A Comment on Remarks by Rubin and Hartigan

Abstract

Consider the following simplified setting of the problem discussed by Dr. Rubin. (Y, R) have a joint distribution over a population of units in which Y is a variable of interest and R = 0 for a unit if it is a nonrespondent and R = 1 otherwise. Dr. Rubin considers the problem of specifying the joint distribution of (Y, R) and distinguishes two methods of doing this:

$$({\text{M}}){\text{ Mixture model:}}\,{\text{specify}}\,Y{\text{|}}R\,{\text{and}}\,R,$$

$$({\text{S}})\,{\text{Selection model:}}\,{\text{specify}}\,R|Y\,{\text{and}}\,Y.$$