Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates
AbstractWe 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 39023.
Date of creation: 13 Apr 2012
Date of revision:
EM algorithm; Bayesian framework; Forward-Backward recursions; Hidden Markov models; Measurement errors; Panel data; Unobserved heterogeneity;
Find related papers by JEL classification:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Longitudinal Data; Spatial Time Series
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-06-05 (All new papers)
- NEP-ECM-2012-06-05 (Econometrics)
- NEP-ORE-2012-06-05 (Operations Research)
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