As many, if not most, of the questions here relate to fitting hierarchical models I wanted to note the release of my latent case study which delves into the intricate depth of hierarchical models, from their implicit modeling assumptions (and hence when they’re appropriate and when they’re not) to their inherent degeneracies (which cause slow and inaccurate fits) and how to manage them: https://betanalpha.github.io/assets/case_studies/hierarchical_modeling.html.
For similar publicly-available case studies covering probability theory, modeling and inference, and modeling techniques see https://betanalpha.github.io/writing/.
If you find this useful and/or are interested is supporting more work consider supporting me on Patreon, https://www.patreon.com/betanalpha.