M3 - Moderation and Mediation

Question 1

Part A - Question 1: When a variable acts as a moderator, what does this mean?

​​​​​​When it is testing a causal pathway.
​​​​​​When it is the third variable in a regression model.
​​​​​​That the effect of the IV on the DV depends on the values of another variable.
​​​​​​​When it is the DV in a hypothesis test

Answer 1

​​​​​​That the effect of the IV on the DV depends on the values of another variable.

Question 2

Part A - Question 2: Does a moderator variable need to be categorical?

​​​​​​Yes, moderators must be always be categorical if it is to examine how categories effect the IV.
​​​​​​​No, moderators, can be either categorical or continuous.
​​​​​​​No, moderators can only be continuous if it is to examine how the IV effects the DV.
Yes, moderators must always be categorical if it is to examine how categories effect the DV.

Answer 2

No, moderators, can be either categorical or continuous.

Question 3

Part A - Question 3: According to Baron and Kenny, when is a moderator variable usually introduced?

​​​​​​​When the DV produces quirky results.
​​​​​​​When the IV is unexpectedly significant.
When exploring the strength of the IVs.
​​​​​​​When there is a weak or inconsistent relationship

Answer 3

​​​​​​​When there is a weak or inconsistent relationship

Question 4

Part A - Question 4: Is the relationship between the moderator variable on the IV and DV always linear?

​​​​​​​No, a moderator relationship can be linear, non-linear and stepped.
​​​​​​​Yes, a moderator relationship is always linear.
​​​​​​​No, moderators are mostly non-linear.
Yes, a moderation relationship is linear as multiple regression is a linear model

Answer 4

​​​​​​​No, a moderator relationship can be linear, non-linear and stepped.

Question 5

Part A - Question 5: Is the following regression equation, which is the moderating variable: Y = c + d1x + d2z + d3xz + error

c.
​​​​​​​d1x + d2z.
error.
​​​​​​​d3xz

Answer 5

​​​​​​​d3xz

Question 6

Part A - Question 6: Moderation tests a causal pathway?

Yes, moderation tests a causal pathway.
​​​​​​​No, moderation does not test a causal pathway.
​​​​​​Yes, moderation tests multiple causal pathways.
​​​​​​​No moderation is a regression significance test.

Answer 6

​​​​​​​No, moderation does not test a causal pathway.

Question 7

Part B - Question 1: A moderator variable is another word for:

​​​​​​​Categorical variable.
​​​​​​Interaction variable.
Dependent variable.
​​​​​​​Mediator

Answer 7

​​​​​​Interaction variable.

Question 8

Part B - Question 2: What is centering?

It is the same as creating the mode for a variable.
​​​​​​​When the center of the distribution is used for all variables.
​​​​​​​When every case for a variable is given a mean value.
​​​​​​​When every case for a variable is subtracted from a common value, usually the mean of the variable

Answer 8

​​​​​​​When every case for a variable is subtracted from a common value, usually the mean of the variable

Question 9

Part B - Question 3: While there is debate about centering variables, when examining interactions what is one of the arguments for centering interaction variables?

It creates a cleaner data set.
It helps with transforming data so they are not skewed.
Helps interpret the intercept of the regression output.
Reduces problems associated with multicollinearity.

Answer 9

Reduces problems associated with multicollinearity.

Question 10

Part B - Question 4: Does the method of interpreting the interaction change if other control variables are introduced into the regression model?

​​​​​​The model is different and must be interpreted completely differently.
​​​​​​​The interaction term is not interpreted in the same way, as the beta coefficient may change.
​​​​​​​Once you introduce other variables the interaction must be analysed differently.
​​​​​​The interaction term is interpreted in the same way, however the beta coefficient may change

Answer 10

​​​​​​The interaction term is interpreted in the same way, however the beta coefficient may change

Question 11

Part C - Question 1: What is meant when we use the term non-additivity?

That for different values of independent variables the relationship with the dependent variable and the moderator may differ?.
That the total effect is the sum of the direct and indirect effect.
That we cannot add a categorical and continuous variables.
The moderator needs to be examined in a standardized way

Answer 11

That for different values of independent variables the relationship with the dependent variable and the moderator may differ?.

Question 12

Part C - Question 2: What is an effective way of trying to understand the non-addivity relationship of an interaction variable?

Checking log likelihood change when adding the interaction variable.
Examining the magnitude of the slope of the interaction variable.
Plotting values of the interaction variable.
Doing a significance test

Answer 12

Plotting values of the interaction variable.

Question 13

Part C - Question 3: What utility can be used with SPSS to help plot interactions?

R utility.
Amos utility.
Process utility.
Stata utility

Answer 13

Process utility.

Question 14

Part C - Question 4: A plot of simple slopes with a significant interaction should have lines that are:

Similar slopes for all lines.
Exactly parallel slopes.
Slopes that are not parallel.
The same slopes for all lines.

Answer 14

Slopes that are not parallel.

Question 15

Part D - Question 1: A mediation analyses is examining what?

