Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2} | {}

Parameter: λ₁₃

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₂²λ₂₃-σ₁₂σ₁₃-σ₁₁σ₂₂λ₂₃+σ₁₁σ₂₃

Single Door Criterion:

{2} ⊥ {3} | {1}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₃₃

Total Effect of X₁ on X₃: λ₁₂λ₂₃+λ₁₃

Path-specific Effect of X₁ on X₃: λ₁₂λ₂₃ Identified

Algebraic Equations:

σ₁₁σ₁₂²λ₁₂λ₂₃-σ₁₂²σ₁₃-σ₁₁²σ₂₂λ₁₂λ₂₃+σ₁₁σ₁₂σ₂₃

Vanishing Ideal

Zero Vanishing Ideal