Discrete parameter in Stan

Can you help take a careful look at it? The link to the problem is here: Sampling error: Unrecoverable error evaluating the log probability at the initial value. I am not sure where it has an additional problem, if that is the case though.

On the other hand, for assessing the quality of our assumption on the choice of the prior and likelihood, besides plotting the obtained posterior distribution versus observed values, is \hat{R} the good measure? In particular, if lots of \hat{R} > 1.05 (assume our posterior distribution is comprised of a bunch of vectors, each components of a vector are inferred results), this should not only imply MCMC not converging well within a fixed number of iterations, but also imply the poor quality of our choice for prior?