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: λ₂₄ Identified

Algebraic Equations:

σ₁₃²σ₂₂λ₂₄+σ₁₃σ₁₄σ₂₃+σ₁₁σ₂₃²λ₂₄-σ₁₃²σ₂₄-σ₁₁σ₂₂σ₃₃λ₂₄+σ₁₁σ₂₄σ₃₃-σ₁₁σ₂₃σ₃₄

Single Door Criterion:

{2} ⊥ {4} | {1,3}

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: ω₂₃ Identified

Algebraic Equations:

-σ₂₃+ω₂₃

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₄²σ₂₃²-2σ₁₃σ₁₄σ₂₃σ₂₄+σ₁₃²σ₂₄²-σ₁₄²σ₂₂σ₃₃-σ₁₁σ₂₄²σ₃₃+2σ₁₃σ₁₄σ₂₂σ₃₄+2σ₁₁σ₂₃σ₂₄σ₃₄-σ₁₁σ₂₂σ₃₄²-σ₁₃²σ₂₂σ₄₄-σ₁₁σ₂₃²σ₄₄+σ₁₁σ₂₂σ₃₃σ₄₄+σ₁₃²σ₂₂ω₄₄+σ₁₁σ₂₃²ω₄₄-σ₁₁σ₂₂σ₃₃ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄+λ₁₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}
{1} ⊥ {3,4} | {2}

Vanishing Ideal

Constraint Set:

σ₁₂

All constraints are determinantal

Trek-separation:

{1} ⊥ {2} | ({},{})