Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₄λ₁₂-σ₂₄,
σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}
{1} ⊥ {2} | {4}

Instrumental Variable:

4 | {}

Parameter: λ₁₃

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₄σ₂₂λ₂₃-σ₁₄σ₂₃-σ₁₂σ₂₄λ₂₃+σ₁₃σ₂₄,
σ₁₂²λ₂₃-σ₁₂σ₁₃-σ₁₁σ₂₂λ₂₃+σ₁₁σ₂₃

Single Door Criterion:

{2} ⊥ {3,4} | {1}
{2} ⊥ {3} | {1,4}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃

Parameter: ω₁₄ Identified

Algebraic Equations:

-σ₁₄+ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₁₄σ₂₂+σ₁₂σ₂₄+σ₁₄ω₂₂,
σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₃₃

Parameter: ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₄₄+ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃+λ₁₃

Path-specific Effect of X₁ on X₃: λ₁₂λ₂₃ Identified

Algebraic Equations:

σ₁₄²σ₂₂λ₁₂λ₂₃-σ₁₄σ₂₃σ₂₄-σ₁₁σ₂₄²λ₁₂λ₂₃+σ₁₃σ₂₄²,
σ₁₁σ₁₄σ₂₂λ₁₂λ₂₃-σ₁₁σ₁₂σ₂₄λ₁₂λ₂₃+σ₁₂σ₁₃σ₂₄-σ₁₁σ₂₃σ₂₄,
σ₁₁σ₁₂²λ₁₂λ₂₃-σ₁₂²σ₁₃-σ₁₁²σ₂₂λ₁₂λ₂₃+σ₁₁σ₁₂σ₂₃

Vanishing Ideal

Constraint Set:

σ₁₂σ₁₄-σ₁₁σ₂₄

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {1,4} | ({1},{})