What is Mediation?

• Refers to a situation when the relationship between a predictor variable and outcome variable can be explained by their relationship to a third variable (the mediator).

Plain English: Mediation is like a “middle man” or a relay race. The predictor passes the baton to the mediator, who then runs to the finish line (the outcome). If the predictor (X) affects the outcome (Y), mediation explains how or why that happens.

Example: Does stress cause illness? Maybe stress (X) lowers your immune system (Mediator), which then leads to illness (Y). The immune system mediates the relationship.

Baron & Kenny (1986)

• Mediation was historically tested through three regression models:

  • Predicting the outcome from the predictor variable.
  • Predicting the mediator from the predictor variable.
  • Predicting the outcome from both the predictor variable and the mediator.

State of the Art (2026): While Baron & Kenny’s steps are great for understanding the concept, they are no longer considered sufficient for testing mediation in modern analytics. They have low statistical power (high chance of missing a real effect). Today, we focus on the Indirect Effect itself, usually tested via Bootstrapping.

Baron & Kenny (1986)

• Four conditions of mediation (Classic View):

  • The predictor must significantly predict the outcome variable.*
  • The predictor must significantly predict the mediator.
  • The mediator must significantly predict the outcome variable.
  • The predictor variable must predict the outcome variable less strongly in model 3 than in model 1.

Baron & Kenny (1986): Limitations

• How much of a reduction in the relationship between the predictor and outcome is necessary to infer mediation?

• People tend to look for a change in significance, which can lead to the ‘all or nothing’ thinking that p-values encourage.

• Two solutions:

  • The Sobel test (Older)
  • Bootstrapping the indirect effect and confidence intervals (Modern Standard)

Sobel Test

• An alternative is to estimate the indirect effect and its significance using the Sobel test (Sobel, 1982).
• If the Sobel test is significant, there is significant mediation.
• We are going to use the Aroian Test version of Sobel which corrects for the standard error of the a and b paths.

Note: The Sobel test assumes that the indirect effect (ab) is normally distributed. This is often not* true, especially in smaller samples. This makes the Sobel test “conservative” (harder to find significant results).

Bootstrapping (The Gold Standard)

• What is bootstrapping?

  • A procedure where you run an analysis many times (e.g., 5,000 or 10,000 times) to create an average effect and confidence interval of the effect.
  • Bootstrapped datasets are created by randomly picking a sample from your dataset with replacement.
  • Think about this like the lottery, if they put the balls back after every draw.
  • If the confidence interval of the indirect (mediation) effect does not cross zero, then that implies that mediation has occurred.

Why it’s better: Bootstrapping does not assume the data are normally distributed. It builds a distribution based on your specific data. This makes it the most accurate and powerful method for testing mediation today.

Mediation: Data Screening

• Mediation models usually occur in stages - meaning separate models are run with different IV / DV combinations.

• Sometimes people call these “steps”, but do not confuse this with hierarchical regression.

• So, what does that do for data screening?

  • Screen both the IV and the Mediator at the same time predicting the DV.
  • This way you are screening the final anticipated stage of the mediation model and are screening all the variables.
  • You can also use the fake regression procedure to do all three variables at once.

Mediation: Example

• Does Facebook use mediate the relationship between previous knowledge and exam scores?
• Implying that the overuse of Facebook prevents people from studying, so they do differently on their exam?
• Important not to have missing data, so you are comparing models that all use the same data points.

library(rio)
master <- import("data/mediation.sav")
str(master)

## 'data.frame':    240 obs. of  3 variables:
##  $ previous: num  3 2 1 1 1 1 1 1 1 1 ...
##   ..- attr(*, "format.spss")= chr "F1.0"
##   ..- attr(*, "display_width")= int 14
##  $ facebook: num  3.67 5 4 4.5 4.5 ...
##   ..- attr(*, "format.spss")= chr "F8.2"
##   ..- attr(*, "display_width")= int 14
##  $ exam    : num  1 1 2 7 6 1 2 1 1 1 ...
##   ..- attr(*, "format.spss")= chr "F8.2"
##   ..- attr(*, "display_width")= int 10

summary(master)

