Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₃λ₁₂-σ₂₃,
σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}
{1} ⊥ {2} | {3}

Instrumental Variable:

3 | {}

Parameter: λ₁₄

Parameter: λ₂₄

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃σ₂₃λ₃₄-σ₁₄σ₂₃-σ₁₂σ₃₃λ₃₄+σ₁₂σ₃₄,
σ₁₃²λ₃₄-σ₁₃σ₁₄-σ₁₁σ₃₃λ₃₄+σ₁₁σ₃₄,
-σ₁₂σ₁₄σ₂₃+σ₁₁σ₂₃²λ₃₄-σ₁₂²σ₃₃λ₃₄+σ₁₂²σ₃₄

Single Door Criterion:

{3} ⊥ {2,4} | {1}
{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

-σ₁₃+ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₁₃σ₂₂+σ₁₂σ₂₃+σ₁₃ω₂₂,
σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₄ Identified

Algebraic Equations:

σ₁₃²λ₁₂λ₂₄+σ₁₃²λ₁₄-σ₁₁σ₃₃λ₁₂λ₂₄-σ₁₁σ₃₃λ₁₄+σ₁₄σ₃₃-σ₁₃σ₃₄,
σ₁₁σ₁₃σ₂₃λ₁₂λ₂₄+σ₁₁σ₁₃σ₂₃λ₁₄-σ₁₁σ₁₂σ₃₃λ₁₂λ₂₄-σ₁₁σ₁₂σ₃₃λ₁₄+σ₁₂σ₁₄σ₃₃-σ₁₁σ₂₃σ₃₄,
σ₁₁²σ₂₃²λ₁₂λ₂₄+σ₁₁²σ₂₃²λ₁₄-σ₁₁σ₁₂²σ₃₃λ₁₂λ₂₄-σ₁₁σ₁₂²σ₃₃λ₁₄+σ₁₂²σ₁₄σ₃₃-σ₁₁σ₁₂σ₂₃σ₃₄

Back Door Criterion:

{1} ⊥ {2,4} | {3}

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄

Vanishing Ideal

Constraint Set:

σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {1,3} | ({1},{})