Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}

Parameter: λ₁₃

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₂²λ₁₄-σ₁₁σ₂₂λ₁₄+σ₁₄σ₂₂-σ₁₂σ₂₄

Single Door Criterion:

{1} ⊥ {4} | {2}

Parameter: λ₂₃

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂²λ₂₄-σ₁₂σ₁₄-σ₁₁σ₂₂λ₂₄+σ₁₁σ₂₄

Single Door Criterion:

{2} ⊥ {4} | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₃

Parameter: ω₃₃

Parameter: ω₃₄ Identified

Algebraic Equations:

-σ₁₃σ₁₄σ₂₂+σ₁₂σ₁₄σ₂₃+σ₁₂σ₁₃σ₂₄-σ₁₁σ₂₃σ₂₄-σ₁₂²σ₃₄+σ₁₁σ₂₂σ₃₄+σ₁₂²ω₃₄-σ₁₁σ₂₂ω₃₄

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₂₂+2σ₁₂σ₁₄σ₂₄-σ₁₁σ₂₄²-σ₁₂²σ₄₄+σ₁₁σ₂₂σ₄₄+σ₁₂²ω₄₄-σ₁₁σ₂₂ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃+λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₂λ₂₃+σ₁₁λ₁₃-σ₁₃

Back Door Criterion:

{1} ⊥ {2,3,4} | {}

Path-specific Effect of X₁ on X₃: λ₁₂λ₂₃

Total Effect of X₁ on X₄: λ₁₂λ₂₄+λ₁₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}

Vanishing Ideal

Zero Vanishing Ideal