You can try a non-centered parameterization for your hierarchy. This is often nicer to sample. A zero-avoiding prior on kappa, like Gamma(2,1), can also help, although you are technically making a strong assumption when you do that (that the the different sub-divisions must be at least somewhat different. Estimating sigma = 0 on the hierarchical parameter is a valid result, it rejects the present of hierarchy (e.g. all units are the same). In practice, I find that a very small but non-zero sigma is good enough.)
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