Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,3} | {}

Parameter: λ₁₄

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₂λ₂₃-σ₁₃

Instrumental Variable:

1 | {}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₂σ₁₃λ₃₄-σ₁₂σ₁₄-σ₁₁σ₂₃λ₃₄+σ₁₁σ₂₄

Instrumental Variable:

2 | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃ Identified

Algebraic Equations:

σ₁₃σ₂₂-σ₁₂σ₂₃+σ₁₂ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₁₃²σ₂₂+2σ₁₂σ₁₃σ₂₃-σ₁₂²σ₃₃+σ₁₂²ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

-σ₁₃σ₁₄σ₂₃+σ₁₃²σ₂₄+σ₁₂σ₁₄σ₃₃-σ₁₁σ₂₄σ₃₃-σ₁₂σ₁₃σ₃₄+σ₁₁σ₂₃σ₃₄+σ₁₂σ₁₃ω₃₄-σ₁₁σ₂₃ω₃₄

Parameter: ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3} | {}

Total Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄+λ₁₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄ Identified

Algebraic Equations:

σ₁₁σ₁₂σ₁₃λ₁₂λ₂₃λ₃₄-σ₁₂σ₁₃σ₁₄-σ₁₁²σ₂₃λ₁₂λ₂₃λ₃₄+σ₁₁σ₁₃σ₂₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Vanishing Ideal

Zero Vanishing Ideal