
Parameter: λ24 Identified
Algebraic Equations:
σ12λ24-σ14
Instrumental Variable:
1 | {}
1 | {3}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω12 Identified
Algebraic Equations:
-σ12+ω12
Parameter: ω22 Identified
Algebraic Equations:
-σ22+ω22
Parameter: ω24 Identified
Algebraic Equations:
σ14σ22-σ12σ24+σ12ω24
Parameter: ω33 Identified
Algebraic Equations:
-σ33+ω33
Parameter: ω44 Identified
Algebraic Equations:
-σ142σ22+2σ12σ14σ24-σ122σ44+σ122ω44
Constraint Set:
σ34,
σ23,
σ13
All constraints are determinantal
Trek-separation:
{3} ⊥ {1,2,4} | ({},{})
{1,3} ⊥ {1,2,4} | ({1},{})
{2,3} ⊥ {1,2,4} | ({2},{})
{4,3} ⊥ {1,2,4} | ({4},{})
{1,3} ⊥ {2,4} | ({},{2})
{1,2,3} ⊥ {1,2,4} | ({1,2},{})
{1,4,3} ⊥ {1,2,4} | ({1,4},{})
{2,4,3} ⊥ {1,2,4} | ({2,4},{})
Algebraic Equations:
σ12λ24-σ14
Instrumental Variable:
1 | {}
1 | {3}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω12 Identified
Algebraic Equations:
-σ12+ω12
Parameter: ω22 Identified
Algebraic Equations:
-σ22+ω22
Parameter: ω24 Identified
Algebraic Equations:
σ14σ22-σ12σ24+σ12ω24
Parameter: ω33 Identified
Algebraic Equations:
-σ33+ω33
Parameter: ω44 Identified
Algebraic Equations:
-σ142σ22+2σ12σ14σ24-σ122σ44+σ122ω44
Vanishing Ideal
Constraint Set:
σ34,
σ23,
σ13
All constraints are determinantal
Trek-separation:
{3} ⊥ {1,2,4} | ({},{})
{1,3} ⊥ {1,2,4} | ({1},{})
{2,3} ⊥ {1,2,4} | ({2},{})
{4,3} ⊥ {1,2,4} | ({4},{})
{1,3} ⊥ {2,4} | ({},{2})
{1,2,3} ⊥ {1,2,4} | ({1,2},{})
{1,4,3} ⊥ {1,2,4} | ({1,4},{})
{2,4,3} ⊥ {1,2,4} | ({2,4},{})