Summary Formulas AMDA spring lecture 1 to 12

Formule blad AMDA
Part 1 lecture 1 Moderation:
- Case 1. Interaction in regression analysis: Ŷ = (b0+ b2 Z) + (b1+ b3
Z) X
Part 1 lecture 2 Mediation:
- Causal steps approach: XŶ = ßŶX , XZ =ßZX , ZŶ (controlling
for X) = ßŶZ.X , XŶ (controlling for Z) = ßŶX.Z
- c = total effect, a = indirect effect part 1, b = indirect effect part 2,
c’ = direct effect c = c’ + ab or c – c’ = ab
ab ab t at b
- Sobel test  z= = 2 2 2 2 2 2 or z= 2 2
SEab √ b s a + a s b+ S a s b √ ta +t b +1
- Amount mediation  bŶX-bŶX.Z
b ind
- Proportion mediated  Pmed =
bt o t
- Completely standardized effect  abcs= ßZX ßŶZ.X
- Proportion of variance explained  R2= u + v + w,
Total: Rtot2= u + w or Rtot2= rŶX2, Direct: Rdir2= u or Rdir2=
rŶ(X.Z)2, Indirect (mediated): R2med = w or R2med= rŶX2-
rŶ(X.Z)2= rŶX2+ rŶZ2-R2

Part 1 Within-subjects design moderation and mediation:
- Predict Ŷ from covariate  Ŷ1 = b0(1) + b1(1)Z & Ŷ2 = b0(2) + b1(2)Z.
- Stable covariate and moderation  ^
D yi =
(b0(2) – b0(1)) (=constant) + (b1(2) – b1(1))
(=regression weight)
- Varying covariate and mediation  ^ D yi =
(b0(2) – b0(1)) (=direct effect) + (b1(Z2 –Z1)
(=indirect effect)
- Total effect  ^ D y = Ŷ2 – Ŷ1
- Change in Z  ^ D z = ^Z 2 – ^Z 1
- Change in Ŷ due to change in Z (indirect
effect)  ^ D y(ind)= b1( ^Z 2 – ^Z 1)
- Change in Ŷ not due to change in Z (direct effect)  ^
D y(dir)=b0(2) – b0(1)
- Varying covariate, moderation added  D y = ^
(b0(2) – b0(1)) (=constant, average direct effect) +
¿ ¿(Z2 + Z1) (=moderation)+ ¿ ¿(Z2 – Z1)
(=mediation).  ^ D y =d0 + d1Zsum + d2Zdif
- Three regression equations [Ŷ2–Ŷ1] = c+ eŶ,
[Z2–Z1] = a+ eZ
[Ŷ2–Ŷ1] = c’+ b(Z2–Z1)+ d(Z1+ Z2)/2 + eŶ*