# Why is it recommended to keep use.u=T (in bootMer) when doing parametric bootstrap for lmer models?

I am performing a parametric bootstrap with the intention of using the simulated values to create confidence intervals for my coefficients in a mixed model. I saw that it was generally recommended to set use.u=T in the bootMer function in R's lme4 package and I was wondering why? I would think that resampling the random effects would make sense in order to capture the full uncertainty.

For clarification, if I were to rerun the model on a dataset collected more recently, the actual levels (or categories) would be the same, just the values that would be different.

If there are further resources/papers that go into this, that would be helpful.

In mixed effects models, uncertainty arises from both the fixed effects, which represent the population-level trends, and random effects, which capture the variations at the group or cluster level. The parameter use.u in the bootMer function determines how the random effects are treated during the bootstrap procedure.
When use.u = TRUE, the bootstrapping process involves resampling the random effects. This means that for each bootstrap sample, new random effects are generated based on the estimated variance components from the original model. This approach reflects the inherent variability in the random effects, providing a better measure of the overall uncertainty in the model parameters. On the other hand, setting use.u = FALSE fixes the random effects as estimated from the original data and only resamples the residuals. This method can underestimate the total uncertainty because it does not account for the variability in the random effects.
For practical applications, especially when constructing confidence intervals for coefficients, we need to account for all sources of variability. Confidence intervals that incorporate the variability of both fixed and random effects are more accurate and reflective of the true uncertainty in the parameter estimates. This is particularly important in scenarios where new datasets may have the same levels or categories but different values. By using use.u = TRUE, you simulate this situation in the bootstrap procedure, leading to more robust and reliable confidence intervals.