This might be a trivial problem but wondering if there's a known model formulation for this problem:
- Ordered Categorical observed variable with k levels
- Trying to estimate the parameter (theta) of a latent Bernoulli/Binomial variable
- The latent and observed related by a k-length vector of probabilities
- e.g. if observed=5 for a particular data point, data point has a 0.92 probability of success on the latent, observed=4 data point=0.81 success etc.
Does what I'm asking make sense? Or have I thought myself into a corner?