Week 8 Moderation & Mediation

Question 1

What is Path Analysis?

Answer 1

*A path analysis involves developing a theoretical model of direct and indirect paths among a set of variables, and testing which paths are significant

Question 2

What is a casual sequence in Path Analysis?

Answer 2

A variable can affect another variable directly or indirectly through other mediator variables.

• If there is a hypothetical causal sequence of 3 (or more) variables, the middle variable is considered a mediator (indirect effect).
• Suggesting representation of at least part of the chain of events leading to changes in the DV

Question 3

When might we use Path Analysis?

Answer 3

when you want to model observed variables through the direct and indirect effects of a mediating variable or, alternatively when you want to assess the impact (change) of the interaction of two variables on the relationship between two other variables (moderation)

Question 4

Baron & Kenny (1986) have done important work on moderation & mediation variables. But what are they?

Answer 4

*a third variable plays an important role in governing the relationship between two other variables

Question 5

What is a path diagram?

Answer 5

A path model is a diagram that outlines independent, intermediary, and dependent variables.

Question 6

What is replacing Path Analysis in popularity?

Answer 6

Mediation & Moderation Path Analysis may be undertaken as a series of multiple regression equations in SPSS; although, structural equation modelling is most often used and growing in popularity as it has greater complexity (AMOS, MPlus, Liseral).

Question 7

What is a mediating relationship?

Answer 7

• A mediating relationship attempts to identify a variable or variables through the IV, which acts to influence the DV.
• A Mediator is an indirect effect
• To “mediate” something is to stand in between two other things and pass on the effect of one to the other

Question 8

What is a moderating Relationship?

Answer 8

A moderating relationship is one where the relationship between the IV and DV change as a function of the level of a third (Moderator) variable

Question 9

What is the difference between a moderator & a mediator?

Answer 9

A moderator is an interaction effect

whereas a mediator is an indirect effect which impacts the DV

Question 10

How does Mediation & Moderation go beyond Multiple Regression?

Answer 10

Generally in regression we ask a question like “Does X predict Y?” we are looking at a direct relationship
*Moderators can look at when X causes Y
*Mediators can look at how or why X causes Y
Mediators have greater complexity & thus greater explanatory power

Question 11

our assumptions are initially the same as that of regular regression analysis, what are they?

Answer 11

*Sample size
*Outliers
*Normality, linearity, homoscedasticity.
*Multicollinearity and Singularity
*Levels of measurement – ensure reliable measures
Care needs to be taken with
1. Curvilinear relationships – ensure you check linearity
2. Interaction terms – don’t forget to centre your data (i.e. convert data to deviation scores!)

Question 12

What are the additional assumptions checks required for Mediation?

Answer 12

1. There is a significant relationship between the IV & DV
2. A significant relationship between IV & mediator exists
3. The mediator predicts DV after controlling for IV - HMR
4. The relationship between the DV and IV is reduced when the mediator is in the equation.

Question 13

What do Preacher & Hayes (2008) propose, NB: This is an opposing view to Baron & Kenny (1986)?

Answer 13

they propose that it is not necessary to have a significant relationship between the 3 paths (a x b = indirect effect on c)

Question 14

Jose (2013) has 3 requirements for mediation to occur, what are they?

Answer 14

1. In mediation we’re trying to gain greater depth of understanding about the Direct association or effect by checking the indirect path as well in the model.
2. Researchers need to predict all 3 relationships.
3. For mediation to occur, the proposed indirect path would be anticipated to reduce the strength of the “direct effect” once it is included in the model.

Question 15

When is a variable confirmed as a mediator?

Answer 15

A variable is confirmed as a mediator if;

• There is a sig relationship between the IV & DV
• There is a sig relationship between the IV & mediator
• The mediator still predicts the DV after controlling for the IV
• The relationship between the DV & the IV is reduced when the mediator is in the equation.

Question 16

So what does a mediator do again?

Answer 16

• A mediator variable explains the relationship between the predictor and criterion.
• A 3rd variable changes or adds further explanation of the relationship occurring between the predictor and criterion.

