Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₁₄+σ₁₁σ₂₃²λ₁₄-σ₁₄σ₂₃²+σ₁₃σ₂₃σ₂₄-σ₁₁σ₂₂σ₃₃λ₁₄+σ₁₄σ₂₂σ₃₃-σ₁₃σ₂₂σ₃₄

Single Door Criterion:

{1} ⊥ {4} | {2,3}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃

Single Door Criterion:

{2} ⊥ {1,3} | {}
{2} ⊥ {3} | {1}

Parameter: λ₂₄

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: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃

Parameter: ω₄₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄+λ₂₄

Path-specific Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂²λ₂₃λ₃₄-σ₁₃σ₁₄σ₂₂σ₂₃+σ₁₁σ₂₂σ₂₃²λ₂₃λ₃₄-σ₁₁σ₂₃²σ₂₄-σ₁₁σ₂₂²σ₃₃λ₂₃λ₃₄+σ₁₁σ₂₂σ₂₃σ₃₄

Vanishing Ideal

Constraint Set:

σ₁₂

All constraints are determinantal

Trek-separation:

{1} ⊥ {2} | ({},{})