Consider constraining site-level R(t) deviations to sum to 0

[kaitejohnson]

Goal

Explore how this might work for the aspatial model, might improve identifiability

Context

Suggestion from @athowes to improve identifiability, in particular might be helpful when there are deviations that could be due to site/subpopulation level changes and also could be due to deviation in "central/global" $R(t)$ Suggests something like: sum(subpop_level_errors[t]) ~ normal(0, <small_number> *<n_subpops>)

Requirements

• [ ] Rmd to explore implementation of different model components and compare outputs

Out of scope for this PR

• Idea of this PR is just to see how this impacts outputs/diagnostics/etc. Before adding this component to the model we would want to do some evaluation to ensure it improved performance (e.g. what we have in the pipeline repo for a single forecast date)

[athowes]

I don't know the extent to which this would improve forecast accuracy. It should make NUTS slightly easier to run. Aside from those, if you'd like to make statements about the relative sizes of the different trends/components in the model then I think it's useful to have the sum-to-zeros.

[dylanhmorris]

This would also have the (imo) salutary effect of making the n=1 site model reduce to a non-hierarchical model, which is not currently the case. CC @damonbayer @sbidari