Hi,
I would like to estimate the eta shrinkage of an augmented DeepNLME model. The base model has a very high shrinkage (0.7-0.9) because it is modelling a very wide variety of behaviours of many different types of ion channels and it is not informed by the covariates that would be predictive of those behaviours. Some channels don’t have certain types of behaviours, setting EBEs to 0 for parts modelling them and so high shrinkage is I think expected and reasonable.
My hypothesis was that once I regress from the informative covariates towards base NLME model randeffs, augment and refit the Omega, the shrinkage would decrease. However, once I augment and refit the Omega, the augmented model eta shrinkage has some negative values, which would mean that EBEs have a larger SD than the matching Omega value. And I am not sure whether this is an artefact of the way EBEs are set via augment internally or a model issue.
Does ηshrinkage use augmented EBEs for shrinkage calculations or non-augmented ones?
If it uses the augmented ones, would it be as simple as manually passing the pop through the fitted NN to obtain pred ebes, subtract them from emprical_bayes(aug_refit_fpm) element-wise and calculate shrinkages myself to get the actual shrinkage related to randeffs modelling the remaining post-augment between subject variability?