Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {2,3} | {}
{1} ⊥ {3} | {2}

Parameter: λ₁₄ Identified

Algebraic Equations:

σ₁₃²λ₁₄-σ₁₁σ₃₃λ₁₄+σ₁₄σ₃₃-σ₁₃σ₃₄

Single Door Criterion:

{1} ⊥ {2,4} | {3}
{1} ⊥ {4} | {2,3}

Parameter: λ₃₄ Identified

Algebraic Equations:

σ₁₃²λ₃₄-σ₁₃σ₁₄-σ₁₁σ₃₃λ₃₄+σ₁₁σ₃₄

Single Door Criterion:

{3} ⊥ {2,4} | {1}
{3} ⊥ {4} | {1,2}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₂₂ Identified

Algebraic Equations:

-σ₂₂+ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₁₄²σ₃₃+2σ₁₃σ₁₄σ₃₄-σ₁₁σ₃₄²-σ₁₃²σ₄₄+σ₁₁σ₃₃σ₄₄+σ₁₃²ω₄₄-σ₁₁σ₃₃ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄+λ₁₄ Identified

Each Parameter Identified

Back Door Criterion:


{1} ⊥ {2,3,4} | {}
{1} ⊥ {3,4} | {2}

Vanishing Ideal

Constraint Set:

σ₂₄,
σ₂₃,
σ₁₂

All constraints are determinantal

Trek-separation:

{2} ⊥ {1,3,4} | ({},{})
{1,2} ⊥ {1,3,4} | ({1},{})
{3,2} ⊥ {1,3,4} | ({3},{})
{4,2} ⊥ {1,3,4} | ({4},{})
{1,2} ⊥ {1,3,4} | ({},{1})
{1,3,2} ⊥ {1,3,4} | ({1,3},{})
{1,4,2} ⊥ {1,3,4} | ({1,4},{})
{3,4,2} ⊥ {1,3,4} | ({3,4},{})
{3,1,2} ⊥ {1,3,4} | ({3},{1})
{4,1,2} ⊥ {1,3,4} | ({4},{1})
{1,2,3} ⊥ {3,1,4} | ({1},{3})
{1,2,3} ⊥ {1,3,4} | ({},{1,3})