Parameter: λ12 Identified
Algebraic Equations:
σ11λ12-σ12
Single Door Criterion:
{1} ⊥ {2} | {}
Parameter: λ13
Parameter: λ14
Parameter: λ23 Identified
Algebraic Equations:
σ122λ23-σ12σ13-σ11σ22λ23+σ11σ23
Single Door Criterion:
{2} ⊥ {3,4} | {1}
Parameter: λ34 Identified
Algebraic Equations:
σ12σ13λ34-σ12σ14-σ11σ23λ34+σ11σ24
Instrumental Variable:
2 | {1}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω13
Parameter: ω14
Parameter: ω22 Identified
Algebraic Equations:
σ122-σ11σ22+σ11ω22
Parameter: ω33
Parameter: ω44
Total Effect of X1 on X3: λ12λ23+λ13
Path-specific Effect of X1 on X3: λ12λ23 Identified
Algebraic Equations:
σ11σ122λ12λ23-σ122σ13-σ112σ22λ12λ23+σ11σ12σ23
Total Effect of X1 on X4: λ12λ23λ34+λ13λ34+λ14
Path-specific Effect of X1 on X4: λ12λ23λ34 Identified
Algebraic Equations:
σ11σ122λ12λ23λ34-σ122σ14-σ112σ22λ12λ23λ34+σ11σ12σ24
Path-specific Effect of X1 on X4: λ13λ34
Total Effect of X2 on X4: λ23λ34 Identified
Each Parameter Identified
Back Door Criterion:
{2} ⊥ {3,4} | {1}
Algebraic Equations:
σ11λ12-σ12
Single Door Criterion:
{1} ⊥ {2} | {}
Parameter: λ13
Parameter: λ14
Parameter: λ23 Identified
Algebraic Equations:
σ122λ23-σ12σ13-σ11σ22λ23+σ11σ23
Single Door Criterion:
{2} ⊥ {3,4} | {1}
Parameter: λ34 Identified
Algebraic Equations:
σ12σ13λ34-σ12σ14-σ11σ23λ34+σ11σ24
Instrumental Variable:
2 | {1}
Parameter: ω11 Identified
Algebraic Equations:
-σ11+ω11
Parameter: ω13
Parameter: ω14
Parameter: ω22 Identified
Algebraic Equations:
σ122-σ11σ22+σ11ω22
Parameter: ω33
Parameter: ω44
Total Effect of X1 on X3: λ12λ23+λ13
Path-specific Effect of X1 on X3: λ12λ23 Identified
Algebraic Equations:
σ11σ122λ12λ23-σ122σ13-σ112σ22λ12λ23+σ11σ12σ23
Total Effect of X1 on X4: λ12λ23λ34+λ13λ34+λ14
Path-specific Effect of X1 on X4: λ12λ23λ34 Identified
Algebraic Equations:
σ11σ122λ12λ23λ34-σ122σ14-σ112σ22λ12λ23λ34+σ11σ12σ24
Path-specific Effect of X1 on X4: λ13λ34
Total Effect of X2 on X4: λ23λ34 Identified
Each Parameter Identified
Back Door Criterion:
{2} ⊥ {3,4} | {1}