Imagine I want to regress y on x1, ..., xk. I have missing values in the dependent variable, as well as in some of the independent variables, and have used multiple imputation to create D imputed datasets.
So I run the regression using each of the datasets, combine the estimated parameters and standard errors using Rubin's rules, etc. I can also obtain predicted values of y.
My question is: can I obtain predicted residuals? I would have thought that since I can predict yhat, it would be acceptable to use yhat to predict residuals ... particularly for observations without missing values of y, but also when there D imputed values of y, just by averaging them first.
However, the Stata manual states that this is not appropriate:
"The MI predictions should be treated as a final result; they should not be used as intermediate results in computations. For example, MI estimates of the linear predictor cannot be used to compute residuals as is done in non-MI analysis. Instead, completed-data residuals should be calculated for each imputed dataset ... "
Is there any reason why I should not calculate residuals in the way I described, or by predicting separate residuals for each imputed dataset, and then averaging those? Thanks.