Question 17

What was the Jose (2013) mediation example we went through in class?

Answer 17

We’re interested whether Gratitude mediates (MV) the direct effect of the level of PLE on level of Happiness.

IV = Predictor – Positive Life Events (PLE)
DV = Criterion/Outcome – Happiness 
MV = Mediator – Gratitude

Direct path: PLE will predict Happiness.
Indirect path model: Gratitude would mediate the relationship between PLE and Happiness

Question 18

What are the 3 steps required to run the Jose’ model?

Answer 18

3 steps (regressions) are required:

1. Happiness to be regressed onto PLE (line a. Direct Effect)
2. Happiness to be regressed onto PLE & Gratitude (line b.)
3. Gratitude to be regressed on PLE (line c.)

Question 19

So all 3 questions were yes, thus the mediator model has met the criteria to undertake mediation according to Baron & Kenny (1986); what next?

Answer 19

1. test if the indirect effect is sig?
   i. e., is the drop in association between PLE & Happiness a significant drop?
2. Does Gratitude explain some of the variance in Happiness initially explained by PLE?

Question 20

So how do I test whether significant mediation has occurred?

Answer 20

• Calculatte the z values from the output (known as Sobel’s test):
  1. a x b =
  2. square root of a x b (provides the standard error of the indirect effect) which is then divided by a x b

NB: a and b are t scores produced by the output

Question 21

So how did Jose (2013) example turn out?

Answer 21

We can conclude that the relationship between PLE &
Happiness is partially mediated by Gratitude.
*Reduction from .49 (.07) to .27 (07) in regressions from PLE to Happiness shows mediation but ONLY partial mediation. PLE did not become non significant in HMR, therefore, only Partially mediated.

Question 22

Any other notes on calculating the estimate of indirect effects in Mediation?

Answer 22

Always include the confidence intervals

Question 23

What is the major purpose of moderation?

Answer 23

The major purpose of Moderation relates to the interaction of 2 variables, regardless of whether they are a combination of categorical or continuous measures.

*To create an interaction term, variables need to be centred, that is the scores need to be converted to deviation scores (value minus mean or converting to a mean of zero) to assist and not have multicollinearity presenting as not an issue

Question 24

What is another term for moderation?

Answer 24

Moderation means the same thing as interaction.
*When we say that ability moderates the effect of TV viewing on achievement, this is the same thing as saying that ability and TV viewing interact in their effect on achievement

Question 25

What can moderator variables do?

Answer 25

Moderator variables may strengthen or weaken the relationships between independent and dependent variables
*Moderation is best seen as an interaction Effect, one variable depends on the level of another variable

Question 26

When would I use moderation?

Answer 26

You need strong theoretical underpinnings for moderation to be used in research
*Moderation uses the same principle as the main effects & interactions in ANOVA
e.g. I’m interested in the effect of education & gender on income. Really asking whether levels of education show a different relationship for males or females on income.
OR Do males and females present differing slopes in education on the income in the regression equation

Question 27

How do I prepare my data for Moderation analysis?

Answer 27

*I need to create a new moderator variable (aka interaction), such as social support
*A moderator variable can be a combination of 2 continuous variables or a discrete variable plus a continuous variable
*copy each variable into new column
*Centre them individually (value minus mean i.e. deviation scores)
*Multiple to 2 together
this creates moderator variable

Question 28

What is a problem with centring both the variables that will become the moderator variable?

Answer 28

if both are negatives, the moderator will become a positive!

*Jose suggests only centring one to avoid this

Question 29

What does centring achieve?

Answer 29

Centring accommodates and controls for multicollinearity when the original values are already in the regression

Question 30

So how do I run an interaction term in Moderation?

Answer 30

*place 3 variables in the analysis.
*Place original variables of
(step1) social support,
then (step 2) gender as predictors in HMR model.
*3rd step of HMR - place the interaction term in to assess whether differences emerge on depression with the addition of the moderator.
*think of it like the interaction in ANOVA,