It would be really nice to have flexibility in the linear mixed model to model the response as a function of $y$, but still return estimates with respect to $y$, i.e.,
$f(y) = X\beta + uj + e{ij}$,
but return $\hat \mu$ as the average of $y$, not $f(y)$.
Here, we should only have to require that $f$ has an inverse. We will need find and then compute the inverse on each unit the linear mixed model has predicted onto in the estimation and bootstrap MSE estimation processes.
It would be really nice to have flexibility in the linear mixed model to model the response as a function of $y$, but still return estimates with respect to $y$, i.e., $f(y) = X\beta + uj + e{ij}$, but return $\hat \mu$ as the average of $y$, not $f(y)$.
Here, we should only have to require that $f$ has an inverse. We will need find and then compute the inverse on each unit the linear mixed model has predicted onto in the estimation and bootstrap MSE estimation processes.