Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}

Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₂²λ₁₃-σ₁₁σ₂₂λ₁₃+σ₁₃σ₂₂-σ₁₂σ₂₃

Single Door Criterion:

{1} ⊥ {3} | {2}

Parameter: λ₁₄

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₂²λ₂₃-σ₁₂σ₁₃-σ₁₁σ₂₂λ₂₃+σ₁₁σ₂₃

Single Door Criterion:

{2} ⊥ {3} | {1}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₃₄-σ₁₃σ₁₄σ₂₂-2σ₁₂σ₁₃σ₂₃λ₃₄+σ₁₂σ₁₄σ₂₃+σ₁₁σ₂₃²λ₃₄+σ₁₂σ₁₃σ₂₄-σ₁₁σ₂₃σ₂₄+σ₁₂²σ₃₃λ₃₄-σ₁₁σ₂₂σ₃₃λ₃₄-σ₁₂²σ₃₄+σ₁₁σ₂₂σ₃₄

Single Door Criterion:

{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

-σ₁₂²σ₁₃σ₁₄σ₂₃+σ₁₁σ₁₃σ₁₄σ₂₂σ₂₃+σ₁₂²σ₁₃²σ₂₄-σ₁₁σ₁₃²σ₂₂σ₂₄+σ₁₂³σ₁₄σ₃₃-σ₁₁σ₁₂σ₁₄σ₂₂σ₃₃-σ₁₁σ₁₂²σ₂₄σ₃₃+σ₁₁²σ₂₂σ₂₄σ₃₃-σ₁₂³σ₁₃σ₃₄+σ₁₁σ₁₂σ₁₃σ₂₂σ₃₄+σ₁₁σ₁₂²σ₂₃σ₃₄-σ₁₁²σ₂₂σ₂₃σ₃₄+σ₁₁σ₁₃²σ₂₂ω₂₄-2σ₁₁σ₁₂σ₁₃σ₂₃ω₂₄+σ₁₁²σ₂₃²ω₂₄+σ₁₁σ₁₂²σ₃₃ω₂₄-σ₁₁²σ₂₂σ₃₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₁₃²σ₂₂+2σ₁₂σ₁₃σ₂₃-σ₁₁σ₂₃²-σ₁₂²σ₃₃+σ₁₁σ₂₂σ₃₃+σ₁₂²ω₃₃-σ₁₁σ₂₂ω₃₃

Parameter: ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃+λ₁₃ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3} | {}

Total Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄+λ₁₃λ₃₄+λ₁₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄ Identified

Algebraic Equations:

σ₁₁σ₁₂²σ₁₃²σ₂₂λ₁₂λ₂₃λ₃₄-σ₁₂²σ₁₃²σ₁₄σ₂₂-σ₁₁²σ₁₃²σ₂₂²λ₁₂λ₂₃λ₃₄-2σ₁₁σ₁₂³σ₁₃σ₂₃λ₁₂λ₂₃λ₃₄+σ₁₂³σ₁₃σ₁₄σ₂₃+2σ₁₁²σ₁₂σ₁₃σ₂₂σ₂₃λ₁₂λ₂₃λ₃₄+σ₁₁σ₁₂σ₁₃σ₁₄σ₂₂σ₂₃+σ₁₁²σ₁₂²σ₂₃²λ₁₂λ₂₃λ₃₄-σ₁₁σ₁₂²σ₁₄σ₂₃²-σ₁₁³σ₂₂σ₂₃²λ₁₂λ₂₃λ₃₄+σ₁₂³σ₁₃²σ₂₄-2σ₁₁σ₁₂²σ₁₃σ₂₃σ₂₄+σ₁₁²σ₁₂σ₂₃²σ₂₄+σ₁₁σ₁₂⁴σ₃₃λ₁₂λ₂₃λ₃₄-2σ₁₁²σ₁₂²σ₂₂σ₃₃λ₁₂λ₂₃λ₃₄+σ₁₁³σ₂₂²σ₃₃λ₁₂λ₂₃λ₃₄-σ₁₂⁴σ₁₃σ₃₄+σ₁₁σ₁₂²σ₁₃σ₂₂σ₃₄+σ₁₁σ₁₂³σ₂₃σ₃₄-σ₁₁²σ₁₂σ₂₂σ₂₃σ₃₄

Path-specific Effect of X₁ on X₄: λ₁₃λ₃₄ Identified

Algebraic Equations:

σ₁₂²σ₁₃²σ₂₂λ₁₃λ₃₄-σ₁₁σ₁₃²σ₂₂²λ₁₃λ₃₄+σ₁₃²σ₁₄σ₂₂²-2σ₁₂³σ₁₃σ₂₃λ₁₃λ₃₄+2σ₁₁σ₁₂σ₁₃σ₂₂σ₂₃λ₁₃λ₃₄-2σ₁₂σ₁₃σ₁₄σ₂₂σ₂₃+σ₁₁σ₁₂²σ₂₃²λ₁₃λ₃₄+σ₁₂²σ₁₄σ₂₃²-σ₁₁²σ₂₂σ₂₃²λ₁₃λ₃₄-σ₁₂σ₁₃²σ₂₂σ₂₄+σ₁₂²σ₁₃σ₂₃σ₂₄+σ₁₁σ₁₃σ₂₂σ₂₃σ₂₄-σ₁₁σ₁₂σ₂₃²σ₂₄+σ₁₂⁴σ₃₃λ₁₃λ₃₄-2σ₁₁σ₁₂²σ₂₂σ₃₃λ₁₃λ₃₄+σ₁₁²σ₂₂²σ₃₃λ₁₃λ₃₄+σ₁₂²σ₁₃σ₂₂σ₃₄-σ₁₁σ₁₃σ₂₂²σ₃₄-σ₁₂³σ₂₃σ₃₄+σ₁₁σ₁₂σ₂₂σ₂₃σ₃₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Vanishing Ideal

Zero Vanishing Ideal