Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}

Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {3} | {}

Parameter: λ₁₄

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₂₄-2σ₁₂σ₁₃σ₂₃λ₂₄+σ₁₃σ₁₄σ₂₃+σ₁₁σ₂₃²λ₂₄-σ₁₃²σ₂₄+σ₁₂²σ₃₃λ₂₄-σ₁₂σ₁₄σ₃₃-σ₁₁σ₂₂σ₃₃λ₂₄+σ₁₁σ₂₄σ₃₃+σ₁₂σ₁₃σ₃₄-σ₁₁σ₂₃σ₃₄

Single Door Criterion:

{2} ⊥ {4} | {1,3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₃₄-σ₁₃σ₁₄σ₂₂-2σ₁₂σ₁₃σ₂₃λ₃₄+σ₁₂σ₁₄σ₂₃+σ₁₁σ₂₃²λ₃₄+σ₁₂σ₁₃σ₂₄-σ₁₁σ₂₃σ₂₄+σ₁₂²σ₃₃λ₃₄-σ₁₁σ₂₂σ₃₃λ₃₄-σ₁₂²σ₃₄+σ₁₁σ₂₂σ₃₄

Single Door Criterion:

{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₂σ₁₃-σ₁₁σ₂₃+σ₁₁ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₃λ₃₄+λ₁₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄ Identified

Algebraic Equations:

σ₁₁σ₁₃²σ₂₂λ₁₂λ₂₄-2σ₁₁σ₁₂σ₁₃σ₂₃λ₁₂λ₂₄+σ₁₂σ₁₃σ₁₄σ₂₃+σ₁₁²σ₂₃²λ₁₂λ₂₄-σ₁₂σ₁₃²σ₂₄+σ₁₁σ₁₂²σ₃₃λ₁₂λ₂₄-σ₁₂²σ₁₄σ₃₃-σ₁₁²σ₂₂σ₃₃λ₁₂λ₂₄+σ₁₁σ₁₂σ₂₄σ₃₃+σ₁₂²σ₁₃σ₃₄-σ₁₁σ₁₂σ₂₃σ₃₄

Path-specific Effect of X₁ on X₄: λ₁₃λ₃₄ Identified

Algebraic Equations:

σ₁₁σ₁₃²σ₂₂λ₁₃λ₃₄-σ₁₃²σ₁₄σ₂₂-2σ₁₁σ₁₂σ₁₃σ₂₃λ₁₃λ₃₄+σ₁₂σ₁₃σ₁₄σ₂₃+σ₁₁²σ₂₃²λ₁₃λ₃₄+σ₁₂σ₁₃²σ₂₄-σ₁₁σ₁₃σ₂₃σ₂₄+σ₁₁σ₁₂²σ₃₃λ₁₃λ₃₄-σ₁₁²σ₂₂σ₃₃λ₁₃λ₃₄-σ₁₂²σ₁₃σ₃₄+σ₁₁σ₁₃σ₂₂σ₃₄

Vanishing Ideal

Zero Vanishing Ideal