Latent Markov models for longitudinal data

"Preface Latent Markov models represent an important class of latent variable models for the analysis of longitudinal data, when the response variables measure common characteristics of interest which are not directly observable. Typically, the response variables are categorical, even if nothing precludes that they have a di erent nature. These models nd application in many relevant elds, such as educational and health sciences, when the latent characteristics correspond, for instance, to a certain type of ability or to the quality-of-life. Important applications are also in the study of certain human behaviors which are relevant for the social and economic research. The main feature that distinguishes latent Markov models from other models for longitudinal data is that the individual characteristics of interest, and their evolution in time, are represented by a latent process which follows a Markov chain. This implies that we are in the eld of discrete latent variable models, where the latent variables may assume a nite number of values. Latent Markov models are then strongly related to the latent class model, which represents an important tool for classifying a sample of subjects on the basis of a series of categorical response variables. The latter model is based on a discrete latent variable, the di erent values of which correspond to di erent subpopulations (named latent classes) having a common distribution about the response variables. The latent Markov model may be seen as an extension of the latent class model in which subjects are allowed to move between the latent classes during the period of observation"--