Hidden Markov and mixture panel data models for ordinal variables derived from original continuous responses

We evaluate the use of two different model formulations by proposing a modeling framework which extends the stochastic volatility models and the stochastic frontier models by considering an hidden Markov model formulation or a model made by a mixture of latent auto-regressive stochastic processes both of first order. Those models are suitable statistical tools to be fitted to many available panel data in various applicative cases. The proposed model formulation is especially tailored for ordinal data when they are derived as a grouping of a different scale. We show some features of the models estimation which is carried out by means of the maximum likelihood. In the illustrative example we recall the available function of the library LMest on the R environment which is tailored to carry out the estimation of the models. Further, we provide some results of a case study to evaluate efficiency of a public organization by showing how the results can help policy makers.