Hi there,

a bit of background: I am trying to model the effects of seven government interventions on the number of new COVID infections across multiple countries in a semi-mechanistic model. So far, I was able to get a reasonable fit with just population-level effects for the interventions. Now, I want to include country-level slopes for the interventions, but this is challenging because the interventions were implemented in close succession in most countries. As a result, the effects of interventions are negatively correlated (â€śone effect stealing from the otherâ€ť) both at the population- and also at the country-level. Further, the posterior estimate of the between-country standard deviation differs greatly across interventions. However, I have the strong prior belief that one measure should not vary by multiple orders of magnitude more than the other. Nevertheless, it is one of the goals of the analysis to find out if some interventions exhibit more variation between countries than others.

So far, I have modeled the population-level and country-level slopes with a non-centered parametrization using the Cholesky Decomposition for sampling the varying slopes from a multivariate normal. Although I put quite informative priors on the between-country standard deviations `tau ~ student_t(4, 0, 0.04)`

, my posterior estimate for two interventions is off the charts: tau = 0.5 [0.3, 0.7] and they are also highly negatively correlated (rho = -0.7). For all other interventions, the posterior estimate is practically zero. It is very unlikely that just these two interventions should vary that much. Besides, the model doesnâ€™t converge well (the intercept and varying intercept cannot be reliably estimated).

**My question:** What could be informative priors for tau that incorporate my prior belief that the slope of one intervention does not vary too much more than the the slope from another? At the same time, the prior should not be too informative, so that I can still figure out if some interventions vary more than others.

I had two ideas so far. One was to set a prior on the total variation and then set informative priors on the proportion of the total variation that is explained by each intervention. Yet, I couldnâ€™t figure out how to do this properly.

Another idea was to do something like this

```
tau ~ student_t(4, 0, omega);
omega ~ half-normal(0, 0.1);
```

Does it make sense to pursue one of these ideas further or am I overlooking a better approach? Maybe also the data just doesnâ€™t allow it to estimate varying slopes reliably in this case, which is a bit my feelingâ€¦

I would be very interested to hear your ideas!