Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂,
σ₁₃σ₂₄λ₁₂-σ₂₃σ₂₄-σ₁₂σ₃₄λ₁₂+σ₂₂σ₃₄

Single Door Criterion:

{1} ⊥ {2,4} | {}
{1} ⊥ {2} | {4}

Parameter: λ₁₃

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₄λ₂₃-σ₃₄,
σ₁₂²λ₂₃-σ₁₂σ₁₃-σ₁₁σ₂₂λ₂₃+σ₁₁σ₂₃

Single Door Criterion:

{2} ⊥ {3} | {1}
{2} ⊥ {3} | {1,4}

Instrumental Variable:

4 | {}
4 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂,
-σ₁₃σ₂₂σ₂₄+σ₁₂σ₂₃σ₂₄+σ₁₃σ₂₄ω₂₂-σ₁₂σ₃₄ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

-σ₂₄+ω₂₄

Parameter: ω₃₃

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:

σ₁₁σ₂₄λ₁₂λ₂₃-σ₁₂σ₃₄,
σ₁₃σ₂₄²λ₁₂λ₂₃-σ₁₂σ₂₄σ₃₄λ₁₂λ₂₃-σ₂₃σ₂₄σ₃₄+σ₂₂σ₃₄²,
σ₁₁σ₁₂²λ₁₂λ₂₃-σ₁₂²σ₁₃-σ₁₁²σ₂₂λ₁₂λ₂₃+σ₁₁σ₁₂σ₂₃

Vanishing Ideal

Constraint Set:

σ₁₄,
σ₁₂σ₁₃σ₂₄-σ₁₁σ₂₃σ₂₄-σ₁₂²σ₃₄+σ₁₁σ₂₂σ₃₄

All constraints are determinantal

Trek-separation:

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