Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {2,3} | {}
{1} ⊥ {3} | {2}

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₁₄+σ₁₁σ₂₃²λ₁₄-σ₁₄σ₂₃²+σ₁₃σ₂₃σ₂₄-σ₁₁σ₂₂σ₃₃λ₁₄+σ₁₄σ₂₂σ₃₃-σ₁₃σ₂₂σ₃₄

Single Door Criterion:

{1} ⊥ {4} | {2,3}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃

Single Door Criterion:

{2} ⊥ {1,3} | {}
{2} ⊥ {3} | {1}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₃₄-σ₁₃σ₁₄σ₂₂+σ₁₁σ₂₃²λ₃₄-σ₁₁σ₂₃σ₂₄-σ₁₁σ₂₂σ₃₃λ₃₄+σ₁₁σ₂₂σ₃₄

Single Door Criterion:

{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₄ Identified

Algebraic Equations:

σ₁₃σ₁₄σ₂₂σ₂₃-σ₁₃²σ₂₂σ₂₄+σ₁₁σ₂₂σ₂₄σ₃₃-σ₁₁σ₂₂σ₂₃σ₃₄+σ₁₃²σ₂₂ω₂₄+σ₁₁σ₂₃²ω₂₄-σ₁₁σ₂₂σ₃₃ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃²σ₂₂+σ₁₁σ₂₃²-σ₁₁σ₂₂σ₃₃+σ₁₁σ₂₂ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₁σ₁₄²σ₂₃⁴-2σ₁₁σ₁₃σ₁₄σ₂₃³σ₂₄+σ₁₁σ₁₃²σ₂₃²σ₂₄²-σ₁₃²σ₁₄²σ₂₂²σ₃₃-2σ₁₁σ₁₄²σ₂₂σ₂₃²σ₃₃-σ₁₁²σ₂₃²σ₂₄²σ₃₃+σ₁₁σ₁₄²σ₂₂²σ₃₃²+2σ₁₃³σ₁₄σ₂₂²σ₃₄+4σ₁₁σ₁₃σ₁₄σ₂₂σ₂₃²σ₃₄+2σ₁₁²σ₂₃³σ₂₄σ₃₄-2σ₁₁σ₁₃σ₁₄σ₂₂²σ₃₃σ₃₄-σ₁₁σ₁₃²σ₂₂²σ₃₄²-2σ₁₁²σ₂₂σ₂₃²σ₃₄²+σ₁₁²σ₂₂²σ₃₃σ₃₄²-σ₁₃⁴σ₂₂²σ₄₄-2σ₁₁σ₁₃²σ₂₂σ₂₃²σ₄₄-σ₁₁²σ₂₃⁴σ₄₄+2σ₁₁σ₁₃²σ₂₂²σ₃₃σ₄₄+2σ₁₁²σ₂₂σ₂₃²σ₃₃σ₄₄-σ₁₁²σ₂₂²σ₃₃²σ₄₄+σ₁₃⁴σ₂₂²ω₄₄+2σ₁₁σ₁₃²σ₂₂σ₂₃²ω₄₄+σ₁₁²σ₂₃⁴ω₄₄-2σ₁₁σ₁₃²σ₂₂²σ₃₃ω₄₄-2σ₁₁²σ₂₂σ₂₃²σ₃₃ω₄₄+σ₁₁²σ₂₂²σ₃₃²ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄+λ₁₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}
{1} ⊥ {3,4} | {2}

Total Effect of X₂ on X₄: λ₂₃λ₃₄ Identified

Each Parameter Identified

Vanishing Ideal

Constraint Set:

σ₁₂

All constraints are determinantal

Trek-separation:

{1} ⊥ {2} | ({},{})