I just saw the Efficient Bayesian Structural Equation Modeling in Stan preprint by Ed Merkle, @bgoodri and colleagues. This looks great! Section 4 discussed some issues specifying latent variable models in Stan, which I have had trouble with for a long time.
If possible, I am hoping to seek some more general clarifications on these issues. I suppose this post could also serve others who wanted to raise questions? My questions are

I had tried to set up individual priors for freely estimated latent covariance parameters, manually construct the covariance matrix, and then let Stan reject values that lead to nonpositive definiteness, as Section 4.1 suggested. However, in my case the model often does not initialize after rejecting the initial covariance values to a maximum times. If the model were set up correctly, would this issue simply be due to the prior informativeness, as the paper discussion suggested?

For the signswitching issue of the latent variable loadings, the paper suggested postprocessing MCMC samples, by fixing one loading (say \lambda^*) to always positive and processing other related parameter samples according to the sign of the sampled \lambda^*. I was curious, for a latent covariance parameter (say \psi_{AB}, does it matter which latent variableās \lambda^* this covariance parameterās sign is based on? E.g. for a two factor latent variable model, should the sign of the factor covariance parameter \psi_{AB} be based on the sampled values of factor Aās fixed loading, \lambda^*_A, or those from factor B \lambda^*_B ? I am also curious if there can be more discussion on how ālegalā such post processing is in terms of MCMC parameter inference. Though I had resorted to constraining all loadings to positive in the past, which is much less elegant.
Let me know if these descriptions are not clear. Thanks for any input from the forum!
Best,
Marco