Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 207 / 3 / 3 / b

Write the complete-data model as $p_{\theta }(y\mid a)$ and the missingness model as $q_{\psi }(r\mid y,a)$. Under MAR,Therefore the observed-data likelihood factorizes asWith distinct parameters, the first factor does not involve $\theta$. Maximizing or integrating the second factor therefore gives the same likelihood inference for $\theta$ as modeling the missingness process explicitly. Hence MAR plus distinctness makes missingness ignorable.