Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,4} | {}

Parameter: λ₁₃

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₄σ₂₂λ₂₃-σ₁₄σ₂₃-σ₁₂σ₂₄λ₂₃+σ₁₂σ₃₄,
σ₁₂σ₁₄λ₂₃-σ₁₃σ₁₄-σ₁₁σ₂₄λ₂₃+σ₁₁σ₃₄,
σ₁₂²λ₂₃-σ₁₂σ₁₃-σ₁₁σ₂₂λ₂₃+σ₁₁σ₂₃

Single Door Criterion:

{2} ⊥ {3} | {1}
{2} ⊥ {3} | {1,4}

Instrumental Variable:

4 | {1}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂λ₂₄-σ₁₄

Instrumental Variable:

1 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₂-σ₁₂σ₂₄+σ₁₂ω₂₄

Parameter: ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₂₂+2σ₁₂σ₁₄σ₂₄-σ₁₂²σ₄₄+σ₁₂²ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃+λ₁₃

Path-specific Effect of X₁ on X₃: λ₁₂λ₂₃ Identified

Algebraic Equations:

σ₁₁σ₁₄σ₂₂λ₁₂λ₂₃-σ₁₂σ₁₄σ₂₃-σ₁₁σ₁₂σ₂₄λ₁₂λ₂₃+σ₁₂²σ₃₄,
σ₁₁σ₁₂σ₁₄λ₁₂λ₂₃-σ₁₂σ₁₃σ₁₄-σ₁₁²σ₂₄λ₁₂λ₂₃+σ₁₁σ₁₂σ₃₄,
σ₁₁σ₁₂²λ₁₂λ₂₃-σ₁₂²σ₁₃-σ₁₁²σ₂₂λ₁₂λ₂₃+σ₁₁σ₁₂σ₂₃

Total Effect of X₁ on X₄: λ₁₂λ₂₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,4} | {}

Vanishing Ideal

Constraint Set:

σ₁₃σ₁₄σ₂₂-σ₁₂σ₁₄σ₂₃-σ₁₂σ₁₃σ₂₄+σ₁₁σ₂₃σ₂₄+σ₁₂²σ₃₄-σ₁₁σ₂₂σ₃₄

All constraints are determinantal

Trek-separation:

{2,1,3} ⊥ {1,2,4} | ({2},{1})