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

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  • F. Bartolucci

    ()

  • A. Farcomeni

    ()

  • F. Pennoni

    ()

Abstract

We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. We illustrate the general version of the LM model which includes individual covariates, and several constrained versions. Constraints 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). We also illustrate in detail maximum likelihood estimation through the Expectation–Maximization algorithm, which may be efficiently implemented by recursions taken from the hidden Markov literature. 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 mention issues related to Bayesian inference of LM models. Possibilities for further developments are given among the concluding remarks. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 433-465, September.
  • Handle: RePEc:spr:testjl:v:23:y:2014:i:3:p:433-465
    DOI: 10.1007/s11749-014-0381-7
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    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, April.
    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.
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    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, January.
    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.
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    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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    Cited by:

    1. Francesco Dotto & Alessio Farcomeni & Maria Grazia Pittau & Roberto Zelli, 2019. "A dynamic inhomogeneous latent state model for measuring material deprivation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(2), pages 495-516, February.
    2. Francesco Bartolucci & Fulvia Pennoni & Giorgio Vittadini, 2016. "Causal Latent Markov Model for the Comparison of Multiple Treatments in Observational Longitudinal Studies," Journal of Educational and Behavioral Statistics, , vol. 41(2), pages 146-179, April.
    3. Alessio Farcomeni, 2015. "Latent class recapture models with flexible behavioural response," Statistica, Department of Statistics, University of Bologna, vol. 75(1), pages 5-17.
    4. Lekkas, Peter & Paquet, Catherine & Howard, Natasha J. & Daniel, Mark, 2017. "Illuminating the lifecourse of place in the longitudinal study of neighbourhoods and health," Social Science & Medicine, Elsevier, vol. 177(C), pages 239-247.
    5. Pennoni, Fulvia & Romeo, Isabella, 2016. "Latent Markov and growth mixture models for ordinal individual responses with covariates: a comparison," MPRA Paper 72939, University Library of Munich, Germany.
    6. Fulvia Pennoni & Ewa Genge, 2020. "Analysing the course of public trust via hidden Markov models: a focus on the Polish society," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 399-425, June.
    7. Amirali Kani & Wayne S. DeSarbo & Duncan K. H. Fong, 2018. "A Factorial Hidden Markov Model for the Analysis of Temporal Change in Choice Models," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 5(3), pages 162-177, December.
    8. Tullio, Federico & Bartolucci, Francesco, 2019. "Evaluating time-varying treatment effects in latent Markov models: An application to the effect of remittances on poverty dynamics," MPRA Paper 91459, University Library of Munich, Germany.
    9. Gordon Anderson & Alessio Farcomeni & Maria Grazia Pittau & Roberto Zelli, 2019. "Rectangular latent Markov models for time‐specific clustering, with an analysis of the wellbeing of nations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(3), pages 603-621, April.
    10. Hans Jørn Juhl & Morten H. J. Fenger & John Thøgersen, 2017. "Will the Consistent Organic Food Consumer Step Forward? An Empirical Analysis," Journal of Consumer Research, Oxford University Press, vol. 44(3), pages 519-535.
    11. Gordon Anderson & Alessio Farcomeni & Grazia Pittau & Roberto Zelli, 2017. "Rectangular latent Markov models for time-specific clustering," Working Papers tecipa-589, University of Toronto, Department of Economics.
    12. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    13. Ingmar Visser & Maarten Speekenbrink, 2014. "Comments on: Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 478-483, September.
    14. Ulf Böckenholt & Blakeley McShane, 2014. "Comments on: Latent Markov models: a review of the general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 469-472, September.
    15. Alessio Farcomeni, 2015. "Generalized Linear Mixed Models Based on Latent Markov Heterogeneity Structures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1127-1135, December.
    16. Antonello Maruotti & Jan Bulla & Tanya Mark, 2019. "Assessing the influence of marketing activities on customer behaviors: a dynamic clustering approach," METRON, Springer;Sapienza Università di Roma, vol. 77(1), pages 19-42, April.

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    More about this item

    Keywords

    EM algorithm; Bayesian framework; Forward–Backward recursions; Hidden Markov models; Measurement errors; Panel data; Unobserved heterogeneity; 60G25; 6207; 62F15; 62M02; 62P25;
    All these keywords.

    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; Spatio-temporal Models

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