A causal pathway, and whether there is and intervening variable between the IV and DV.
There are non-additive and non-linear relationships.
The strength of a linear relationship.
Whether the strength of IV and DV is affected by another variable.

Answer 15

A causal pathway, and whether there is and intervening variable between the IV and DV.

Question 16

Part D - Question 2: If using regression Baron and Kenny suggest how many regression models should be run:

One: This tests the total effect.
Four: This tests all the paths in the causal pathway, a b, c & c`.
Three: This tests the total effect, direct and indirect effect.
Two: This will allow the total effect and mediated effect.

Answer 16

Three: This tests the total effect, direct and indirect effect.

Question 17

Part D - Question 3: Using the Baron and Kenny approach, and the figures here, when is full mediation identified?

When c is not significant.
When c is reduced in magnitude compared to c. When c is not significant and c was originally significant.
When b is not significant

Answer 17

When c` is not significant and c was originally significant.

Question 18

Part D - Question 4: Using the Baron and Kenny approach, and the figures here, when is partial mediation identified?

Part D - Q3

When b is not significant.
When c is not significant.
When c is not significant and c was originally significant. When c is reduced in magnitude compared to c

Answer 18

When c` is reduced in magnitude compared to c

Question 19

Part D - Question 5: Using the Baron and Kenny approach, and the figures here, when is no mediation?

Part D - Q3

When b is not significant.
When c is not significant.
When c is not significant and c was originally significant. When c is reduced in magnitude compared to c

Answer 19

When b is not significant.

Question 20

Part E - Question 1: Mediation can be used to test multiple causal pathways. How many independent variables are used in the Bosco Rowland article examining alcohol management strategies?

Three.
One.
Eleven.
Two

Answer 20

Eleven.

Question 21

Part E - Question 2: What statistical program is used to test for mediation?

Mplus.
Stata.
SPSS.
R

Answer 21

Mplus.

Question 22

Part E - Question 3: Must mediation analyses be done with only continuous variables?

No, the IV, MV and DV can be either binary or continuous.
Yes, but the IV can be binary/dichotomous.
Yes, mediation must be done with continuous variables for IV, MV & DV.
No, however, the DV must always be continuous

Answer 22

No, the IV, MV and DV can be either binary or continuous.

Question 23

Part F - Question 1: When using SPSS to run a mediation analyses, what three key output results are produced?

Total effect (a*b), direct effect (c`); and indirect effect (c).
Total effect (a*b*c), direct effect (a*b); and indirect effect (c).
Total effect (c), direct effect (c`); and indirect effect (a*b).
Total effect (c`), direct effect (c); and indirect effect (a).
Check

Answer 23

Total effect (c), direct effect (c`); and indirect effect (a*b).

Question 24

Part F - Question 2: Mediation can expressed in the following way:

direct effect = total effect + indirect effect.
total effect = direct effect - indirect effect.
indirect effect = direct effect + total effect.
total effect = direct effect + indirect effect

Answer 24

total effect = direct effect + indirect effect

Question 25

Part F - Question 3: Mathematically, mediation can also be expressed in the following way:

c` =  c +   (a*b).
c =  c’ +   (a*b).
c =  c’ +   (a*b*c).
(a*b) =  c’ +   c

Answer 25

c = c’ + (a*b).

Question 26

Part F - Question 4: Mediation effect sizes can be used to assess:

Whether paths are significantly mediated.
How much of the total effect is mediated.
The magnitude of the mediator regression coefficients.
The percentage of variance in the mediated model

Answer 26

How much of the total effect is mediated.

Question 27

Part F - Question 5: According to Fergusson (2009), a moderate to large effect size is greater than:

<= .04.
>=.64.
>=.25.
<= .25.

Answer 27

> =.25.

Question 28

What is moderation in statistical analysis?

Answer 28

Moderation is when the impact of the IV on the DV depends on the value of the MV

Rather than being a strictly causal link, a moderation analysis tests the strength of the impact of the IV on the DV under changing conditions of MV

Interaction equation can be expressed as:
Y = a + b1x + b2z + b3xz

Question 29

When should you use a moderation analysis?

Answer 29

single or multiple IVs
categorical, dichotomous or continuous IVs
single, categorical or continuous DVs
If variables are binary then you would do a probit regression analysis (binary DV)

Question 30

What are the assumptions of moderation analysis?

Answer 30

As moderation analysis is a regression analysis still need to ensure assumptions are met

1 - linearity - there must be a linear relationship between the IV and the DV
2 - residuals are normally distributed
3 - no multicollinearity (IVs must not be high correlated)

Question 31

What is centring, what does it do and when should it be used?

Answer 31

Centring is used with moderation regression analysis when there is evidence of colinearity or multicollinearity between IVs
- colinearity likely between IVs and interaction because the interaction term comes from the individual IVs
- centring can occur with any meaningful constant, but often the grand mean is used
- subtract the data from the grand mean or constant before creating the interaction term
- centring can also help with the interpretation of the interaction
NOTE: if the data is nonlinear, it must be transformed first before centring

Question 32

Explain how you would undertake a moderation analysis.

