Lecture 26 - Moderation Analysis

Question 1

What is moderation analysis in other words?

Answer 1

A model that includes an interaction effect, so one variable influencing the effect of another variable

Question 2

What does a moderator do?

Answer 2

A moderator moderates behaviour (duh), so in moderation analysis there is a variable that moderates the influence of another variable.

Question 3

What is moderation in fancy words?

Answer 3

Moderation occurs when the relationship between two variables depends on a third variable.
The third variable is referred to as the moderator variable or simply the moderator.
The effect of a moderating variable is characterized statistically as an interaction.
Conceptually, it’s moderation

Question 4

What is the regression equation for moderation?

Answer 4

Look at figure 1.
The variables include

• The intercept (b0)
• The standalone effect of the predictor (b1)
• The standalone effect of the moderator (b2)
• The interaction effect between predictor and moderator (b3)

Question 5

How do we determine which variable is the moderator and which is the predictor?

Answer 5

It’s extremely arbitrary (WOOO ARBITRARY IS BACK GUYS).
They are simply two continuous predictor variables that have an interaction between them. Since an interaction effect is perfectly symmetrical, it doesn’t matter which variable is what.

It’ll become clearer when i bring in the example

Question 6

How can you visualize a conceptual moderation effect?

Answer 6

With a diagram.
Look at figure 2.

Question 7

How is a moderation diagram different from a mediation diagram?

Answer 7

Besides the obvious differences, in a mediation diagram, the arrows go into the variables, showing they go through the mediator.
In a moderation diagram, the arrow goes to the line, showing that a moderator doesn’t directly affect the variables, rather it influences the effect of another variable.

Question 8

What does a statistical moderation model look like?

Answer 8

Look at figure 5 (shhhh), it represents the regression equation in diagram form. To see the full moderation analysis, you need all 3 boxes.

(This also helps understand why it doesn’t matter which predictor variable is labelled as moderator. They’re multiplied together, so it’ll be the same.
23=6, and 32=6, changing the order doesn’t matter)

Question 9

What does the regression equation/model tell us?

Answer 9

It tells you specifically what the model is predicting for each beta coefficients.

Question 10

How do you visualize an interaction effect with a 3d plot?

Answer 10

Look at figure 3.
The left graph shows that without an moderation/interaction, the plane of data is flat. If you looked at the graph from the side where the arrows end, it would be a straight line.

The right graph shows that with a moderation/interaction effect, the plane looks like a pringles chip (use this to remember how interaction effect looks in 3d).
Different levels of videogames on aggression for different levels of callous traits.
If you looked at the graph from the same side as before, you’d see a jumble of data kinda like a skewed bowtie (or farfalle for eli)

Question 11

What is the example used in the book? (just read the answer so you’re aware and have another example, but ill discuss johnny’s one cus it is superior (i watched the lecture first))

Answer 11

Outcome is aggression
Predictors are Hours spent playing violent video games; and presence of callous traits.
They labelled callous traits as moderator, but it could be either since symmetrical interaction effect.

Question 12

Whats the example study that johnny uses (just read the answer)

Answer 12

The outcome is wakefulness (so how awake you’re feeling)
The two predictor variables are
The amount of coffee that they drank
The number of hours they’ve been awake for
(Si there will be an interaction effect)

Question 13

What would an interaction effect look like in this example?

Answer 13

The effect of coffee on your wakefulness depends on how long you’ve been awake for already.
Since interaction effects are symmetrical, you could also interpret it as
The effect of # of hours wake on your wakefulness depends on how much coffee you’ve drunk.

Question 14

What would a mediation effect look like?

Answer 14

A mediation analysis is for modelling the dependence between 2 variables
In this example, if hours awake is strongly associated with wakefulness. This association is mediated by coffee consumption.
Because maybe if you’re awake for longer, you consume more coffee. There is a direct association between one predictor variable and the other.

Question 15

So based on what we’ve learnt, how is mediation different to moderation?

Answer 15

In mediation, there is a dependence between variables, one predictor variable directly affects the other predictor variable.

In moderation, there is an interaction effect, one predictor variable influences the other predictor variable’s effect on the outcome.

Question 16

Why is mediation mentioned in moderation?

Answer 16

We are still doing a regression, so we need to be aware of possible mediation.
One of our core assumptions is multi collinearity, so we want to be aware if there is a strong dependence between predictor variables, because that affects our interpretation of our output.

