Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {2,3} | {}
{1} ⊥ {3} | {2}

Parameter: λ₁₄

Parameter: λ₂₃

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₂₄+σ₁₃σ₁₄σ₂₃+σ₁₁σ₂₃²λ₂₄-σ₁₃²σ₂₄-σ₁₁σ₂₂σ₃₃λ₂₄+σ₁₁σ₂₄σ₃₃-σ₁₁σ₂₃σ₃₄

Single Door Criterion:

{2} ⊥ {4} | {1,3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₃₄-σ₁₃σ₁₄σ₂₂+σ₁₁σ₂₃²λ₃₄-σ₁₁σ₂₃σ₂₄-σ₁₁σ₂₂σ₃₃λ₃₄+σ₁₁σ₂₂σ₃₄

Single Door Criterion:

{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₃

Parameter: ω₃₃

Parameter: ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄+λ₁₄

Path-specific Effect of X₁ on X₄: λ₁₃λ₃₄ Identified

Algebraic Equations:

σ₁₁σ₁₃²σ₂₂λ₁₃λ₃₄-σ₁₃²σ₁₄σ₂₂+σ₁₁²σ₂₃²λ₁₃λ₃₄-σ₁₁σ₁₃σ₂₃σ₂₄-σ₁₁²σ₂₂σ₃₃λ₁₃λ₃₄+σ₁₁σ₁₃σ₂₂σ₃₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄+λ₂₄

Path-specific Effect of X₂ on X₄: λ₂₃λ₃₄

Vanishing Ideal

Constraint Set:

σ₁₂

All constraints are determinantal

Trek-separation:

{1} ⊥ {2} | ({},{})