1469 0.9975 16.8766 1.0000 98.0000 0.0001
Model:
coeff se t p LLCI ULCI
constant 9.4738 0.6609 14.3352 0.0000 8.1623 10.7852
predictor -0.3812 0.0928 -4.1081 0.0001 -0.5654 -0.1971
Standardized coefficients:
coeff
predictor -0.3833
***********************************************************************
Outcome Variable: outcome
Model Summary:
R R-sq MSE F df1 df2 p
0.7292 0.5317 0.6081 55.0760 2.0000 97.0000 0.0000
Model:
coeff se t p LLCI ULCI
constant 46.5259 0.9080 51.2386 0.0000 44.7237 48.3281
predictor 0.6722 0.0784 8.5694 0.0000 0.5165 0.8279
mediator1 -0.1824 0.0789 -2.3121 0.0229 -0.3389 -0.0258
Standardized coefficients:
coeff
predictor 0.6446
mediator1 -0.1740
***********************************************************************
Bootstrapping progress:
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**************** DIRECT AND INDIRECT EFFECTS OF X ON Y ****************
Direct effect of X on Y:
effect se t p LLCI ULCI c'_cs
0.6722 0.0784 8.5694 0.0000 0.5165 0.8279 0.6446
Indirect effect(s) of X on Y:
Effect BootSE BootLLCI BootULCI
mediator1 0.0695 0.0353 0.0100 0.1483
Completely standardized indirect effect(s) of X on Y:
Effect BootSE BootLLCI BootULCI
mediator1 0.0667 0.0339 0.0097 0.1436
******************** ANALYSIS NOTES AND ERRORS ************************
Level of confidence for all confidence intervals in output: 95
Number of bootstraps for percentile bootstrap confidence intervals: 5000