I have a question about boostrapping confidence intervals for the random effects (BLUPs) of a multilevel model.
I'm currently using bootMer and there is an argument use.u=TRUE that allows one to treat the BLUPs as fixed instead of re-estimating them. Since the BLUPs are random variables it would seem appropriate to re-estimate them at each bootstrap, and indeed the default option is use.u=FALSE.
However the underlying assumption is that my clusters are a random sample of clusters drawn from a population of clusters. In my case I am running a survey experiment in 26 countries (this is the cluster of interest) which in reality were not randomly drawn. And while I am interested in drawing inferences about the larger population of countries from which my sample is drawn, I am also interested in the cluster specific effects, AKA the BLUPs, for each one of these clusters. Because of this I'm resorting to performing bootstrap to get valid confidence intervals for these "estimates".
In this case would it be OK to set use.u=TRUE?
A related question was asked here: https://stats.stackexchange.com/questions/417518/how-to-get-confidence-intervals-for-modeled-data-of-lmer-model-in-r-with-bootmer
however I'm not sure if the answer travelled to my case. Anyone have ideas?
