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: λ₂₄

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: ω₁₂ Identified

Algebraic Equations:

-σ₁₂+ω₁₂

Parameter: ω₁₄

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₂₄

Parameter: ω₃₃ Identified

Algebraic Equations:

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

Parameter: ω₄₄

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 Identified

Algebraic Equations:

σ₁₂²σ₁₃²σ₂₂λ₂₃λ₃₄-σ₁₂σ₁₃²σ₁₄σ₂₂-σ₁₁σ₁₃²σ₂₂²λ₂₃λ₃₄-2σ₁₂³σ₁₃σ₂₃λ₂₃λ₃₄+σ₁₂²σ₁₃σ₁₄σ₂₃+2σ₁₁σ₁₂σ₁₃σ₂₂σ₂₃λ₂₃λ₃₄+σ₁₁σ₁₃σ₁₄σ₂₂σ₂₃+σ₁₁σ₁₂²σ₂₃²λ₂₃λ₃₄-σ₁₁σ₁₂σ₁₄σ₂₃²-σ₁₁²σ₂₂σ₂₃²λ₂₃λ₃₄+σ₁₂²σ₁₃²σ₂₄-2σ₁₁σ₁₂σ₁₃σ₂₃σ₂₄+σ₁₁²σ₂₃²σ₂₄+σ₁₂⁴σ₃₃λ₂₃λ₃₄-2σ₁₁σ₁₂²σ₂₂σ₃₃λ₂₃λ₃₄+σ₁₁²σ₂₂²σ₃₃λ₂₃λ₃₄-σ₁₂³σ₁₃σ₃₄+σ₁₁σ₁₂σ₁₃σ₂₂σ₃₄+σ₁₁σ₁₂²σ₂₃σ₃₄-σ₁₁²σ₂₂σ₂₃σ₃₄

Vanishing Ideal

Zero Vanishing Ideal