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. Constraints 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 depression in a panel of adolescents, where the random effects are highly dimensional and separately evolve over time.