Lecture 8: Mediation

Question 1

What is mediation?

Answer 1

Is a hypothesised causal mechanism by which one variable affects another variable

A mediator M of X1 to Y is another variable M reached on the pathway from X1 to Y

A mediator will cause the outcome variable Y when controlling for X1

Question 2

In a mediated model how do calculate the direct/indirect effect?

Answer 2

Direct effect = c’ comes from MLR

Indirect effect (or mediated effect) = a * b

Total effect c = direct + indirect effect (c’ + (a * b))

Question 3

How do we estimate pathways c, a & b?

mediation

Answer 3

Estimate pathway c (total effect) - simple linear regression between original independent and dependent variables - use B

Estimate pathway a - run a simple linear regression between original independent variable and mediator - use B1 as the estimate

Estimate pathway B - run a MLR using mediator and X1 as independent variables –> B2 for mediator is the estimate

Question 4

How do we calculate c’ using estimate coefficients of direct effect, x1 and mediator

Answer 4

c = c' + (a*b)
c' = c - (a * b)

or in a three step model inputting

Question 5

How do we test if there is a mediated effect?

Answer 5

Baron & Kenny - 4 steps

1. Test to see if casual variable X1 associates to Y
   - SLR
2. Test pathway A (is causal variable X1 associated to mediator)
   - SLR
3. Test pathway B
   - MLR between mediator and outcome Y controlling for X1
   - M is associated with Y adjusting for X1
4. Test pathway c’:
   - Can check for MLR from step 3
   - Check the beta coefficient for X1 - is it significantly different from 0?

• If there is complete mediation this beta coefficient will not be significantly different from 0 - as when controlling for mediator (when this value is constant) there is no relationship between increasing/decreasing X1 and increasing/decreasing Y - i.e direct path c’ is 0
• Partial mediation exists if beta coefficient for X1 is significantly different from 0 - i.e. X1 has some effect on Y even after controlling from effect of M. c’ will be smaller to c in absolute values

Question 6

What methods are used to test for indirect mediation?

Answer 6

• Sobel test (normal theory approach)

- Nonparametric approach –> bootstrapping

Question 7

How does the sobel method indicate whether there is an indirect effect?

Answer 7

Calculates a Z statistic

If the absolute value is < 1.96 then the Z we fail to reject the null hypothesis that the indirect effect is 0

The test can be done using an online calculator

Z = ab/SE(ab)

Question 8

What is the indirect effect?

Answer 8

In mediation the indirect effect is the impact of ab towards the dependent variable

Using Baron & Kenny steps steps 2&3 estimate the indirect effect and existence of his is sufficient to justify mediation

However newer methods - sobel test - recommend only testing the indirect effect to establish mediation

Question 9

What is entered on the online calculator

Answer 9

a - coefficient for a (X1 - M)
b - coefficient for b (M coefficient in MLR)

standard error of these

Question 10

Why does the sobel test work better for larger sample sizes?

Answer 10

As it uses a skewed sampling distribution of ab - hence larger values may have more a bigger range

Using larger samples reduces the skewness

Question 11

What is the non-parametric version of the sobel test?

Answer 11

Bootstrapping

• The indirect effect is significant if the confidence interval doesn’t include 0
• To do a bias corrected bootstrap - use a process macro this is done as the mean of the bootstrap may estimate from the original value

Question 12

Why does a significant indirect effect matter?

Answer 12

It means there is significant mediation