Testing the goodness of fit of a model involving nonignorable missing data is a first step, that cannot be overlooked. Of course, it is impossible to get a goodness of fit test for the process of missingness, as it is only partially observed. So applying a goodness of fit test to the marginal model (which include the process of missingness) is a necessary preliminary step. If the null hypothesis is rejected, then we can suspect an incorrect specification of i) the missingness process or of ii) the main statistical model for the data. But, if the null hypothesis is not rejected, we can go ahead, as usual, in similar situations.
If the null hypothesis is rejected, and if we have a strong belief that our main statistical model is correct, then we can suspect the missingness process. Building a test for the missingness process itself is not mathematically possible with similar data.
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