##     previous        facebook          exam       
##  Min.   :1.000   Min.   :1.750   Min.   : 1.000  
##  1st Qu.:1.000   1st Qu.:3.750   1st Qu.: 1.000  
##  Median :1.000   Median :4.250   Median : 1.000  
##  Mean   :1.571   Mean   :4.143   Mean   : 1.825  
##  3rd Qu.:2.000   3rd Qu.:4.750   3rd Qu.: 2.000  
##  Max.   :7.000   Max.   :5.000   Max.   :11.000  
##                  NA's   :1

master <- na.omit(master)

Mediation: c Path

• The c path: X –> Y: \[b = 0.32, t(237) = 3.63, p < .001\]

model1 <- lm(exam ~ previous, data = master)
summary(model1)

## 
## Call:
## lm(formula = exam ~ previous, data = master)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9092 -0.6477 -0.6477  0.3523  8.4062 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.33228    0.16749   7.955 7.37e-14 ***
## previous     0.31539    0.08689   3.630 0.000348 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.496 on 237 degrees of freedom
## Multiple R-squared:  0.05266,    Adjusted R-squared:  0.04867 
## F-statistic: 13.17 on 1 and 237 DF,  p-value: 0.0003476

Mediation: a Path

• The a path: X –> M: \[b = -0.09, t(237) = -2.17, p = .031\]

model2 <- lm(facebook ~ previous, data = master)
summary(model2)

## 
## Call:
## lm(formula = facebook ~ previous, data = master)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.44609 -0.44609  0.05391  0.55391  1.35640 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.28817    0.08195  52.330   <2e-16 ***
## previous    -0.09208    0.04251  -2.166   0.0313 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.732 on 237 degrees of freedom
## Multiple R-squared:  0.01941,    Adjusted R-squared:  0.01527 
## F-statistic: 4.692 on 1 and 237 DF,  p-value: 0.03131

Mediation: b, c’ Path

• Add in the b and c’ paths: X + M –> Y
• b Path: \[b = -0.61, t(237) = -4.77, p < .001\]
• c’ Path: \[b = 0.26, t(237) = 3.09, p = .002\]

model3 <- lm(exam ~ previous + facebook, data = master)
summary(model3)

## 
## Call:
## lm(formula = exam ~ previous + facebook, data = master)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.6065 -0.7666 -0.3117  0.3850  7.9999 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.93294    0.56791   6.925 4.09e-11 ***
## previous     0.25954    0.08397   3.091  0.00224 ** 
## facebook    -0.60647    0.12705  -4.773 3.18e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.432 on 236 degrees of freedom
## Multiple R-squared:  0.1361, Adjusted R-squared:  0.1288 
## F-statistic: 18.59 on 2 and 236 DF,  p-value: 3.194e-08

Mediation: Interpretation

• Previous experience positively impacts exam scores (c path = 0.32).
• Previous experience negatively impacts Facebook time (a path = -0.09).
• Controlling for previous experience, Facebook time negatively impacts exam scores (b path = -0.61).
• Controlling for Facebook scores, previous experience positively impacts exam scores (c’ path = 0.26).
• So, did mediation happen? Is a change from 0.31 to 0.26 important?

Mediation: Sobel Test

• The Aroian Test: \(Z = \frac{a \times b}{\sqrt{b^2 \times SD_a^2 + a^2 \times SD_b^2 + SD_a^2 \times SD_b^2}}\)

• If the indirect effect is larger than the error, we would conclude that the addition of the M variable changed the c path.

  • Fill in the correct coefficient numbers
  • Note if you use this code provided and fill in X and M in the correct order, you will not need to change the Sobel code.

#aroian sobel
a <- coef(model2)[2]
b <- coef(model3)[3]
SEa <- summary(model2)$coefficients[2,2]
SEb <- summary(model3)$coefficients[3,2]
zscore <- (a*b)/(sqrt((b^2*SEa^2)+(a^2*SEb^2)+(SEa^2*SEb^2)))
zscore

## previous 
## 1.937494

#two tailed test 
pnorm(abs(zscore), lower.tail = F)*2

##   previous 
## 0.05268497

Mediation: Sobel Test

• Z = 1.93, p = .053
• We would conclude that no mediation had occurred.

