ABSTRACT
In this chapter these models extended in two ways. First, it showed how a Markov Chain Monte Carlo (MCMC) algorithm used to fit such models. An important feature of the MCMC approach is that it decomposes the computational algorithm into separate steps, for each of which there is a relatively straightforward estimation procedure. This provides a chain sampled from the full posterior distribution of the limits from which one can calculate uncertainty intervals based upon quantiles etc. The second advantage is that the decomposition into separate steps allows one to easily extend the procedure to estimation of very general models, and an illustration how this can provided. In this chapter a stochastic MCMC algorithm proposed. It deals with incomplete data vectors and to use informative prior distributions. The algorithm extended to the non-linear factor case using a Metropolis Hastings step when sampling the multilevel factor values, as in Zhu and Lee.