Question 17

How can a correlation matrix indicate if we have multi collinearity?

Answer 17

Look at your two predictor variables, there should be a negligible correlation between them. If there is (e.g. r=0), this indicates no multi collinearity.

Question 18

What else should you do?

Answer 18

You can look at VIF, which is the formal assessment, however
VISUALIZE YOUR DATA
Make scatter plots.

Question 19

Why do we love scatter plots?

Answer 19

They can tell you about your association between predictor and outcome variables.

They can tell you about multicollinearity
You can use them to check for outliers
If they look weird, you’ve probably got an interaction effect going on

Question 20

Whats a good way to understand your interaction effect?

Answer 20

Divide one of your predictor variables into different levels (e.g. 0-100ml of coffee, 100-200ml, etc.)

This allows you to see if the association between the other predictor variable and the outcome variable changes depending on your moderator.

Question 21

Regression model for prediction.

Answer 21

Once you’ve got your equation, then chuck it into R to receive your regression estimates.
From this you can then make predictions of the outcome.
You can also find the t-value and test significance from there

(We won’t have to make the calculations ourselves, so im telling you what you can do with the data.)

Question 22

What do you do with the regression predictions?

Answer 22

Calculate the prediction of the outcome variable for every participant.
Look at figure 4 to see what the equation would look like.
You insert your beta coefficient predictions (the regression weights), then insert the participants values for each predictor variable.

Question 23

What specific meaning do beta coefficients have when an interaction term are included?

Answer 23

For the individual predictors they represent the regression of the outcome on that predictor when the other predictor is zero.
E.g. with johnnys example, b1 represents the relationship between hours awake and wakefulness when the amount of coffee drunk is zero.

Question 24

What issue do you notice if you apply the same logic to b2?

Answer 24

Well, b2 would represent the relationship between amount of coffee drunk and wakefulness, when the hours awake is zero…
wait a second, that don’t make sense, how can you drink coffee whilst asleep? hmmmm, lets go to the next flashcard to see a solution to this dilemma

Question 25

What is grand mean centering?

Answer 25

Also know as centering, it refers to the process of transforming a variable into deviations around a fixed point, in this case being the grand mean.

Question 26

How is centering done?

Answer 26

Well, JASP does it for you, but it’s done by taking each score and subtracting it from the mean of all scores. This centers the score around a point which you can then set as zero, with each score deviating from ‘zero’ by a certain amount.
You keep the variation in the score which is the important bit, but it allows you to calculate b when an interaction effect is involved.

Question 27

What is the highest-order predictor?
What are lower-order predictors?

Answer 27

Order refers to how many variables are involved.
Therefore, the highest-order predictor is the interaction parameter, cus it has 2 variables.
The lower-order variables are just the predictors by themselves.

Question 28

How are they both affected by centering?

Answer 28

Highest-order predictors aren’t affected by centering in any way.
Lower-order predictors are affected, but in a positive way.
When calculating b2, instead of it being when hours awake is zero, it’s now when hours awake is the average number. The coffee consumption is also centered, but its a good thing overall.

Question 29

In what case can you ignore centering?

Answer 29

If the interaction effect is significant. Because why look at the individual effect on the outcome if it differs based on the other variable? So you’d just look at the interaction effect.

Question 30

In figure 4, the regression weight of the moderator and the interaction effect are kinda small? is this an issue?

Answer 30

• it depends on the standard error
• in the simulated data, the standard error for the interaction effect is very small, so the t-value is very large, so it doesn’t matter.

Question 31

Is how we analyse total/explained variance different since we added a moderator?

Answer 31

No, since our model includes the interaction effect, so the explained variance includes this effect, you don’t need to do anything extra.
It’s the same as ANOVA and regression, we are just finding the proportion of explained and unexplained variance.

Question 32

Would our explained variance be different if we didn’t include the interaction effect?

Answer 32

Duh, it wouldn’t predict the data as well since the effect changes at different levels, so the line isn’t linear. By including the interaction effect, we account for that and make a better prediction.

Question 33

Why is the procedure so similar to other analysis methods, why is everything all the same?

Answer 33

Because the method we use is a good method. Where it fails is if we use bad measurements, or if we poorly operationalize the variables.
Danny’s lecture talks about this, but its mainly that if we don’t measure the interaction effect/aren’t aware of it, then we fucked up.

