Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₃λ₁₂-σ₂₃,
σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}
{1} ⊥ {2} | {3}

Instrumental Variable:

3 | {}

Parameter: λ₁₃

Parameter: λ₁₄

Parameter: λ₂₄

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₁₃σ₂₂+σ₁₂σ₂₃+σ₁₃ω₂₂,
σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₄

Parameter: ω₃₃

Parameter: ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₄ Identified

Algebraic Equations:

σ₁₃λ₁₂λ₂₄+σ₁₃λ₁₄-σ₃₄,
σ₁₁λ₁₂λ₂₄+σ₁₁λ₁₄-σ₁₄

Back Door Criterion:

{1} ⊥ {2,4} | {}

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄

Vanishing Ideal

Constraint Set:

σ₁₄σ₂₃-σ₁₂σ₃₄,
σ₁₃σ₁₄-σ₁₁σ₃₄,
σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

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