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Mediation analysis


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Practical statistics for practical people: presentation on mediation analysis.

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Mediation analysis

  1. 1. Mediation analysis Practical statistics for practical people
  2. 2. Who uses mediation analysis?
  3. 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. 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. 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. 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. 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. 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. 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. 10. How about moderation?
  11. 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. 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. 13. Moderation in a nutshell ● Moderation can be assessed by looking at whether Mo X is a significant predictor for Y.
  14. 14. Moderation: a practical example ● Parenting respect has a protective effect against mental illness and delinquency. ● Could that effect be dependant on gender?
  15. 15. Let’s spice things up a bit…
  16. 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. 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. 18. The end