Latent (Hidden) Markov models and the LMest package in R

Longitudinal data analysis is being more and more widely used to analyse multivariate continuous and categorical panel data. Latent (Hidden) Markov (LM) models are able to detect the underlying latent structures by summarizing the time-specific vector of responses through the corresponding latent variable, thus achieving a suitable data reduction. Time-varying and time-fixed covariates can, where available, be included in the measurement model. In such a way, it is possible to account for unobserved heterogeneity, which is allowed to be time varying. Otherwise, when the covariates are supposed to affect the latent trait underlying the responses they influence the initial and the transition probabilities of the latent process through a multinomial logit parameterization. Within this framework it is possible to assess the effect of a certain treatment or policy when the corresponding variable is included among these covariates. The LM models allows us to dynamically cluster units in homogeneous latent groups according to the observed responses and covariates. Prediction of the overall sequence of latent states for a sample unit is performed according to local and global decoding. The former is constructed by maximizing the estimated posterior probabilities and the latter tracks the latent state of a unit across time on the basis of the most likely sequence of states. The models are illustrated through the package LMest in R, which is designed to handle longitudinal data and to estimate the LM models. Several distinguishing features of the package will be shown, along with real data applications arising in different fields to illustrate the interpretation of the results.