Parameter: λ₁₂

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₂σ₁₃λ₁₄-σ₁₁σ₂₃λ₁₄+σ₁₄σ₂₃-σ₁₃σ₂₄,
σ₁₂²λ₁₄-σ₁₁σ₂₂λ₁₄+σ₁₄σ₂₂-σ₁₂σ₂₄

Single Door Criterion:

{1} ⊥ {3,4} | {2}
{1} ⊥ {4} | {2,3}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₂₂λ₂₃-σ₂₃,
σ₁₂λ₂₃-σ₁₃

Single Door Criterion:

{2} ⊥ {3} | {}
{2} ⊥ {3} | {1}

Instrumental Variable:

1 | {}

Parameter: λ₂₄ Identified

Algebraic Equations:

σ₁₂σ₁₃σ₂₃λ₂₄-σ₁₃σ₁₄σ₂₃-σ₁₁σ₂₃²λ₂₄+σ₁₃²σ₂₄-σ₁₂²σ₃₃λ₂₄+σ₁₂σ₁₄σ₃₃+σ₁₁σ₂₂σ₃₃λ₂₄-σ₁₁σ₂₄σ₃₃-σ₁₂σ₁₃σ₃₄+σ₁₁σ₂₃σ₃₄,
σ₁₂²σ₂₃²λ₂₄-σ₁₂σ₁₄σ₂₃²-σ₁₁σ₂₂σ₂₃²λ₂₄+σ₁₂σ₁₃σ₂₃σ₂₄-σ₁₂²σ₂₂σ₃₃λ₂₄+σ₁₂σ₁₄σ₂₂σ₃₃+σ₁₁σ₂₂²σ₃₃λ₂₄-σ₁₁σ₂₂σ₂₄σ₃₃-σ₁₂²σ₂₃σ₃₄+σ₁₁σ₂₂σ₂₃σ₃₄

Single Door Criterion:

{2} ⊥ {4} | {1,3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₂₃²λ₃₄-σ₂₃σ₂₄-σ₂₂σ₃₃λ₃₄+σ₂₂σ₃₄,
σ₁₃σ₂₃λ₃₄-σ₁₃σ₂₄-σ₁₂σ₃₃λ₃₄+σ₁₂σ₃₄

Single Door Criterion:

{3} ⊥ {1,4} | {2}
{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₂₃²-σ₂₂σ₃₃+σ₂₂ω₃₃,
σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₂₃²+2σ₁₃σ₁₄σ₂₃σ₂₄-σ₁₃²σ₂₄²+σ₁₄²σ₂₂σ₃₃-2σ₁₂σ₁₄σ₂₄σ₃₃+σ₁₁σ₂₄²σ₃₃+2σ₁₂σ₁₃σ₂₄σ₃₄-2σ₁₁σ₂₃σ₂₄σ₃₄-σ₁₂²σ₃₄²+σ₁₁σ₂₂σ₃₄²-σ₁₂σ₁₃σ₂₃σ₄₄+σ₁₁σ₂₃²σ₄₄+σ₁₂²σ₃₃σ₄₄-σ₁₁σ₂₂σ₃₃σ₄₄+σ₁₂σ₁₃σ₂₃ω₄₄-σ₁₁σ₂₃²ω₄₄-σ₁₂²σ₃₃ω₄₄+σ₁₁σ₂₂σ₃₃ω₄₄,
-σ₁₄²σ₂₂σ₂₃²+2σ₁₂σ₁₄σ₂₃²σ₂₄-σ₁₂σ₁₃σ₂₃σ₂₄²+σ₁₄²σ₂₂²σ₃₃-2σ₁₂σ₁₄σ₂₂σ₂₄σ₃₃+σ₁₁σ₂₂σ₂₄²σ₃₃+2σ₁₂²σ₂₃σ₂₄σ₃₄-2σ₁₁σ₂₂σ₂₃σ₂₄σ₃₄-σ₁₂²σ₂₂σ₃₄²+σ₁₁σ₂₂²σ₃₄²-σ₁₂²σ₂₃²σ₄₄+σ₁₁σ₂₂σ₂₃²σ₄₄+σ₁₂²σ₂₂σ₃₃σ₄₄-σ₁₁σ₂₂²σ₃₃σ₄₄+σ₁₂²σ₂₃²ω₄₄-σ₁₁σ₂₂σ₂₃²ω₄₄-σ₁₂²σ₂₂σ₃₃ω₄₄+σ₁₁σ₂₂²σ₃₃ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃

Total Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄+λ₁₂λ₂₄+λ₁₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₃λ₃₄

Path-specific Effect of X₁ on X₄: λ₁₂λ₂₄

Total Effect of X₂ on X₄: λ₂₃λ₃₄+λ₂₄ Identified

Each Parameter Identified

Back Door Criterion:


{2} ⊥ {3,4} | {1}

Vanishing Ideal

Constraint Set:

σ₁₃σ₂₂-σ₁₂σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {2,3} | ({},{2})