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If you have fit m models to m datasets in multiple imputation, what is the approach to assessing the pooled results if some of the m models have issues?

For example, you fit a glm to 20 data sets generated from multiple imputation and are interested in the statistical significance of the coefficients (inferences) from the pooled results. Let's say 5 of the models have influential points that, if removed, affect the inference results of the models.

Or maybe the residual structure of 5 (or whatever number) of the models doesn't fit the assumptions of the glm.

In these cases, how do you assess the pooled coefficient results? Does it depend on the number of models that have issues, the extent of the issues, a combination of both? Other considerations?

Andy
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