Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,3,4} | {}
{1} ⊥ {2,4} | {3}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂λ₂₄-σ₁₄

Instrumental Variable:

1 | {}
1 | {3}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₂-σ₁₂σ₂₄+σ₁₂ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₃₃+ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

-σ₃₄+ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₂₂+2σ₁₂σ₁₄σ₂₄-σ₁₂²σ₄₄+σ₁₂²ω₄₄

Total Effect of X₁ on X₄: λ₁₂λ₂₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}
{1} ⊥ {2,4} | {3}

Vanishing Ideal

Constraint Set:

σ₂₃,
σ₁₃

All constraints are determinantal

Trek-separation:

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