Factor analysis with wrong number of latent variables

Questions v5
5

A few things:

  1. I posted too soon (sorry!) because when I increased the tune and target_accept parameters, the sampling did converge wthout divergences.
  2. The problem of model latent variables being unequal to real latent variables is an issue both when they are too large and when they are too small. I believe this is an active area of research, but I’m happy to have input.
    • When your model has too few latent variables, then you are creating a multimodality in the posterior with modes at coverage of any subset of the true latent variables and more more modes at average values between latent variables.
    • When the model has too many latent variables, then you get a different kind of multimodality where multiple model latent variables get collapsed onto one true latent variable.
  3. Since all of these issues involve multimodality in the posterior, I wonder if there has been working regarding covering different modes of the posterior with different chains.

Thanks in any case!
Opher