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Regarding the first point A model like this gives biased result due to unmeasured confounding (unavailable variables): e.g. very sick patients are excluded from rehabilitation and very fit patients do not need much rehabilitation. No modelling solution will be able to "fix" this. You'll want to state this as a limitation of your study and ...


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I wonder if this difference could be due to some sort of weighting performed by the model to account for different number of cases in each group. The difference between the results of lmer and your manual computations is due to that you are manually computing fixed effects-estimates of the group means (and their sample variance) a.k.a. BLUEs (best linear ...


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