Maximum Likelihood for Incomplete Data

Question 1

What are the two common factorisations of the joint model f(y, r | θ, ψ) = f( Yobs, Ymis, r | θ, ψ)

Answer 1

1. Selection model factorisation:
   f(y, r | θ, ψ) = f( r | y, ψ) * f(y | θ)
2. Pattern mixture factorisation:
   f(y, r | θ, ψ) = f( y | r, θ) * f(r | ψ)

Question 2

Given missingness is MAR or MCAR and θ, ψ distinct, how is θ estimated

Answer 2

θhat = arg max(θ) L(θ | Yobs)