AngusMcLure
commented
9 months ago Implemented something like this by allowing users to set the prior on either the total variance of nested random effects or individual components. Choosing the former (the default) means that both that the implied prior for individual components has more weight on smaller variances, and that it is somewhat more informative. Also it has the (perhaps nice) property that increasing the number of levels of clustering doesn't a priori increase or decrease the total variance and uncertainty in prevalence
Consider making the default prior on the sd's of group-effects on highly-nested hierarchical models depend on how far down the hierarchy they are. The lower down the hierarchy, the less informative the data is (because there's less data at that specific level) so a stronger prior may be appropriate.
Consider this quote from Daniel Simpson et al Penalising model component complexity: A principled, practical approach to constructing priors
"D3: When re-using the prior for a different analysis, changes in the problem should be reflected in the prior. A prior specification should be explicit about what needs to be changed when applying it to a similar but different problem. An easy example is that the prior on the scaling parameter of a spline model needs to depend on the number of knots (Sørbye and Rue, 2014). A less clear cut example occurs when inferring a deep multi-level model. In this case, the data is less informative about variance components further down the hierarchy, and hence it may be desirable to specify a stronger prior on these model components"