Definition

"Latent Markov models" refer to a class of models that are very similar to hidden Markov models for time-series. However, at least according to the authors of the book, "Latent Markov" is a name more suitable in the context of longitudinal data. Besides observed data, these models include a latent process (sequence of latent variables) for each individual, which follows a Markov chain with a finite number of states. Recall that longitudinal data are made of (typically short) sequences of repeated observations for a (typically large) sample of individuals. This type of data is very common in social sciences and medicine. In contrast, time-series data consists of a long, but single, sequence of data that typically is very long.

Typically, longitudinal data also includes individual covariates may be time-constant or time-varying. Both types may be include in a Latent Markov model to directly affect the responses (in addition to latent states) or directly the latent states (that then affect the responses). These versions are deeply discussed in the book together with other extensions to deal, for instance, with multilevel longitudinal data in which individuals are clustered in groups with different unobservable characteristics.