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: 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 Identified

Algebraic Equations:

σ₁₂σ₁₃σ₁₄σ₂₃-σ₁₁σ₁₄σ₂₃²-σ₁₂σ₁₃²σ₂₄+σ₁₁σ₁₃σ₂₃σ₂₄-σ₁₂²σ₁₄σ₃₃+σ₁₁σ₁₄σ₂₂σ₃₃+σ₁₂²σ₁₃σ₃₄-σ₁₁σ₁₃σ₂₂σ₃₄+σ₁₃²σ₂₂ω₁₄-2σ₁₂σ₁₃σ₂₃ω₁₄+σ₁₁σ₂₃²ω₁₄+σ₁₂²σ₃₃ω₁₄-σ₁₁σ₂₂σ₃₃ω₁₄

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 Identified

Algebraic Equations:

-σ₁₃²σ₁₄²σ₂₂²σ₃₃+2σ₁₂σ₁₃σ₁₄²σ₂₂σ₂₃σ₃₃-σ₁₂²σ₁₄²σ₂₃²σ₃₃+2σ₁₂σ₁₃²σ₁₄σ₂₂σ₂₄σ₃₃-2σ₁₂²σ₁₃σ₁₄σ₂₃σ₂₄σ₃₃-2σ₁₁σ₁₃σ₁₄σ₂₂σ₂₃σ₂₄σ₃₃+2σ₁₁σ₁₂σ₁₄σ₂₃²σ₂₄σ₃₃-σ₁₂²σ₁₃²σ₂₄²σ₃₃+2σ₁₁σ₁₂σ₁₃σ₂₃σ₂₄²σ₃₃-σ₁₁²σ₂₃²σ₂₄²σ₃₃+2σ₁₃³σ₁₄σ₂₂²σ₃₄-6σ₁₂σ₁₃²σ₁₄σ₂₂σ₂₃σ₃₄+4σ₁₂²σ₁₃σ₁₄σ₂₃²σ₃₄+2σ₁₁σ₁₃σ₁₄σ₂₂σ₂₃²σ₃₄-2σ₁₁σ₁₂σ₁₄σ₂₃³σ₃₄-2σ₁₂σ₁₃³σ₂₂σ₂₄σ₃₄+4σ₁₂²σ₁₃²σ₂₃σ₂₄σ₃₄+2σ₁₁σ₁₃²σ₂₂σ₂₃σ₂₄σ₃₄-6σ₁₁σ₁₂σ₁₃σ₂₃²σ₂₄σ₃₄+2σ₁₁²σ₂₃³σ₂₄σ₃₄+2σ₁₂²σ₁₃²σ₂₂σ₃₄²-2σ₁₁σ₁₃²σ₂₂²σ₃₄²-4σ₁₂³σ₁₃σ₂₃σ₃₄²+4σ₁₁σ₁₂σ₁₃σ₂₂σ₂₃σ₃₄²+2σ₁₁σ₁₂²σ₂₃²σ₃₄²-2σ₁₁²σ₂₂σ₂₃²σ₃₄²+σ₁₂⁴σ₃₃σ₃₄²-2σ₁₁σ₁₂²σ₂₂σ₃₃σ₃₄²+σ₁₁²σ₂₂²σ₃₃σ₃₄²-σ₁₃⁴σ₂₂²σ₄₄+4σ₁₂σ₁₃³σ₂₂σ₂₃σ₄₄-4σ₁₂²σ₁₃²σ₂₃²σ₄₄-2σ₁₁σ₁₃²σ₂₂σ₂₃²σ₄₄+4σ₁₁σ₁₂σ₁₃σ₂₃³σ₄₄-σ₁₁²σ₂₃⁴σ₄₄-2σ₁₂²σ₁₃²σ₂₂σ₃₃σ₄₄+2σ₁₁σ₁₃²σ₂₂²σ₃₃σ₄₄+4σ₁₂³σ₁₃σ₂₃σ₃₃σ₄₄-4σ₁₁σ₁₂σ₁₃σ₂₂σ₂₃σ₃₃σ₄₄-2σ₁₁σ₁₂²σ₂₃²σ₃₃σ₄₄+2σ₁₁²σ₂₂σ₂₃²σ₃₃σ₄₄-σ₁₂⁴σ₃₃²σ₄₄+2σ₁₁σ₁₂²σ₂₂σ₃₃²σ₄₄-σ₁₁²σ₂₂²σ₃₃²σ₄₄+σ₁₃⁴σ₂₂²ω₄₄-4σ₁₂σ₁₃³σ₂₂σ₂₃ω₄₄+4σ₁₂²σ₁₃²σ₂₃²ω₄₄+2σ₁₁σ₁₃²σ₂₂σ₂₃²ω₄₄-4σ₁₁σ₁₂σ₁₃σ₂₃³ω₄₄+σ₁₁²σ₂₃⁴ω₄₄+2σ₁₂²σ₁₃²σ₂₂σ₃₃ω₄₄-2σ₁₁σ₁₃²σ₂₂²σ₃₃ω₄₄-4σ₁₂³σ₁₃σ₂₃σ₃₃ω₄₄+4σ₁₁σ₁₂σ₁₃σ₂₂σ₂₃σ₃₃ω₄₄+2σ₁₁σ₁₂²σ₂₃²σ₃₃ω₄₄-2σ₁₁²σ₂₂σ₂₃²σ₃₃ω₄₄+σ₁₂⁴σ₃₃²ω₄₄-2σ₁₁σ₁₂²σ₂₂σ₃₃²ω₄₄+σ₁₁²σ₂₂²σ₃₃²ω₄₄

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 Identified

Each Parameter Identified

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Vanishing Ideal

Zero Vanishing Ideal