判断因果效应可识别的方程方法

EQUATION METHOD ON THE DETERMINATION OF IDENTIFIABILITY FOR CAUSAL EFFECT

运用方程组求解的方法来解决一类因果效应可识别的充要条件的问题 .只要运用该方程组解的性质便可判断在一类条件独立假设之下因果效应是否可识别 .通过 3个例子分别验证了在各自假设之下因果效应的可识别性 .

The identifiability for causal effects under a type of assumptions based on conditional independence in a causal model is treated by equation method. Using this approach,one only needs to justify the properties of equations, arriving at the purpose of determing whether causal effect is identifiable. Three examples are presented to show the feasibility of the method. Consider the causal model (X,Y,Z), where X is treatment variables with values 0 and 1 and Y is response variable with values 0 and 1 and Z is the covariate variable with values 1,…,K, dividing the population into K subpopulations. The conditional independence counterfactual assumptions is (X⊥Y 0|Z∈B j),j=1,…,m, where Y 0 is the potential response. Define the matrix A K×m=(a ij) with a ij=I B j(i). Then for any observational distribution P, the causal effect is identifiable with respect to the counterfactual assumptions if and only if (a) Equations A′Γ=V P have at least one solution Γ 0=(Γ 01,…,Γ 0K)′, such that 0< Γ 0j<P(Z=j|X=1), where V P=(V P1,…,V Pm)′ with V Pj=P(Y=1|X=0,Z∈B j)· P(Z=j|X=1) and (b) Any solution Γ=(Γ 1,…,Γ K)′ to the equation A′Γ=0 must also satisfy ∑jΓ j=0. Under the identifibale case, the causal effect of nontreatment in the treatment subpopulation equals to ∑jΓ 0j,where Γ 0 is any solution in (a).