Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃,
σ₁₂λ₂₃-σ₁₃

Single Door Criterion:

{2} ⊥ {3} | {}
{2} ⊥ {3} | {1}

Instrumental Variable:

1 | {}

Parameter: λ₂₄

Parameter: λ₃₄

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂ Identified

Algebraic Equations:

-σ₁₂+ω₁₂

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃

Parameter: ω₃₄

Parameter: ω₄₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄+λ₂₄ Identified

Algebraic Equations:

σ₂₂λ₂₃λ₃₄+σ₂₂λ₂₄-σ₂₄,
σ₁₂λ₂₃λ₃₄+σ₁₂λ₂₄-σ₁₄

Back Door Criterion:

{2} ⊥ {3,4} | {}
{2} ⊥ {3,4} | {1}

Path-specific Effect of X₂ on X₄: λ₂₃λ₃₄

Vanishing Ideal

Constraint Set:

σ₁₄σ₂₃-σ₁₃σ₂₄,
σ₁₄σ₂₂-σ₁₂σ₂₄,
σ₁₃σ₂₂-σ₁₂σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {2,3,4} | ({},{2})
{3,1,2} ⊥ {2,3,4} | ({3},{2})
{4,1,2} ⊥ {2,3,4} | ({4},{2})