Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂,
σ₁₄σ₂₃λ₁₂-σ₂₃σ₂₄-σ₁₂σ₃₄λ₁₂+σ₂₂σ₃₄

Single Door Criterion:

{1} ⊥ {2,3} | {}
{1} ⊥ {2} | {3}

Parameter: λ₁₄

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₃λ₂₄-σ₃₄,
σ₁₂²λ₂₄-σ₁₂σ₁₄-σ₁₁σ₂₂λ₂₄+σ₁₁σ₂₄

Single Door Criterion:

{2} ⊥ {4} | {1}
{2} ⊥ {4} | {1,3}

Instrumental Variable:

3 | {}
3 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂,
-σ₁₄σ₂₂σ₂₃+σ₁₂σ₂₃σ₂₄+σ₁₄σ₂₃ω₂₂-σ₁₂σ₃₄ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

-σ₂₃+ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄ Identified

Algebraic Equations:

σ₁₁σ₂₃λ₁₂λ₂₄-σ₁₂σ₃₄,
σ₁₄σ₂₃²λ₁₂λ₂₄-σ₁₂σ₂₃σ₃₄λ₁₂λ₂₄-σ₂₃σ₂₄σ₃₄+σ₂₂σ₃₄²,
σ₁₁σ₁₂²λ₁₂λ₂₄-σ₁₂²σ₁₄-σ₁₁²σ₂₂λ₁₂λ₂₄+σ₁₁σ₁₂σ₂₄

Vanishing Ideal

Constraint Set:

σ₁₃,
σ₁₂σ₁₄σ₂₃-σ₁₁σ₂₃σ₂₄-σ₁₂²σ₃₄+σ₁₁σ₂₂σ₃₄

All constraints are determinantal

Trek-separation:

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