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:

σ₁₃²σ₂₂λ₂₄-2σ₁₂σ₁₃σ₂₃λ₂₄+σ₁₃σ₁₄σ₂₃-σ₁₃²σ₂₄+σ₁₂²σ₃₃λ₂₄-σ₁₂σ₁₄σ₃₃+σ₁₂σ₁₃σ₃₄

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₃₄-σ₁₃σ₁₄σ₂₂-2σ₁₂σ₁₃σ₂₃λ₃₄+σ₁₂σ₁₄σ₂₃+σ₁₂σ₁₃σ₂₄+σ₁₂²σ₃₃λ₃₄-σ₁₂²σ₃₄

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:

-σ₁₂σ₁₄σ₂₃²+σ₁₂σ₁₃σ₂₃σ₂₄+σ₁₂σ₁₄σ₂₂σ₃₃-σ₁₂²σ₂₄σ₃₃-σ₁₂σ₁₃σ₂₂σ₃₄+σ₁₂²σ₂₃σ₃₄+σ₁₃²σ₂₂ω₂₄-2σ₁₂σ₁₃σ₂₃ω₂₄+σ₁₂²σ₃₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₁₃²σ₂₂+2σ₁₂σ₁₃σ₂₃-σ₁₂²σ₃₃+σ₁₂²ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄²σ₂₃²-2σ₁₃σ₁₄σ₂₃σ₂₄+σ₁₃²σ₂₄²-σ₁₄²σ₂₂σ₃₃+2σ₁₂σ₁₄σ₂₄σ₃₃+2σ₁₃σ₁₄σ₂₂σ₃₄-2σ₁₂σ₁₄σ₂₃σ₃₄-2σ₁₂σ₁₃σ₂₄σ₃₄+σ₁₂²σ₃₄²-σ₁₃²σ₂₂σ₄₄+2σ₁₂σ₁₃σ₂₃σ₄₄-σ₁₂²σ₃₃σ₄₄+σ₁₃²σ₂₂ω₄₄-2σ₁₂σ₁₃σ₂₃ω₄₄+σ₁₂²σ₃₃ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}

Total Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄+λ₁₂λ₂₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}

Total Effect of X₂ on X₄: λ₂₃λ₃₄+λ₂₄ Identified

Each Parameter Identified

Vanishing Ideal

Zero Vanishing Ideal