Mediation: All Together + Bootstrapping

State of the Art (2026): In professional data science settings, while MeMoBootR is excellent for learning and quick “all-in-one” analysis, you will often see the lavaan package (for Structural Equation Modeling) or the mediation package used for complex mediation models. These are the industry standards for publication-quality analysis.

# Ensure a CRAN mirror is set
if(is.null(getOption("repos"))) {
  options(repos = c(CRAN = "https://cloud.r-project.org"))
}

# Install devtools if missing
if (!requireNamespace("devtools", quietly = TRUE)) {
  install.packages("devtools")
}

# Install MeMoBootR if missing
if (!requireNamespace("MeMoBootR", quietly = TRUE)) {
  message("Installing MeMoBootR from GitHub...")
  tryCatch({
    devtools::install_github("doomlab/MeMoBootR", force = TRUE, upgrade = "never", quiet = TRUE)
  }, error = function(e) {
    warning("Failed to install MeMoBootR: ", e$message)
  })
}

## Installing MeMoBootR from GitHub...

# Load the package
if (require("MeMoBootR")) {
  #no missing data allowed
  med_results <- mediation1(y = "exam",
                            x = "previous", 
                            m = "facebook", 
                            df = master)
} else {
  message("MeMoBootR package is not available. Mediation results cannot be generated.")
  # Create a dummy object to prevent future errors
  med_results <- list(
    datascreening = list(fulldata = NULL, correl = NULL, linearity = NULL, normality = NULL, homogen = NULL),
    model1 = NULL, model2 = NULL, model3 = NULL,
    indirect.effect = NULL, z.score = NULL, p.value = NULL,
    boot.results = NULL, boot.ci = NULL, diagram = NULL
  )
}

## Loading required package: MeMoBootR

## Warning in library(package, lib.loc = lib.loc, character.only = TRUE,
## logical.return = TRUE, : there is no package called 'MeMoBootR'

## MeMoBootR package is not available. Mediation results cannot be generated.

Mediation: MeMoBootR

• The MeMoBootR package gives you data screening, each step of the mediation, and the bootstrapping results!
• The data screening does not include accuracy or missing data, so that should be completed first.

head(med_results$datascreening$fulldata)

## NULL

med_results$datascreening$correl

## NULL

med_results$datascreening$linearity

## NULL

med_results$datascreening$normality

## NULL

med_results$datascreening$homogen

## NULL

Mediation: MeMoBootR

• For each of our stages of mediation, you can print out the models:

summary(med_results$model1)

## Length  Class   Mode 
##      0   NULL   NULL

summary(med_results$model2)

## Length  Class   Mode 
##      0   NULL   NULL

summary(med_results$model3)

## Length  Class   Mode 
##      0   NULL   NULL

Mediation: MeMoBootR

• Next, you can get the Sobel test results:

med_results$indirect.effect

## NULL

med_results$z.score

## NULL

med_results$p.value

## NULL

Mediation: MeMoBootR

• Last, let’s get the bootstrapped results:

  • The indirect effect would be reported as: \(0.06, 95\% CI[-0.01, 0.12]\)

med_results$boot.results

## NULL

med_results$boot.ci

## NULL

med_results$diagram

## NULL

Moderation

• The combined effect of two variables on another is known conceptually as moderation, and in statistical terms as an interaction effect.

Plain English: Moderation is the “It Depends” variable. If I ask, “Does eating pizza make you happy?”, you might say, “It depends on if I’m hungry.” Hunger is the moderator.

• In statistics, we say the relationship between X and Y changes depending on the level of Z.
• Graphically, this looks like non-parallel lines. If the lines cross or fan out, you have an interaction.

• Do violent video games make people aggressive?

  • DV: Aggression

  • IV:

    • Callous unemotional traits
    • Number of hours spent playing video games per week
    • Interaction

Conceptual Moderation Model

• If callous-unemotional traits were a moderator then we’re saying that the strength or direction of the relationship between game playing and aggression depends on the strength of callous-unemotional traits.

Conceptual Moderation Model

• If the X variable was categorical, you are basically checking if the separate groups (levels) have different slopes for the non-categorical variable.

