Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,3} | {}

Parameter: λ₁₄

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₂λ₂₃-σ₁₃

Instrumental Variable:

1 | {}

Parameter: λ₂₄

Parameter: λ₃₄

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₃σ₂₂-σ₁₂σ₂₃+σ₁₂ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₁₃²σ₂₂+2σ₁₂σ₁₃σ₂₃-σ₁₂²σ₃₃+σ₁₂²ω₃₃

Parameter: ω₃₄

Parameter: ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}

Total Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄+λ₁₂λ₂₄+λ₁₄ Identified

Algebraic Equations:

σ₁₁λ₁₂λ₂₃λ₃₄+σ₁₁λ₁₂λ₂₄+σ₁₁λ₁₄-σ₁₄

Back Door Criterion:

{1} ⊥ {2,3,4} | {}

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄+λ₂₄

Path-specific Effect of X₂ on X₄: λ₂₃λ₃₄

Vanishing Ideal

Zero Vanishing Ideal