Parameter: λ₁₂

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃,
σ₁₂λ₂₃-σ₁₃

Single Door Criterion:

{2} ⊥ {3} | {}
{2} ⊥ {3} | {1}

Instrumental Variable:

1 | {}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂σ₂₃²λ₂₄-σ₁₄σ₂₃²+σ₁₃σ₂₃σ₂₄-σ₁₂σ₂₂σ₃₃λ₂₄+σ₁₄σ₂₂σ₃₃-σ₁₂σ₂₃σ₃₄,
σ₁₂σ₁₃σ₂₃λ₂₄-σ₁₃σ₁₄σ₂₃+σ₁₃²σ₂₄-σ₁₂²σ₃₃λ₂₄+σ₁₂σ₁₄σ₃₃-σ₁₂σ₁₃σ₃₄

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₂₃²λ₃₄-σ₂₃σ₂₄-σ₂₂σ₃₃λ₃₄+σ₂₂σ₃₄,
σ₁₃σ₂₃λ₃₄-σ₁₃σ₂₄-σ₁₂σ₃₃λ₃₄+σ₁₂σ₃₄

Single Door Criterion:

{3} ⊥ {1,4} | {2}
{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₃-σ₁₃σ₂₄+σ₁₃ω₂₄,
σ₁₄σ₂₂-σ₁₂σ₂₄+σ₁₂ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₂₃²+2σ₁₃σ₁₄σ₂₃σ₂₄-σ₁₃²σ₂₄²+σ₁₄²σ₂₂σ₃₃-2σ₁₂σ₁₄σ₂₄σ₃₃+2σ₁₂σ₁₃σ₂₄σ₃₄-σ₁₂²σ₃₄²-σ₁₂σ₁₃σ₂₃σ₄₄+σ₁₂²σ₃₃σ₄₄+σ₁₂σ₁₃σ₂₃ω₄₄-σ₁₂²σ₃₃ω₄₄,
-σ₁₄²σ₂₂σ₂₃²+2σ₁₂σ₁₄σ₂₃²σ₂₄-σ₁₂σ₁₃σ₂₃σ₂₄²+σ₁₄²σ₂₂²σ₃₃-2σ₁₂σ₁₄σ₂₂σ₂₄σ₃₃+2σ₁₂²σ₂₃σ₂₄σ₃₄-σ₁₂²σ₂₂σ₃₄²-σ₁₂²σ₂₃²σ₄₄+σ₁₂²σ₂₂σ₃₃σ₄₄+σ₁₂²σ₂₃²ω₄₄-σ₁₂²σ₂₂σ₃₃ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃

Total Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄+λ₁₂λ₂₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄+λ₂₄ Identified

Each Parameter Identified

Vanishing Ideal

Constraint Set:

σ₁₃σ₂₂-σ₁₂σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {2,3} | ({},{2})