Parameter: λ₁₂

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₁σ₂₃²λ₁₄-σ₁₄σ₂₃²+σ₁₂²σ₃₃λ₁₄-σ₁₁σ₂₂σ₃₃λ₁₄+σ₁₄σ₂₂σ₃₃-σ₁₂σ₂₄σ₃₃+σ₁₂σ₂₃σ₃₄

Single Door Criterion:

{1} ⊥ {4} | {2,3}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₁σ₂₃²λ₂₄+σ₁₂²σ₃₃λ₂₄-σ₁₂σ₁₄σ₃₃-σ₁₁σ₂₂σ₃₃λ₂₄+σ₁₁σ₂₄σ₃₃-σ₁₁σ₂₃σ₃₄

Single Door Criterion:

{2} ⊥ {4} | {1,3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₂σ₁₄σ₂₃+σ₁₁σ₂₃²λ₃₄-σ₁₁σ₂₃σ₂₄+σ₁₂²σ₃₃λ₃₄-σ₁₁σ₂₂σ₃₃λ₃₄-σ₁₂²σ₃₄+σ₁₁σ₂₂σ₃₄

Single Door Criterion:

{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

-σ₂₃+ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄²σ₂₃²-σ₁₄²σ₂₂σ₃₃+2σ₁₂σ₁₄σ₂₄σ₃₃-σ₁₁σ₂₄²σ₃₃-2σ₁₂σ₁₄σ₂₃σ₃₄+2σ₁₁σ₂₃σ₂₄σ₃₄+σ₁₂²σ₃₄²-σ₁₁σ₂₂σ₃₄²-σ₁₁σ₂₃²σ₄₄-σ₁₂²σ₃₃σ₄₄+σ₁₁σ₂₂σ₃₃σ₄₄+σ₁₁σ₂₃²ω₄₄+σ₁₂²σ₃₃ω₄₄-σ₁₁σ₂₂σ₃₃ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄

Vanishing Ideal

Constraint Set:

σ₁₃

All constraints are determinantal

Trek-separation:

{1} ⊥ {3} | ({},{})