In this chapter, we discuss inference about the full-data distribution under the ignorability assumption. Under the full-data model factorization
p(y, r, | x,ω) = p(y | x,θ(ω)) p(r | y,x,ψ(ω)), (6.1) missing at random implies
p(r | y,x,ψ(ω)) = p(r | yobs,x,ψ(ω)). (6.2) Ignorability arises under the additional restriction of a priori independence between the parameters of the full-data response model θ and the parameters of the missing data mechanism ψ. Under ignorability, we only need to specify the full-data response model, not the missing data mechanism. In the following we suppress the dependence on x to maintain clarity.