Thank you for the intersting information, the type of missingness is "missing at random" (MAR), i.e., the missingness can be related to fully avaiable covariates. Furthermore, approx 20 % of the data are missing, I have approx 1000 data for each of 10 different sites (thus, 10.000 data nested witin sites).

Unfortunately I can't open your provided link, "ovid login failure", could you please send me title/authors of the publication? Thanks!

They key thing I want to understand is how imputed values are correctly considered within regression analysis, since 1.) They do not really add additional information to the data but only additional data points, thus, the result should be some kind of "pseudoreplication", 2.) Imputed values are connected to uncertainties, and the question is how to propagate this uncertainties to the SE's of regression coefficients.