
Parameter: λ24 Identified
Algebraic Equations:
σ23λ24-σ34,
σ12λ24-σ14
Instrumental Variable:
1 | {}
1 | {3}
3 | {}
3 | {1}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω12 Identified
Algebraic Equations:
-σ12+ω12
Parameter: ω22 Identified
Algebraic Equations:
-σ22+ω22
Parameter: ω23 Identified
Algebraic Equations:
-σ23+ω23
Parameter: ω24 Identified
Algebraic Equations:
-σ23σ24+σ22σ34+σ23ω24,
σ14σ22-σ12σ24+σ12ω24
Parameter: ω33 Identified
Algebraic Equations:
-σ33+ω33
Parameter: ω44 Identified
Algebraic Equations:
2σ23σ24σ34-σ22σ342-σ232σ44+σ232ω44,
-σ14σ22σ34+2σ12σ24σ34-σ12σ23σ44+σ12σ23ω44,
-σ142σ22+2σ12σ14σ24-σ122σ44+σ122ω44
Constraint Set:
σ13,
σ14σ23-σ12σ34
All constraints are determinantal
Trek-separation:
{1} ⊥ {3} | ({},{})
{1,3} ⊥ {2,4} | ({},{2})
Algebraic Equations:
σ23λ24-σ34,
σ12λ24-σ14
Instrumental Variable:
1 | {}
1 | {3}
3 | {}
3 | {1}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω12 Identified
Algebraic Equations:
-σ12+ω12
Parameter: ω22 Identified
Algebraic Equations:
-σ22+ω22
Parameter: ω23 Identified
Algebraic Equations:
-σ23+ω23
Parameter: ω24 Identified
Algebraic Equations:
-σ23σ24+σ22σ34+σ23ω24,
σ14σ22-σ12σ24+σ12ω24
Parameter: ω33 Identified
Algebraic Equations:
-σ33+ω33
Parameter: ω44 Identified
Algebraic Equations:
2σ23σ24σ34-σ22σ342-σ232σ44+σ232ω44,
-σ14σ22σ34+2σ12σ24σ34-σ12σ23σ44+σ12σ23ω44,
-σ142σ22+2σ12σ14σ24-σ122σ44+σ122ω44
Vanishing Ideal
Constraint Set:
σ13,
σ14σ23-σ12σ34
All constraints are determinantal
Trek-separation:
{1} ⊥ {3} | ({},{})
{1,3} ⊥ {2,4} | ({},{2})