Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,3} | {}
{1} ⊥ {2} | {3}

Parameter: λ₁₄

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: ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

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:

σ₁₁²σ₂₃²λ₁₂λ₂₄+σ₁₁σ₁₂²σ₃₃λ₁₂λ₂₄-σ₁₂²σ₁₄σ₃₃-σ₁₁²σ₂₂σ₃₃λ₁₂λ₂₄+σ₁₁σ₁₂σ₂₄σ₃₃-σ₁₁σ₁₂σ₂₃σ₃₄

Vanishing Ideal

Constraint Set:

σ₁₃

All constraints are determinantal

Trek-separation:

{1} ⊥ {3} | ({},{})