@rpgoldman I hope @junpenglao answer your questions.
I’m not that familiar with underline implementation, but from what I know GLM is for simple regression models (as @junpenglao explained when only weights are the latent variables), even it seems hierarchical regression is not possible with GLM (since the hyper-priors are not the weights of some observed input).
Even though this article has the title “GLM: Hierarchical Linear Regression” at the end it says,
Finally, readers of my blog will notice that we didn’t use glm() here as it does not play nice with hierarchical models yet.
This is just an suggestion, I think this article should have a small section or few sentences to tell the reasons why they do not use GLM with hierarchical models even-though title says so. Otherwise, the title is somewhat misleading.
It is always good to discuss about such limitations, because that could save the time of users/developer that they spend trying to do something that is not supported at the moment.