Latent Markov models

The book aims at providing the reader with a complete overview of latent Markov models (named also Hidden Markov models in the related statistical literature) with special attention to the interpretation of the model assumptions and to their practical use. It outlines their roles for modern applications and the main bibliography on this topic. Several datasets, covering fields of economics, education, and sociology are used to illustrate the proposed approaches.

It provides the reader with the essential background about latent variable models, and in particular the latent class model. It explains the Markov chain model that, together with latent class model, represents a useful paradigm for latent Markov models. The assumptions of the basic version of the latent Markov model are illustrated in the presence of univariate or multivariate responses without covariates. Maximum likelihood estimation through the Expectation-Maximization algorithm is introduced. Then, it shows some constrained versions of the basic latent Markov model based on parsimonious and interpretable parametrizations. The inclusion of the individual covariates is introduced with the random-effects and the multilevel extensions of the model.

The book also covers some more advanced topics, such as the performance of criteria for selecting the number of latent states and path prediction. It introduces Bayesian inference as an alternative to maximum likelihood estimation. The examples used to illustrate the content of the book chapters are developed by using the R package named LMest.