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  • $\begingroup$ Welcome to cv, Marco! Did you do the simulation study in order to understand mixed models, or is there a real application behind it? I am asking because linear mixed models assume random effects with fixed variance. Estimation may perhaps be quite robust, but in 58% it breaks down - perhaps you reached a point where heteroscedasticity matters. Nice study, btw :-) Have you tried with fixed variance? $\endgroup$ Commented Jul 31, 2023 at 10:53
  • $\begingroup$ Thanks @Ute! There is a real application behind this simulation study and I try to figure out if LMMs are the right tool to address the problem. Since the heteroscedasticity we observe here is not function of another variable (e.g. variance increases with higher concentration) but a randomly changing variance around a "mean variance" I hoped that nested LMMs could be a promising tool. I tried also with crossed random effects (both variance components are fixed and Independent from each other) and didn't run into any issues. However, this does not map the situation I have in my real data. $\endgroup$ Commented Jul 31, 2023 at 11:51
  • $\begingroup$ Do you have estimates ("guestimates") for the distribution of variances? You could run your experiment with different variance distributions and check where it gives these results $\endgroup$ Commented Jul 31, 2023 at 12:25
  • $\begingroup$ Unfortunately not. Like in the simulation, I have several Projects each with nB Batches and nR replicates. The Batches have one common variance. However, this variance is randomly different between the Projects and this difference is not caused by the uncertainty in the batch variance estimation. In other words, even if I increase the number of batches towards infinite, this random variability of the batch variance across the projects would still be present and I have to consider it. $\endgroup$ Commented Jul 31, 2023 at 12:47
  • $\begingroup$ I could also be wrong. You modelled the sd as following an N(100, 10) distribution, so there is not really much variation (only +- 20% or so). On the other hand, sdRes is very small in comparison to sdB. So it is like you have replicates of the same value in each batch. Is this realistic? / / side question: do you already have data, or are you still planning? $\endgroup$ Commented Jul 31, 2023 at 14:15