Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₂²λ₁₃-σ₁₁σ₂₂λ₁₃+σ₁₃σ₂₂-σ₁₂σ₂₃

Single Door Criterion:

{1} ⊥ {3} | {2}

Parameter: λ₁₄

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₂²λ₂₃-σ₁₂σ₁₃-σ₁₁σ₂₂λ₂₃+σ₁₁σ₂₃

Single Door Criterion:

{2} ⊥ {3} | {1}

Parameter: λ₂₄

Parameter: λ₃₄

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂ Identified

Algebraic Equations:

-σ₁₂+ω₁₂

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

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

Parameter: ω₃₄

Parameter: ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄+λ₁₄ Identified

Algebraic Equations:

σ₁₂²λ₁₃λ₃₄+σ₁₂²λ₁₄-σ₁₁σ₂₂λ₁₃λ₃₄-σ₁₁σ₂₂λ₁₄+σ₁₄σ₂₂-σ₁₂σ₂₄

Back Door Criterion:

{1} ⊥ {3,4} | {2}

Path-specific Effect of X₁ on X₄: λ₁₃λ₃₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄+λ₂₄ Identified

Algebraic Equations:

σ₁₂²λ₂₃λ₃₄+σ₁₂²λ₂₄-σ₁₂σ₁₄-σ₁₁σ₂₂λ₂₃λ₃₄-σ₁₁σ₂₂λ₂₄+σ₁₁σ₂₄

Back Door Criterion:

{2} ⊥ {3,4} | {1}

Path-specific Effect of X₂ on X₄: λ₂₃λ₃₄

Vanishing Ideal

Zero Vanishing Ideal