  Many relevant statistical and econometric models for the analysis of
longitudinal data include a latent process to account for the unobserved
heterogeneity between subjects in a dynamic fashion. Such a process may be
continuous (typically an AR(1)) or discrete (typically a Markov chain). In this
paper, we propose a model for longitudinal data which is based on a mixture of
AR(1) processes with different means and correlation coefficients, but with
equal variances. This model belongs to the class of models based on a
continuous latent process, and then it has a natural interpretation in many
contexts of application, but it is more flexible than other models in this
class, reaching a goodness-of-fit similar to that of a discrete latent process
model, with a reduced number of parameters. We show how to perform maximum
likelihood estimation of the proposed model by the joint use of an
Expectation-Maximisation algorithm and a Newton-Raphson algorithm, implemented
by means of recursions developed in the hidden Markov literature. We also
introduce a simple method to obtain standard errors for the parameter estimates
and a criterion to choose the number of mixture components. The proposed
approach is illustrated by an application to a longitudinal dataset, coming
from the Health and Retirement Study, about self-evaluation of the health
status by a sample of subjects. In this application, the response variable is
ordinal and time-constant and time-varying individual covariates are available.
