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

Listed author(s):
  • Bartolucci, Francesco
  • Farcomeni, Alessio
  • Pennoni, Fulvia

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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 39023.

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Date of creation: 13 Apr 2012
Handle: RePEc:pra:mprapa:39023
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  1. Francesco Bartolucci & Alessio Farcomeni, 2010. "A note on the mixture transition distribution and hidden Markov models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 132-138, March.
  2. Congdon, Peter, 2006. "Bayesian model choice based on Monte Carlo estimates of posterior model probabilities," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 346-357, January.
  3. D. Oakes, 1999. "Direct calculation of the information matrix via the EM," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 479-482.
  4. Wilfried Seidel & Hana Ševčíková, 2004. "Types of likelihood maxima in mixture models and their implication on the performance of tests," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(4), pages 631-654, December.
  5. Bornmann, Lutz & Mutz, Rüdiger & Daniel, Hans-Dieter, 2008. "Latent Markov modeling applied to grant peer review," Journal of Informetrics, Elsevier, vol. 2(3), pages 217-228.
  6. C. P. Robert & T. Rydén & D. M. Titterington, 2000. "Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 57-75.
  7. Francesco Bartolucci & Fulvia Pennoni, 2007. "A Class of Latent Markov Models for Capture–Recapture Data Allowing for Time, Heterogeneity, and Behavior Effects," Biometrics, The International Biometric Society, vol. 63(2), pages 568-578, June.
  8. Luigi Spezia, 2010. "Bayesian analysis of multivariate Gaussian hidden Markov models with an unknown number of regimes," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 1-11, January.
  9. Farcomeni, Alessio, 2011. "Hidden Markov partition models," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1766-1770.
  10. Francesco Bartolucci & Fulvia Pennoni & Giorgio Vittadini, 2011. "Assessment of School Performance Through a Multilevel Latent Markov Rasch Model," Journal of Educational and Behavioral Statistics, , vol. 36(4), pages 491-522, August.
  11. Altman, Rachel MacKay, 2007. "Mixed Hidden Markov Models: An Extension of the Hidden Markov Model to the Longitudinal Data Setting," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 201-210, March.
  12. Francesco Bartolucci, 2006. "Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 155-178.
  13. Bartolucci, Francesco & Farcomeni, Alessio, 2009. "A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 816-831.
  14. Antonello Maruotti, 2011. "Mixed Hidden Markov Models for Longitudinal Data: An Overview," International Statistical Review, International Statistical Institute, vol. 79(3), pages 427-454, December.
  15. C. Yau & O. Papaspiliopoulos & G. O. Roberts & C. Holmes, 2011. "Bayesian non‐parametric hidden Markov models with applications in genomics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 37-57, January.
  16. Francesco Bartolucci & Fulvia Pennoni & Brian Francis, 2007. "A latent Markov model for detecting patterns of criminal activity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 115-132.
  17. S. Bacci & S. Pandolfi & F. Pennoni, 2014. "A comparison of some criteria for states selection in the latent Markov model for longitudinal data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 125-145, June.
  18. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
  19. Richard McHugh, 1956. "Efficient estimation and local identification in latent class analysis," Psychometrika, Springer;The Psychometric Society, vol. 21(4), pages 331-347, December.
  20. Farcomeni Alessio & Arima Serena, 2012. "A Bayesian autoregressive three-state hidden Markov model for identifying switching monotonic regimes in Microarray time course data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-31, June.
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