Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {2,3} | {}
{1} ⊥ {3} | {2}

Parameter: λ₂₃

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: ω₁₄ Identified

Algebraic Equations:

-σ₁₁σ₁₄σ₂₃²+σ₁₁σ₁₃σ₂₃σ₂₄+σ₁₁σ₁₄σ₂₂σ₃₃-σ₁₁σ₁₃σ₂₂σ₃₄+σ₁₃²σ₂₂ω₁₄+σ₁₁σ₂₃²ω₁₄-σ₁₁σ₂₂σ₃₃ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₃

Parameter: ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

σ₁₃²σ₁₄²σ₂₂σ₂₃²-2σ₁₃³σ₁₄σ₂₂σ₂₃σ₂₄+σ₁₃⁴σ₂₂σ₂₄²-σ₁₃²σ₁₄²σ₂₂²σ₃₃-2σ₁₁σ₁₃²σ₂₂σ₂₄²σ₃₃-σ₁₁²σ₂₃²σ₂₄²σ₃₃+σ₁₁²σ₂₂σ₂₄²σ₃₃²+2σ₁₃³σ₁₄σ₂₂²σ₃₄+4σ₁₁σ₁₃²σ₂₂σ₂₃σ₂₄σ₃₄+2σ₁₁²σ₂₃³σ₂₄σ₃₄-2σ₁₁²σ₂₂σ₂₃σ₂₄σ₃₃σ₃₄-2σ₁₁σ₁₃²σ₂₂²σ₃₄²-σ₁₁²σ₂₂σ₂₃²σ₃₄²+σ₁₁²σ₂₂²σ₃₃σ₃₄²-σ₁₃⁴σ₂₂²σ₄₄-2σ₁₁σ₁₃²σ₂₂σ₂₃²σ₄₄-σ₁₁²σ₂₃⁴σ₄₄+2σ₁₁σ₁₃²σ₂₂²σ₃₃σ₄₄+2σ₁₁²σ₂₂σ₂₃²σ₃₃σ₄₄-σ₁₁²σ₂₂²σ₃₃²σ₄₄+σ₁₃⁴σ₂₂²ω₄₄+2σ₁₁σ₁₃²σ₂₂σ₂₃²ω₄₄+σ₁₁²σ₂₃⁴ω₄₄-2σ₁₁σ₁₃²σ₂₂²σ₃₃ω₄₄-2σ₁₁²σ₂₂σ₂₃²σ₃₃ω₄₄+σ₁₁²σ₂₂²σ₃₃²ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄ Identified

Each Parameter Identified

Total Effect of X₂ on X₄: λ₂₃λ₃₄+λ₂₄

Path-specific Effect of X₂ on X₄: λ₂₃λ₃₄

Vanishing Ideal

Constraint Set:

σ₁₂

All constraints are determinantal

Trek-separation:

{1} ⊥ {2} | ({},{})