I am trying to help a friend with a complex modelling problem and was thinking Stan might be suitable, but I am unsure where to start and was hoping someone here might have done something similar in the past. My friend has a large amount of patient data involving clinical psychological measures (e.g., questions related to specific symptoms) gathered both before and after a psychological intervention in the same subjects. She believes there to be latent states within these data – representing different phases of the disorder (during the initial or final time point) or recovery (during the final time point). She would like to estimate the probability of starting in any given state, the probability of transitioning from one state to another and also to predict Time 2 states based on Time 1 data. She has 9 observed variables at each of the two time points (each representing answers to questions on a 4-point ordinal scale). This sounds to me like a latent transition model, and she has been pursuing that approach using the LMest package in R but has come up against various limitations regarding the model implementation.
I believe this situation could be modelled using a variant of the HMMs presented in 10.6 of the manual but I am not sure how to incorporate the multivariate ordinal nature of the observations at each time point. Does anyone have a similar model they would be willing to share? Or am I completely wrong in my thinking?