Bartolucci, Francesco and Farcomeni, Alessio and Pennoni, Fulvia (2012): Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates.

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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 firstorder 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 ExpectationMaximization 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 socioeconomic applications available in the literature.
Item Type:  MPRA Paper 

Original Title:  Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates 
Language:  English 
Keywords:  EM algorithm, Bayesian framework, ForwardBackward recursions, Hidden Markov models, Measurement errors, Panel data, Unobserved heterogeneity 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models; Multiple Variables > C33  Models with Panel Data; Longitudinal Data; Spatial Time Series 
Item ID:  39023 
Depositing User:  Francesco Bartolucci 
Date Deposited:  25. May 2012 13:45 
Last Modified:  13. Feb 2013 14:59 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/39023 