Table 6.

Interaction Decompositions

Number of Components	Decomposition
2-Way Decomposition (No Mediation)^a	TE = CDE + PAI
3-Way Decomposition^b	TE = CDE + PAI + PIE
4-Way Decomposition^c	TE = CDE + INT_ref + INT_med + PIE

(Y₁ − Y₀) = (Y₁₀ − Y₀₀) + (Y₁₁ − Y₁₀ − Y₀₁ + Y₀₀)(M)

(Y₁ − Y₀) = (Y₁₀ − Y₀₀) + (Y₁₁ − Y₁₀ − Y₀₁ + Y₀₀)(M₁) + (Y₀₁ − Y₀₀)(M₁ − M₀)

(Y₁ − Y₀) = (Y₁₀ − Y₀₀) + (Y₁₁ − Y₁₀ − Y₀₁ + Y₀₀)(M₀) + (Y₁₁ − Y₁₀ − Y₀₁ + Y₀₀)(M₁ − M₀) + (Y₀₁ − Y₀₀)(M₁ − M₀)