Conceptual Moderation Model

• However, if X is continuous, we have to find a new way to figure out the shape of the interaction.

Statistical Moderation Model

Centering variables

• The interaction term makes the bs for the main predictors uninterpretable in many situations.

• Centering refers to the process of transforming a variable into deviations around a fixed point.

• Centering solves two problems:

  • Interpretation
  • Multicollinearity

Plain English: Why do we center?

1. Interpretation: In regression, the Intercept is the value of Y when X is 0. If X is “Heart Rate”, 0 is dead. That’s not useful. If we center X (subtract the mean), then 0 becomes the “Average Heart Rate”. Now the intercept is the score for the average person.
2. Multicollinearity: X and XZ are highly correlated because X is inside XZ. Centering breaks this correlation, making the math more stable.

Centering variables

• Easiest way to center to make them useful:

  • Score - Mean for that variable.
  • What does that do?

• Centered variables for main effects have two interpretations

  • Effect of that predictor at the mean value for the sample
  • Average effect of the predictor across a range of scores for the other predictor

Moderation: Simple Slopes

• If the interaction is significant, then you usually ignore the main effects (each variable by itself).
• So what do I do if my interaction is significant? A simple slope analysis
• If variables are categorical, then you are simply looking at the differences across one variable or another

Moderation: Simple Slopes

• For continuous variables, you “create” low, average, and high groups.

  • Low groups are people who are one SD below the mean
  • Average groups are people are at the mean
  • High groups are people who are one SD above the mean
  • However, creating groups is backwards from what you think.

Moderation: Simple Slopes

• We are examining the interaction between hours of video games and unemotional traits to predict aggression
• Think about which variable you want to know the differences in (i.e., low, average, high).
• So at different levels of callousness, we want to examine the relationship between hours of video games and aggression.

master <- import("data/moderation.sav")
str(master)

## 'data.frame':    442 obs. of  4 variables:
##  $ ID        : num  69 55 7 96 130 124 72 139 102 179 ...
##   ..- attr(*, "label")= chr "Case ID"
##   ..- attr(*, "format.spss")= chr "F3.0"
##  $ Aggression: num  13 38 30 23 25 46 41 22 35 23 ...
##   ..- attr(*, "label")= chr "Agression"
##   ..- attr(*, "format.spss")= chr "F2.0"
##  $ Vid_Games : num  16 12 32 10 11 29 23 15 20 20 ...
##   ..- attr(*, "label")= chr "Video Games (Hours per week)"
##   ..- attr(*, "format.spss")= chr "F2.0"
##  $ CaUnTs    : num  0 0 0 1 1 1 2 3 3 3 ...
##   ..- attr(*, "label")= chr "Callous Unemotional Traits"
##   ..- attr(*, "format.spss")= chr "F2.0"

Moderation: Centering

• Center your variables using scale()

  • Using scale = F turns off dividing by SD, which would create z-scores.
  • You can use z-score centering if you wanted the coefficients to be beta. It is likely easier to interpret the b values though.

#center the X and M variable (NOT THE DV)
#when you create these use the final dataset 
master$zvid = scale(master$Vid_Games, scale = F) #mean center, not z score
master$zcal = scale(master$CaUnTs, scale = F)

Moderation: Running

• For data screening, we would screen the model with the interaction, and all other considerations are the same as regression.

• Run the model:

  • You do not have to create an interaction column, to multiply does that automatically for you.
  • Also includes the main effects of each variable by itself.

#run the model to see if the moderation is significant
#use the z score variables!
#be sure to do X*M so the graph is right 
modmodel <- lm(Aggression ~ zvid*zcal, data = master)

Moderation: Interpretation

• Overall model is significant, \(F(3, 438) = 88.46, p < .001, R^2 = .38\)
• Interaction effect is significant, \(b = 0.03, t(438) = 3.88, p < .001\)

summary(modmodel)

## 
## Call:
## lm(formula = Aggression ~ zvid * zcal, data = master)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -29.7144  -6.9087  -0.1923   6.9036  29.2290 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 39.967108   0.475057  84.131  < 2e-16 ***
## zvid         0.169625   0.068473   2.477 0.013616 *  
## zcal         0.760093   0.049458  15.368  < 2e-16 ***
## zvid:zcal    0.027062   0.006981   3.877 0.000122 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.976 on 438 degrees of freedom
## Multiple R-squared:  0.3773, Adjusted R-squared:  0.373 
## F-statistic: 88.46 on 3 and 438 DF,  p-value: < 2.2e-16

Moderation: Simple Slopes

• So, how do we create groups when we have a continuous variable?

