Parameter: λ12 Identified
Algebraic Equations:
σ11λ12-σ12
Single Door Criterion:
{1} ⊥ {2,4} | {}
Parameter: λ13
Parameter: λ23 Identified
Algebraic Equations:
σ14σ22λ23-σ14σ23-σ12σ24λ23+σ12σ34
Parameter: λ24 Identified
Algebraic Equations:
σ12λ24-σ14
Instrumental Variable:
1 | {}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω13
Parameter: ω22 Identified
Algebraic Equations:
σ122-σ11σ22+σ11ω22
Parameter: ω23 Identified
Algebraic Equations:
σ12σ13σ14σ22-σ122σ14σ23-σ122σ13σ24+σ11σ12σ23σ24+σ123σ34-σ11σ12σ22σ34+σ11σ14σ22ω23-σ11σ12σ24ω23
Parameter: ω24 Identified
Algebraic Equations:
σ14σ22-σ12σ24+σ12ω24
Parameter: ω33
Parameter: ω44 Identified
Algebraic Equations:
-σ142σ22+2σ12σ14σ24-σ122σ44+σ122ω44
Total Effect of X1 on X3: λ12λ23+λ13
Path-specific Effect of X1 on X3: λ12λ23 Identified
Algebraic Equations:
σ11σ14σ22λ12λ23-σ12σ14σ23-σ11σ12σ24λ12λ23+σ122σ34
Total Effect of X1 on X4: λ12λ24 Identified
Each Parameter Identified
Back Door Criterion:
{1} ⊥ {2,4} | {}
Algebraic Equations:
σ11λ12-σ12
Single Door Criterion:
{1} ⊥ {2,4} | {}
Parameter: λ13
Parameter: λ23 Identified
Algebraic Equations:
σ14σ22λ23-σ14σ23-σ12σ24λ23+σ12σ34
Parameter: λ24 Identified
Algebraic Equations:
σ12λ24-σ14
Instrumental Variable:
1 | {}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω13
Parameter: ω22 Identified
Algebraic Equations:
σ122-σ11σ22+σ11ω22
Parameter: ω23 Identified
Algebraic Equations:
σ12σ13σ14σ22-σ122σ14σ23-σ122σ13σ24+σ11σ12σ23σ24+σ123σ34-σ11σ12σ22σ34+σ11σ14σ22ω23-σ11σ12σ24ω23
Parameter: ω24 Identified
Algebraic Equations:
σ14σ22-σ12σ24+σ12ω24
Parameter: ω33
Parameter: ω44 Identified
Algebraic Equations:
-σ142σ22+2σ12σ14σ24-σ122σ44+σ122ω44
Total Effect of X1 on X3: λ12λ23+λ13
Path-specific Effect of X1 on X3: λ12λ23 Identified
Algebraic Equations:
σ11σ14σ22λ12λ23-σ12σ14σ23-σ11σ12σ24λ12λ23+σ122σ34
Total Effect of X1 on X4: λ12λ24 Identified
Each Parameter Identified
Back Door Criterion:
{1} ⊥ {2,4} | {}