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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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    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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