Answer 32

Assumptions have been met
To centre data, subtract the original score from the grand mean for each variable before creating interaction variable.

But in the PROCES tool you can just select the mean centering option

Using the PROCESS tool in SPSS

• select Model 1 for moderation
• Set bootstrap samples to 1000 via Bias Corrected method
• Click options and select:
  
  • mean centre
  • heteroscedasticity-consistent SEs
  • OLS/ML confidence intervals
  • Generate data for plotting
• Click Conditioning and select:
  
  • Mean and +/- 1SG from Mean
  • Johnson-Newman

Question 33

Explain how you would interpret the output of a moderation analysis.

Answer 33

1 - R-sq value refers to total variance in the DV explained by main effects and interaction effect

2 - Interpret the interaction term if significant (p < .05)

3 - If interaction term is not significant, remove it from the model, then look to the main effects

4 - check the conditional effects (simple slopes) to help interaction interpretation

5 - Check Johnson-Newman output to determine at which points of the MV the IV significantly predicts the DV

6 - plot interaction effect or simple slopes using PROCESS GGRAPH function

Question 34

What is mediation in statistical analysis?

Answer 34

• mediation is a causal relationship
• mediation occurs when an MV explains the effect of the IV on the DV
  that is iV–>MV–>DV

mediation is expressed as
Total effects = direct + indirect effects
c = c’ + a*b

Question 35

When should you use a mediation analysis?

Answer 35

Multiple IVs - can be categorical or continuous
Single DV - can be categorical or continuous

Use mediation analysis when the impact of the IV
Baron & Kenny (1986) said that mediation should be tested through these 3 linear models:

linear model that IV predicts DV - path c
linear model that IV predicts MV - path a
linear model that IV and MV predict DV - path b (MV–>DV component) path c’ is IV–> DV component

Assumptions are the same as other regression models

• normality
• independence of errors
• homogeneity of error variance (homoscedasticity)
• linearity

Question 36

Explain how you would undertake a mediation analysis.

Answer 36

Options:

• Use Process Utility in SPSS
• Can also use SEM Path Models
• Other Software packages eg Mplus

In SPSS - Test 3 models
1 - IV–>DV - path c
2 - IV–>MV - path a
3 - MV–>DV (path b) and IV –>DV (path c’)

Enter variables into PROCESS Tool
Select Model 4 for Mediation
Click Options and Select:
- Heteroscedasticity-consistent SEs
- OLS/ML confidence interval
- Effect size (mode 4 and 6 only)
- Total effect model (models 4 and 6 only)

All pertinent results are in the Total, Direct and Indirect Effect Table
Total effect is path c
Direct effect is path c’
Indirect effect is path a*b

Select 1000 Bootstrap Samples and Bias Corrected CI method. Run analysis

Question 37

Explain how you would interpret the output of a mediation analysis.

Answer 37

All pertinent results are in the Total, Direct and Indirect Effect Table in SPSS PROCESS Utility output

If Total effect c is significant, and Direct effect c’ is not significant, full mediation has occurred

If Total effect c is significant and Direct effect is significant but reduced relative to direct effect c, partial mediation has occurred

For Indirect effect - look to BootLLCI and ULCI for significance
- If they cross 0 then non-significant, if they do not cross 0 then it is significant and mediation has occured

Effect Size
Kappa squared is preferred and reflects the effect size amount as a percentage of the maximum it could be
eg Kappa2 of .0724 indicates the effect size is 7.24% of the maximum effect it could be

If the Bootstrapped CIs do not cross zero there is 95% confidence that the effect size is significant

Use Fergusons 2009 guidelines for interpreting effect size.
< .04 is trivial
.04-.25 is small
.25 to.64 is moderate
>.64 is large

So the above effect size is small and significant

Question 38

Explain the statistical path conditions for full mediation, partial and no mediation

Answer 38

Full mediation
when c (total effects) becomes non-significant (ie c' is not significant)

Partial mediation
when c is reduced in magnitude (ie beta coefficient becomes smaller)

No mediation
if path a or b are nonsignificant (IV–>MV or MV–DV)

Question 39

What is Kappa squared?

Answer 39

Kappa squared is an effect size measure used in mediation regression analysis
-reflects the effect size as a percentage of the maximum possible mediation effect given the size of the relationship between the IV and the DV
- range = 0-1
1 indicates mediation effect is the maximum (strongest) it could be, 0 indicate mediation effect is the lowest (weakest) it could be

Question 40

What are Fergusons 2009 guidelines and when should they be used

Answer 40

Use for interpreting effect size (Kappa2) and Total Variance Explained (R2)
< .04 is trivial
.04-.25 is small
.25 to.64 is moderate
>.64 is large

Question 41

How do you calculate how much of the total effect is mediated and what does it mean?

Answer 41

Proportion of indirect effects / total effects
= a*b/c x 100
NB The proportion of mediated effect refers to the effect size but it can produce misleading values if the likert scales are different
Therefore Kappa2 is preferable for calculating effect size