Bootstrapped prediction intervals

[palday]

Mentioned to me by @bbolker and broadly similar to a Bayesian posterior predictive distribution....

What if we did a bootstrap and then pulled the fitted/predicted values out and then plotted those to get a sense of that variability

[bbolker]

Compare the design of lme4::bootMer, which takes a model and an arbitrary FUN function argument. By default FUN is set to a function that returns a parameter vector, converting theta to a user-friendly (sd/cor or var/cov) scale. But if FUN is set to predict, you get an analogue of a Bayesian predictive distribution (actually, you'd need simulate() to get a posterior predictive distribution; if you use predict you get parametric uncertainty but not conditional-distribution uncertainty).