Bootstrap to increase robustness of longitudinal models? I'm evaluating repeated measures longitudinal data with mixed effects lme4::lmer().
Due to all discussion in favor of bootstrapping as a strategy to perform internal validation and reducing bias, I bootstrapped my estimates and confidence intervals with bootMer().
The statistician I'm working with asked why I did that, since variance estimates are easily obtained from the R lmer4 or lmerTest output.
I remember reading that, when dealing with models with lots of parameters, bootstrapping SEs to obtain only parameters of interest is generally more reliable than simply inverting the Hessian matrix at the MLE for ALL parameters.
What do you think? Should I keep bootstrapped estimates or leave them?
 A: Unlike maximum likelihood estimation for a well-chosen correlation structure, the cluster bootstrap doesn't really "know" about the correlation structure. The cluster bootstrap allows for a fairly general correlation structure (just as the robust cluster sandwich estimator does) but that's not necessarily enough to be optimal.  The sandwich estimator and the cluster bootstrap do not properly handle imbalanced cases either, i.e., cases where some subjects have many more measurements than others.
The bootstrap distribution doesn't always reflect the sampling distribution, and as a result confidence intervals can be inaccurate if you do your simulation correct, i.e., look at the non-coverage separately in the left and right tails.
Overall I don't find a compelling reason to do the bootstrap in this case and would rather spend time getting the correlation structure right.  For example, random effects without anything else assumes compound symmetry, which is unrealistic for serial data.  There are many good choices for serial correlation structures.  Markov modeling is a another very general and flexible way to go.
