Parameter: λ₂₃

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₂₃²λ₂₄-σ₂₂σ₃₃λ₂₄+σ₂₄σ₃₃-σ₂₃σ₃₄

Single Door Criterion:

{2} ⊥ {1,4} | {3}
{2} ⊥ {4} | {1,3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₂₃²λ₃₄-σ₂₃σ₂₄-σ₂₂σ₃₃λ₃₄+σ₂₂σ₃₄

Single Door Criterion:

{3} ⊥ {1,4} | {2}
{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₃

Parameter: ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₂₄²σ₃₃+2σ₂₃σ₂₄σ₃₄-σ₂₂σ₃₄²-σ₂₃²σ₄₄+σ₂₂σ₃₃σ₄₄+σ₂₃²ω₄₄-σ₂₂σ₃₃ω₄₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄+λ₂₄

Path-specific Effect of X₂ on X₄: λ₂₃λ₃₄

Vanishing Ideal

Constraint Set:

σ₁₄,
σ₁₃,
σ₁₂

All constraints are determinantal

Trek-separation:

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