Semiparametric estimation in generalized additive partial linear models with nonignorable nonresponse data

Estimating the Complier Average Causal Effect with Non-Ignorable Missing Outcomes Using Likelihood Analysis

“…Based on Assumptions 3 and 7, the conditional density of the outcome Y for never-takers and always-takers, as well as the missing data models, are independent of Z. The likelihood function computed on never-takers with (Z i , D i ) = (0, 1) is ( 4) and the likelihood function computed on always-takers with (Z i , D i ) = (1, 0) is (5). We can maximize ( 4) and ( 5) to obtain that the maximum likelihood estimators for (α 1 , ϕ 1 , θ a ) and (α 0 , ϕ 0 , θ n ) are ( α 1 , ϕ 1 , θ a ) and ( α 0 , ϕ 0 , θ n ).…”

“…These unmeasured confounding variables may complicate the inference of causal effects if the missing mechanism is non-ignorable [2,3]. The missingness is named ignorable if it depends on the observed data only; otherwise, it is named non-ignorable [4,5]. Identifying the complier average causal effect becomes challenging in the presence of both non-compliance and non-ignorable missing values, as it is impossible to identify the full data distribution or the causal effect without additional assumptions.…”