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

Missing at random, likelihood ignorability and model completeness