Mediation analysisPractical statistics for practical people

Who uses mediation analysis?

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

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?

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.

Mediation analysis in a nutshellBaron 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

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.

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

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.

How about moderation?

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?

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?

Moderation in a nutshell● Moderation can be assessed by

looking at whether Mo X is a significant predictor for Y.

Moderation: a practical example● Parenting respect has a protective effect

against mental illness and delinquency.● Could that effect be dependant on gender?

Let’s spice things up a bit…

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.

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

The end