Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates

Abstract

We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal data. The main assumption behind these models is that the response variables are conditionally independent given a latent process which follows a first-order Markov chain. We first illustrate the more general version of the LM model which includes individual covariates.We then illustrate several constrained versions of the general LM model, which make the model more parsimonious and allow us to consider and test hypotheses of interest. These constraints may be put on the conditional distribution of the response variables given the latent process (measurement model) or on the distribution of the latent process (latent model). For the general version of the model we also illustrate in detail maximum likelihood estimation through the Expectation-Maximization algorithm, which may be efficiently implemented by recursions known in the hidden Markov literature. We discuss about the model identifiability and we outline methods for obtaining standard errors for the parameter estimates. We also illustrate methods for selecting the number of states and for path prediction. Finally, we illustrate Bayesian estimation method. Models and related inference are illustrated by the description of relevant socio-economic applications available in the literature.

LMest: An R Package for Latent Markov Models for Longitudinal Categorical Data

“…For a comprehensive overview about these models we refer the reader to Bartolucci et al (2013) and Bartolucci et al (2014b). Both manifest and latent distributions of the model can be parameterized so as to include the effect of individual covariates.…”

“…The illustration closely follows the recent paper by Bartolucci et al (2014b). We also focus on maximum likelihood estimation of these models on the basis of the expectation-maximization (EM) algorithm (Dempster, Laird, and Rubin 1977).…”

“…The package is related to the book by Bartolucci, Farcomeni, and Pennoni (2013), where these models are illustrated in detail from the methodological point of view. Additional insights are given in the discussion paper by Bartolucci, Farcomeni, and Pennoni (2014b).…”

Comments on: Latent Markov models: a review of the general framework for the analysis of longitudinal data with covariates

“…We heartily congratulate Bartolucci, Farcomeni, and Pennoni for their review of latent Markov (LM) models (Bartolucci et al 2014). Not only have they provided a succinct and thorough guide that will benefit researchers seeking to employ LM models for many years to come, but they also have offered their suggestions on a number of further developments to extend the basic LM framework that provide direction for future research.…”

“…In this comment, we would like to pick up on the suggested developments concerning more flexible temporal structures by highlighting two approaches that have proved useful in related domains; we do not view this as criticism of the proposed LM framework but rather as extensions of the review that are advantageous in terms of parsimony and scalability. Bartolucci et al (2014) note that the assumption that the LM model is first-order can sometimes be too restrictive, citing the case where the holding time in one or more states is not memoryless (i.e., geometric) as required by the first-order Markov model. They suggest generalizing the basic first-order Markov model to higher orders to allow for memory.…”