Stochastic models for ordinal panel data with individual and time-varying latent effects

We illustrate a model based approach for clustering when we deal with longitudinal data. The model formulation is specifically tailored when we deal with a continuous variable which is properly discretized so that a univariate ordinal response variable results. We show how to estimates the effects of interest by means of a suitable parameterization based on global logits as well as to group units by considering the unobserved heterogeneity among them. According to the chosen distribution for the latter an hidden Markov model or a mixture of auto-regressive process AR(1) results. The model estimation is carried out by means of the expectation-maximization algorithm and the Newton-Raphson algorithm. Standard errors are obtained by using the observed information matrix. A way to obtain reliable individual prediction is illustrated. We also show an application to real data.