When neither MCAR nor MAR hold, we say the data are Missing Not At Random, abbreviated MNAR.
In the likelihood setting (see end of previous section) the missingness mechanism is termed non-ignorable.
What this means is
- Even accounting for all the available observed information, the reason for observations being missing still depends on the unseen observations themselves.
- To obtain valid inference, a joint model of both Y and R is required (that is a joint model of the data and the missingness mechanism).
- We cannot tell from the data at hand whether the missing observations are MCAR, NMAR or MAR (although we can distinguish between MCAR and MAR).
- In the MNAR setting it is very rare to know the appropriate model for the missingness mechanism.
Hence the central role of sensitivity analysis; we must explore how our inferences vary under assumptions of MAR, MNAR, and under various models. Unfortunately, this is often easier said than done, especially under the time and budgetary constraints of many applied projects.
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