Parameter: λ₁₃

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₃²λ₁₄-σ₁₁σ₃₃λ₁₄+σ₁₄σ₃₃-σ₁₃σ₃₄

Single Door Criterion:

{1} ⊥ {2,4} | {3}
{1} ⊥ {4} | {2,3}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₂λ₂₄-σ₂₄

Single Door Criterion:

{2} ⊥ {1,3,4} | {}
{2} ⊥ {1,4} | {3}
{2} ⊥ {3,4} | {1}
{2} ⊥ {4} | {1,3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃²λ₃₄-σ₁₃σ₁₄-σ₁₁σ₃₃λ₃₄+σ₁₁σ₃₄

Single Door Criterion:

{3} ⊥ {2,4} | {1}
{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₃²σ₂₄²-σ₁₄²σ₂₂σ₃₃-σ₁₁σ₂₄²σ₃₃+2σ₁₃σ₁₄σ₂₂σ₃₄-σ₁₁σ₂₂σ₃₄²-σ₁₃²σ₂₂σ₄₄+σ₁₁σ₂₂σ₃₃σ₄₄+σ₁₃²σ₂₂ω₄₄-σ₁₁σ₂₂σ₃₃ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄+λ₁₄

Path-specific Effect of X₁ on X₄: λ₁₃λ₃₄

Vanishing Ideal

Constraint Set:

σ₂₃,
σ₁₂

All constraints are determinantal

Trek-separation:

{2} ⊥ {1,3} | ({},{})
{1,2} ⊥ {1,3} | ({1},{})
{3,2} ⊥ {1,3} | ({3},{})
{4,2} ⊥ {1,3} | ({4},{})