What is really needed to justify ignoring the response mechanism for modelling purposes?
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With incomplete data, the standard argument for when the response mechanism can be ignored for modelling Purposes requires that realised Missing at Random (MAR) holds for each density in the model and that distinctness of parameters holds for the model's parameter space. We explain why the distinctness of parameters criterion is too general because it allows the validity of an analysis to be determined by a factor different from any of (i) the observed data, (ii) the likelihood used to analyse the data and (iii) the analyst's assumptions about the underlying data generation process. We further explain why realised MAR alone, when applied appropriately, provides sufficient justification for ignoring the response mechanism when making direct likelihood inferences from incomplete data.
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