  • Most people look at “low” as one SD below the mean and “high” as one SD above the mean.
  • Lots of combinations are possible though.

Moderation: Simple Slopes

• Create the low and high versions of the M variable (callousness in this example)

  • Low created by ADDING a SD
  • High created by SUBTRACTING a SD
  • The rule is that we have to bring them to the middle because we centered so that zero is the middle

#create the low and high z score variables 
master$zcallow <- master$zcal + sd(master$zcal) #bring them up
master$zcalhigh <- master$zcal - sd(master$zcal) #bring them down
summary(master)

##        ID          Aggression      Vid_Games         CaUnTs    
##  Min.   :  1.0   Min.   : 9.00   Min.   : 1.00   Min.   : 0.0  
##  1st Qu.:111.2   1st Qu.:32.00   1st Qu.:17.00   1st Qu.:11.0  
##  Median :221.5   Median :40.00   Median :22.00   Median :18.0  
##  Mean   :221.5   Mean   :40.05   Mean   :21.84   Mean   :18.6  
##  3rd Qu.:331.8   3rd Qu.:48.00   3rd Qu.:26.00   3rd Qu.:26.0  
##  Max.   :442.0   Max.   :82.00   Max.   :38.00   Max.   :43.0  
##            zvid.V1                     zcal.V1          
##  Min.   :-2.08438914027e+01   Min.   :-18.595022624400  
##  1st Qu.:-4.84389140271e+00   1st Qu.: -7.595022624430  
##  Median : 1.56108597285e-01   Median : -0.595022624434  
##  Mean   : 1.00000000000e-15   Mean   :  0.000000000000  
##  3rd Qu.: 4.15610859729e+00   3rd Qu.:  7.404977375570  
##  Max.   : 1.61561085973e+01   Max.   : 24.404977375600  
##         zcallow.V1               zcalhigh.V1       
##  Min.   :-8.97732952676   Min.   :-28.21271572210  
##  1st Qu.: 2.02267047324   1st Qu.:-17.21271572210  
##  Median : 9.02267047324   Median :-10.21271572210  
##  Mean   : 9.61769309767   Mean   : -9.61769309767  
##  3rd Qu.:17.02267047320   3rd Qu.: -2.21271572211  
##  Max.   :34.02267047320   Max.   : 14.78728427790

Moderation: Simple Slopes

• Then run the model with the new low and high versions of the variable.
• What do I do with that?
• You look at the other variable because the coefficients for M and X*M will not change.

#run the models
#be sure to X*M
modmodellow <- lm(Aggression ~ zvid*zcallow, data = master)
modmodelhigh <- lm(Aggression ~ zvid*zcalhigh, data = master)

Moderation: Simple Slopes

• At low levels of callousness, video game hours is unrelated to aggression, b = -0.09 …

summary(modmodellow) #low slope

## 
## Call:
## lm(formula = Aggression ~ zvid * zcallow, data = master)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -29.7144  -6.9087  -0.1923   6.9036  29.2290 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  32.656771   0.672018  48.595  < 2e-16 ***
## zvid         -0.090651   0.099105  -0.915 0.360854    
## zcallow       0.760093   0.049458  15.368  < 2e-16 ***
## zvid:zcallow  0.027062   0.006981   3.877 0.000122 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.976 on 438 degrees of freedom
## Multiple R-squared:  0.3773, Adjusted R-squared:  0.373 
## F-statistic: 88.46 on 3 and 438 DF,  p-value: < 2.2e-16

