Generalized linear mixed models based on latent Markov heterogeneity structures

We describe a generalized linear mixed model in which all random effects may evolve over time. Random effects have a discrete support and follow a first-order Markov chain. Con- straints control the size of the parameter space and possibly yield blocks of time-constant random effects. We illustrate with an application to the relationship between health education and depres- sion in a panel of adolescents, where the random effects are highly dimensional and separately evolve over time.