Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,3,4} | {}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₂λ₂₃-σ₁₃

Instrumental Variable:

1 | {}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂λ₂₄-σ₁₄

Instrumental Variable:

1 | {}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₃σ₂₂-σ₁₂σ₂₃+σ₁₂ω₂₃

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₄σ₂₂-σ₁₂σ₂₄+σ₁₂ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₁₃²σ₂₂+2σ₁₂σ₁₃σ₂₃-σ₁₂²σ₃₃+σ₁₂²ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

-σ₁₃σ₁₄σ₂₂+σ₁₂σ₁₄σ₂₃+σ₁₂σ₁₃σ₂₄-σ₁₂²σ₃₄+σ₁₂²ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₂₂+2σ₁₂σ₁₄σ₂₄-σ₁₂²σ₄₄+σ₁₂²ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}

Total Effect of X₁ on X₄: λ₁₂λ₂₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}

Vanishing Ideal

Zero Vanishing Ideal