Question 34

You’ve found a significant moderation effect, how can you figure out what direction the interaction is in?

Answer 34

You do a simple slopes analysis, basically working out the regression equation for the different levels of the moderator (you decide them yourself).
Then you can compare the slopes in terms of both their significance and the value and direction of the b to see if the relationship between predictor and outcome changes at different levels of the moderator.

Question 35

How do you perform a moderation analysis in JASP?

Answer 35

2 methods.
1. Linear regression tab. (Same as multiple regression, but you add the interaction effect into your model (will be demonstrated in the jasp demo)
2. Process module (Done via Hayes configuration, but Johnny couldn’t get it to work during the lecture so I don’t think we will have to do it this way, so just learn linear regression)

Question 36

How do you isolate the interaction effect in JASP?

Answer 36

Do a hierarchical regression, which is where you go to the models tab, and add a new model (model 2) which has the interaction effect (see footnote)
Then make sure you have R squared change enabled under statistics.
You can then look at whether the model including the interaction effect is significant (since JASP compares it to the model above)
The R^2 change tells you how much predictive power the interaction effect adds.

If this is confusing, the JASP demo will explain better

(or you can add the predictors to the null model and put the interaction effect in model 1, you just need to have two models, one without the interaction effect, and the next one with it)

Question 37

How would you convert one of your continuous predictor variables into a categorical variable?

Answer 37

For coffee consumption, you would convert the ml drunk into cups of coffee, make sure to round down if you do so.

This gives you a categorical variable rather than a continuous variable.

Question 38

How is your jasp procedure different if you change coffee consumption into a nominal format?

Answer 38

You perform an ANCOVA since you have one continuous predictor and then a categorical predictor (with different people in each level, since you can’t have drunk 0 cups and 3 cups at the same time, unless you’re a magic man)

Question 39

Why do we need to be aware of which test method we use?

The next few flashcards (til 42) are a bit vague, just try and understand the concept

Answer 39

Johnny went back to the file explaining the different cool things in ANOVA, and why you have to use the correct method.

E.g. if you don’t include baseline differences, you can get nonsignificant, but if you do between samples ANOVA, then boom, significant

Question 40

Does regression give the same result as ANOVAs?

Answer 40

Yes, if you do a linear regression and don’t include baseline differences (through ID), then you get the same non-significant t-value as an ANOVA/2-sample t-test.

When you do include the baseline differences, you get significance and the same t-value as a paired samples T-test/between samples ANOVA

So, its really just the same

Question 41

So what are the differences between regression and ANOVA.

Answer 41

In ANOVA, you work with nominal variables so you can do post hoc tests and contrast analyses.
That isn’t possible with continuous predictive variables, so the options in linear regression are a bit different.

But to reiterate, the core of both analyses are the same, which we can see since we have an ANOVA table when doing linear regression.

Question 42

What does the ANOVA table mean for regression?

Answer 42

Since it gives you the total sum of squares, modelSS, etc.
It is called Equivalences in regression (basically saying its the same shit, different smell)

Question 43

So, how can you tell if there is an interaction/moderation effect?

Answer 43

Lots of ways, a quick way is to just add the interaction to a separate model, and then see if the r^2 change is significant.

Question 44

How can you visualise the interaction effect without converting into nominal format?

Answer 44

By making a flexplot

(Under Descriptives > Flexplot tab)

Add the outcome to dep. variable, and the two predictors to indep. variable. (whichever predictor is at the bottom of the list will be the one divided into groups.

Question 45

What can you learn from a flexplot?

Answer 45

It shows you the slope and error of each equation/model, allowing you to judge the effect of interaction.

Question 46

How do you report a moderation analysis?

Answer 46

You just need to provide a table that summarises the information, an example of which is figure 6. You should also include a table (figure 7)/graph (figure 8) that shows the interaction effect at different levels.

Question 47

What do the different values mean in figure 6?

Answer 47

The estimate is the estimate of the beta coefficient

Question 48

Snazzy little applet, what it do?

Answer 48

Lets you mess around with the interaction effect so you can understand it better.

Question 49

Based on the student study we did, what does the regression coefficient indicate?

Answer 49

It quantifies how much difference there is between every specialization and the reference group.
The reference group is the first occurring group