Moderation: Simple Slopes

• At average levels of callousness, hours of video games predicts increasing aggression, b = 0.17 …

summary(modmodel) #average slope

## 
## Call:
## lm(formula = Aggression ~ zvid * zcal, data = master)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -29.7144  -6.9087  -0.1923   6.9036  29.2290 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 39.967108   0.475057  84.131  < 2e-16 ***
## zvid         0.169625   0.068473   2.477 0.013616 *  
## zcal         0.760093   0.049458  15.368  < 2e-16 ***
## zvid:zcal    0.027062   0.006981   3.877 0.000122 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.976 on 438 degrees of freedom
## Multiple R-squared:  0.3773, Adjusted R-squared:  0.373 
## F-statistic: 88.46 on 3 and 438 DF,  p-value: < 2.2e-16

Moderation: Simple Slopes

• At high levels of callousness, the strength of hours of video games predicting aggression is the strongest, b = 0.43 …

summary(modmodelhigh) #high slope

## 
## Call:
## lm(formula = Aggression ~ zvid * zcalhigh, data = master)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -29.7144  -6.9087  -0.1923   6.9036  29.2290 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   47.277446   0.672520  70.299  < 2e-16 ***
## zvid           0.429901   0.092577   4.644 4.53e-06 ***
## zcalhigh       0.760093   0.049458  15.368  < 2e-16 ***
## zvid:zcalhigh  0.027062   0.006981   3.877 0.000122 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.976 on 438 degrees of freedom
## Multiple R-squared:  0.3773, Adjusted R-squared:  0.373 
## F-statistic: 88.46 on 3 and 438 DF,  p-value: < 2.2e-16

Moderation: Simple Slopes

• Significant interactions will create fan effects of slopes that either get stronger/weaker in strength or switch directions.
• Here, we find that increasing levels of callousness leads to increasing effects of video game time on aggression.

Moderation: Graphing

• We can use the ggplot to create a graph of the moderation effect.
• But we are going to manually draw the lines on a scatterplot graph.

library(ggplot2)
cleanup <- theme(panel.grid.major = element_blank(), 
                panel.grid.minor = element_blank(), 
                panel.background = element_blank(), 
                axis.line.x = element_line(color = "black"),
                axis.line.y = element_line(color = "black"),
                legend.key = element_rect(fill = "white"),
                text = element_text(size = 15))

modgraph <- ggplot(master, aes(zvid, Aggression))

##change Cal to the new moderator label
##change xlab for the new X label
modgraph + 
  xlab("Centered Video Games") + 
  geom_point(color = "gray") +
  geom_abline(aes(intercept = modmodellow$coefficients[1],
                  slope = modmodellow$coefficients[2], 
                  linetype = "-1SD Cal"), size = 1) +
  geom_abline(aes(intercept = modmodel$coefficients[1],
                  slope = modmodel$coefficients[2], 
                  linetype = "Average Cal"), size = 1) +
  geom_abline(aes(intercept = modmodelhigh$coefficients[1],
                  slope = modmodelhigh$coefficients[2], 
                  linetype = "+1SD Cal"), size = 1) +
  scale_linetype_manual(values = c("dotted", "dashed", "solid"),
                        breaks = c("-1SD Cal", "Average Cal", "+1SD Cal"),
                        name = "Simple Slope") +
  cleanup 

Moderation: MeMoBootR

• We can use the MeMoBootR to complete the entire processing, including data screening for us!
• You would enter the raw variables, as the centering is completed for you.

if (exists("moderation1")) {
  mod_model <- moderation1(y = "Aggression",
                           x = "Vid_Games",
                           m = "CaUnTs",
                           df = master)
} else {
  mod_model <- list(
    datascreening = list(fulldata = NULL),
    model1 = NULL,
    interpretation = "MeMoBootR not available.",
    graphslopes = NULL
  )
}

Moderation: MeMoBootR

#data screening
head(mod_model$datascreening$fulldata)

## NULL

#mod_model$datascreening$correl
#mod_model$datascreening$linearity
#mod_model$datascreening$normality
#mod_model$datascreening$homogen

#models
summary(mod_model$model1)

## Length  Class   Mode 
##      0   NULL   NULL

#summary(mod_model$model1low)
#summary(mod_model$model1high)
mod_model$interpretation

## [1] "MeMoBootR not available."

#graphs
mod_model$graphslopes

## NULL

Summary

• In this lecture, we have covered:

  • Mediation
  • Moderation
  • Special packages for these models
  • Follow ups for these models