# Group level distribution for positive parameters in Bayesian multilevel models

I am doing a lot of modeling with models that require some parameters to be positive by design. However, I am struggling to figure out which approach works best when I try to use multilevel modeling with these types of models.

My current approach ist to draw the individual parameters from a lognormal distribution, to ensure the resulting parameters are always positive. I.e.

$$\theta_i \sim lognormal(\mu_\theta,\sigma_\theta^2)$$

However, then I need a method to also determine the group-level parameters $$\mu_\theta$$ and $$\sigma_\theta^2$$. In my modeling experiments, I have tried drawing either the parameter $$\mu_\theta$$ from a normal, or drawing the group-level mode, mean or median from a lognormal or gamma distribution as a hyperprior and then translating this to the distribution parameter. This often gives different results and I am not sure which results should be trusted more.

Are there any guidelines on how to model such purely positive parameters in a multilevel model and which distributions to use a hyperprior?