Latent Markov and growth mixture models for ordinal individual responses with covariates: a comparison

We propose a short review between two alternative ways of modeling stability and change of longitudinal data when time-fixed and time-varying covariates referred to the observed individuals are available. They both build on the foundation of the finite mixture models and are commonly applied in many fields. They look at the data by a different perspective and in the literature they have not been compared when the ordinal nature of the response variable is of interest. The latent Markov model is based on time-varying latent variables to explain the observable behavior of the individuals. The model is proposed in a semi-parametric formulation as the latent Markov process has a discrete distribution and it is characterized by a Markov structure. The growth mixture model is based on a latent categorical variable that accounts for the unobserved heterogeneity in the observed trajectories and on a mixture of normally distributed random variable to account for the variability of growth rates. To illustrate the main differences among them we refer to a real data example on the self reported health status.