Parameter: λ₁₂ Identified

Algebraic Equations:

σ₁₁λ₁₂-σ₁₂

Single Door Criterion:

{1} ⊥ {2,4} | {}
{1} ⊥ {2} | {4}

Parameter: λ₂₃ Identified

Algebraic Equations:

σ₁₂²λ₂₃-σ₁₂σ₁₃-σ₁₁σ₂₂λ₂₃+σ₁₁σ₂₃

Single Door Criterion:

{2} ⊥ {3,4} | {1}
{2} ⊥ {3} | {1,4}

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₃ Identified

Algebraic Equations:

σ₁₁σ₁₃σ₂₂-σ₁₁σ₁₂σ₂₃+σ₁₂²ω₁₃-σ₁₁σ₂₂ω₁₃

Parameter: ω₂₂ Identified

Algebraic Equations:

σ₁₂²-σ₁₁σ₂₂+σ₁₁ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

-σ₁₂²σ₁₃²σ₂₂+2σ₁₂³σ₁₃σ₂₃-2σ₁₁σ₁₂²σ₂₃²+σ₁₁²σ₂₂σ₂₃²-σ₁₂⁴σ₃₃+2σ₁₁σ₁₂²σ₂₂σ₃₃-σ₁₁²σ₂₂²σ₃₃+σ₁₂⁴ω₃₃-2σ₁₁σ₁₂²σ₂₂ω₃₃+σ₁₁²σ₂₂²ω₃₃

Parameter: ω₄₄ Identified

Algebraic Equations:

-σ₄₄+ω₄₄

Total Effect of X₁ on X₃: λ₁₂λ₂₃ Identified

Each Parameter Identified

Vanishing Ideal

Constraint Set:

σ₃₄,
σ₂₄,
σ₁₄

All constraints are determinantal

Trek-separation:

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