Mediation analysis is used to determine if a mediator variable explains the relationship between an independent and dependent variable. Baron and Kenny developed steps for mediation analysis including showing the independent variable predicts the dependent variable, predicts the mediator, and that the mediator predicts the dependent variable while reducing the effect of the independent variable. Total mediation occurs when the mediator fully explains the relationship, while partial mediation means the mediator only partially explains it. Limitations include needing strong theory to support mediators and being unable to manipulate mediators, while temporal precedence of variables and accounting for confounds can strengthen mediation analysis.

1. Mediation analysis
Practical statistics for practical people

2. Who uses
mediation
analysis?

3. What is mediation? A practical example.
● Previous studies have suggested that higher
grades predict higher happiness.
● I hypothesize that good grades boost one’s
self-esteem and then high self-esteem boosts
one’s happiness.
● Self-esteem is a mediator that explains the
underlying mechanism of the relationship
between grades

4. What is mediation? A practical example.
● A gene’s final produce is proteins
● A gene is transcribed into mRNA.
● Could mRNA mediate the production of Protein from a DNA sequence?

5. What is mediation? A practical example.
● The way you were parented influences your
confidence in parenting.
● How you were parented influences your confidence
and self-esteem.
● Could your self-esteem and feelings of confidence
influence your confidence parenting? Self-esteem
would be a mediator between how you were
parented and your confidence in parenting.

6. Mediation analysis in a nutshell
Baron and Kenny’s step for mediation analysis
● Step 1: Check that X is a significant predictor for Y
● Step 2: Check that X is a significant predictor for M
● Step 3: Regress X and M on Y and check that
○ M is a significant predictor of Y
○ X’s predicting power has reduced

7. Total and partial mediation
● Total mediation occurs if the inclusion of the mediator variables drops the
relationship between the independent and the dependent variable to 0.
● Partial mediation occurs when the mediator explains some but not all of the
relationships between dependent and independent variables.

8. Direct, indirect and total effects
● The direct effect corresponds to coefficient c.
● The indirect effect corresponds to the change in magnitude of the effect of X
on Y after controlling for the mediator
○ Indirect effect = (c’ - c) = ab
● The total effect is the sum of the direct effect and indirect effect:
○ Total effect = c + ab

9. The Sobel test and bootstrapping
● The Sobel test assesses the
significance of the indirect effect
○ ab / sigma
● The normality assumption only holds
for large samples.
● The relationship (c - c’) = ab only holds
if the samples to estimate c’ and c, a
and b are identical.
● Estimation of the significance of
effects can be done by bootstrap.

10. How about
moderation?

11. What is moderation? A practical example
● A common finding of social science studies is
that stress causes depression.
● Some researchers hypothesised that this
relationship did not take in account the role of
social support.
● Could stress causes depression only in the
absence of social support?

12. What is moderation? A practical example
● Step 1: A gene’s DNA is transcribed into mRNA.
● Step 2: mRNA is translated into protein.
● Could methylation of the promoter of the
gene moderate the expression of this gene?

13. Moderation in a nutshell
● Moderation can be assessed by
looking at whether Mo X is a
significant predictor for Y.

14. Moderation: a practical example
● Parenting respect has a protective effect
against mental illness and delinquency.
● Could that effect be dependant on gender?

15. Let’s spice things up a bit…

16. Limitation of mediation analysis
● It is important to have strong theoretical support of the presence of
potentially mediating variables before exploring the relationship.
○ This is ultimately only a correlation analysis.
● One must be able to manipulate the proposed mediator in an acceptable and
ethical fashion.
○ Including without affecting the outcome.
● Confounding where competing variables are:
○ Alternative potential mediators
○ Unmeasured cause of the dependant variable
○ Variables with causal effects of both independent and dependent variable.
○ If your graph is wrong, you will ultimately fail at assessing any causal effect.

17. Counter arguments to the limitation
● Temporal precedence
○ If the independant variable precedes the dependent
variable, it supports the directionality
● Non spuriousness and /or no confounds:
○ One should identify other variables and prove they
are not confounding

18. The end