Mediator or Moderator?

[YuJiang]

Hello I have a question to decide whether a variable, M, is mediator or moderator. This is the link for the diagram for X, Y and M: Introduction to Mediation Analysis | UVA Library

This is my mediation analysis:

Mediation Analysis

# Download data online. This is a simulated dataset for this post.
myData <- read.csv('http://static.lib.virginia.edu/statlab/materials/data/mediationData.csv')

Step 1

model.0 <- lm(Y ~ X, myData)
summary(model.0)

Call:
lm(formula = Y ~ X, data = myData)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.0262 -1.2340 -0.3282  1.5583  5.1622 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   2.8572     0.6932   4.122 7.88e-05 ***
X             0.3961     0.1112   3.564 0.000567 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.929 on 98 degrees of freedom
Multiple R-squared:  0.1147,	Adjusted R-squared:  0.1057 
F-statistic:  12.7 on 1 and 98 DF,  p-value: 0.0005671

Step 2

model.M <- lm(M ~ X, myData)
summary(model.M)

Call:
lm(formula = M ~ X, data = myData)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.3046 -0.8656  0.1344  1.1344  4.6954 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.49952    0.58920   2.545   0.0125 *  
X            0.56102    0.09448   5.938 4.39e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.639 on 98 degrees of freedom
Multiple R-squared:  0.2646,	Adjusted R-squared:  0.2571 
F-statistic: 35.26 on 1 and 98 DF,  p-value: 4.391e-08

Step 3

model.Y <- lm(Y ~ X + M, myData)
summary(model.Y)

Call:
lm(formula = Y ~ X + M, data = myData)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.7631 -1.2393  0.0308  1.0832  4.0055 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   1.9043     0.6055   3.145   0.0022 ** 
X             0.0396     0.1096   0.361   0.7187    
M             0.6355     0.1005   6.321 7.92e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.631 on 97 degrees of freedom
Multiple R-squared:  0.373,	Adjusted R-squared:  0.3601 
F-statistic: 28.85 on 2 and 97 DF,  p-value: 1.471e-10

library(mediation)
results <- mediate(model.M, model.Y, treat='X', mediator='M',
                   boot=TRUE, sims=500)
summary(results)

Causal Mediation Analysis 

Nonparametric Bootstrap Confidence Intervals with the Percentile Method

               Estimate 95% CI Lower 95% CI Upper p-value    
ACME             0.3565       0.2235         0.52  <2e-16 ***
ADE              0.0396      -0.2016         0.30   0.800    
Total Effect     0.3961       0.1122         0.63   0.004 ** 
Prop. Mediated   0.9000       0.5081         2.36   0.004 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Sample Size Used: 100 


Simulations: 500 

This is my moderation analysis:

model_interaction <- lm(Y ~ X + M +X*M, data = myData)
summary(model_interaction)

Call:
lm(formula = Y ~ X + M + X * M, data = myData)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.8887 -1.1147  0.0062  1.1226  3.9758 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  0.84237    1.56674   0.538  0.59206   
X            0.22189    0.27122   0.818  0.41531   
M            0.86381    0.32651   2.646  0.00953 **
X:M         -0.03700    0.05033  -0.735  0.46403   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.635 on 96 degrees of freedom
Multiple R-squared:  0.3765,	Adjusted R-squared:  0.357 
F-statistic: 19.32 on 3 and 96 DF,  p-value: 6.972e-10

So if the interaction term is insignificant and the mediation effect is statistically significant, we can say that M is a mediator? Or do you have other suggestions for it? I want to know the only way to test whether a variable is a moderator is to use an interaction term or not?