BLUPs / conditional modes discussion

[vasishth]

"These values are often considered as some sort of “estimates” of the random effects. It can be helpful to think of them this way but it can also be misleading. As we have stated, the random effects are not, strictly speaking, parameters — they are unobserved random variables. We don’t estimate the random effects in the same sense that we estimate parameters."

It could be worth pointing out that in Bayesian LMMs these actually have the status of parameters.