Definitions of the four-way decomposition as applied to the current study
| Definition | Explanation | Application* |
|---|---|---|
Total effect (TE) | Total effect Total effect of X (changing x* to x) on Y | What is the risk of alcohol misuse in adulthood among individuals whose parents misused alcohol relative to individuals whose parents did not misuse alcohol? |
| Controlled direct effect (CDE) | Due to neither mediation nor interaction Effect of X (changing x* to x) on Y, intervening to fix M to m | What would be the risk of alcohol misuse in adulthood among individuals whose parents misused alcohol, relative to individuals whose parents did not misuse alcohol, if everyone had a high level of school performance (ie, above-average school marks)? |
Reference interaction (INTref) | Due to interaction only An additive interaction that operates only if M is present when X is x | What is the combined risk of alcohol misuse in adulthood among individuals whose parents misused alcohol and who had a low level of school performance (ie, at or below-average school marks), if having alcohol misusing parents is not necessary for a low level of school performance? |
Mediated interaction (INTmed) | Due to mediated interaction An additive interaction that operates only if X (changing x* to x) has an effect on M | What is the combined risk of alcohol misuse in adulthood among individuals whose parents misused alcohol and who had a low level of school performance (ie, at or below average school marks), if having alcohol misusing parents is necessary for a low level of school performance? |
Pure indirect effect (PIE) | Due to mediation only Effect of the mediator (changing m* to m) on Y when X is x, multiplied by the effect of X (changing x* to x) on M | What is the risk of alcohol misuse in adulthood among individuals who had a lower level of school performance, if having alcohol misusing parents is necessary for a low level of school performance (ie, at or below-average school marks)? |
Y = Outcome (Alcohol misuse in adulthood).
X = Exposure (Parental alcohol misuse); x* = No; x = Yes.
M = Mediator (School performance); m* = At or below-average school marks; m = Above-average school marks.
*Here, we build on the definitions proposed by Bean et al.23