
Parameter: λ12
Parameter: λ34 Identified
Algebraic Equations:
σ33λ34-σ34,
σ23λ34-σ24
Single Door Criterion:
{3} ⊥ {1,4} | {}
{3} ⊥ {4} | {2}
{3} ⊥ {4} | {1}
{3} ⊥ {4} | {1,2}
Instrumental Variable:
1 | {2}
2 | {}
2 | {1}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω12
Parameter: ω22
Parameter: ω23 Identified
Algebraic Equations:
-σ23+ω23
Parameter: ω33 Identified
Algebraic Equations:
-σ33+ω33
Parameter: ω44 Identified
Algebraic Equations:
σ342-σ33σ44+σ33ω44,
σ24σ34-σ23σ44+σ23ω44
Constraint Set:
σ14,
σ13,
σ24σ33-σ23σ34
All constraints are determinantal
Trek-separation:
{1} ⊥ {3,4} | ({},{})
{2,1} ⊥ {3,4} | ({2},{})
{3,1} ⊥ {3,4} | ({3},{})
{4,1} ⊥ {3,4} | ({4},{})
{1,2,3} ⊥ {3,4} | ({},{3})
{1,2,3} ⊥ {2,3,4} | ({},{2,3})
{1,2,3} ⊥ {1,3,4} | ({},{1,3})
Parameter: λ34 Identified
Algebraic Equations:
σ33λ34-σ34,
σ23λ34-σ24
Single Door Criterion:
{3} ⊥ {1,4} | {}
{3} ⊥ {4} | {2}
{3} ⊥ {4} | {1}
{3} ⊥ {4} | {1,2}
Instrumental Variable:
1 | {2}
2 | {}
2 | {1}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω12
Parameter: ω22
Parameter: ω23 Identified
Algebraic Equations:
-σ23+ω23
Parameter: ω33 Identified
Algebraic Equations:
-σ33+ω33
Parameter: ω44 Identified
Algebraic Equations:
σ342-σ33σ44+σ33ω44,
σ24σ34-σ23σ44+σ23ω44
Vanishing Ideal
Constraint Set:
σ14,
σ13,
σ24σ33-σ23σ34
All constraints are determinantal
Trek-separation:
{1} ⊥ {3,4} | ({},{})
{2,1} ⊥ {3,4} | ({2},{})
{3,1} ⊥ {3,4} | ({3},{})
{4,1} ⊥ {3,4} | ({4},{})
{1,2,3} ⊥ {3,4} | ({},{3})
{1,2,3} ⊥ {2,3,4} | ({},{2,3})
{1,2,3} ⊥ {1,3,4} | ({},{1,3})