  This paper provides further insight into the key concept of missing at random
(MAR) in incomplete data analysis. Following the usual selection modelling
approach we envisage two models with separable parameters: a model for the
response of interest and a model for the missing data mechanism
  (MDM). If the response model is given by a complete density family, then
frequentist inference from the likelihood function ignoring the MDM is valid if
and only if the MDM is MAR. This necessary and sufficient condition also holds
more generally for models for coarse data, such as censoring.
  Examples are given to show the necessity of the completeness of the
underlying model for this equivalence to hold.
