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Maximum likelihood estimation in discrete mixed hidden Markov models using the SAEM algorithm

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  • Delattre, M.
  • Lavielle, M.

Abstract

Mixed hidden Markov models have been recently defined in the literature as an extension of hidden Markov models for dealing with population studies. The notion of mixed hidden Markov models is particularly relevant for modeling longitudinal data collected during clinical trials, especially when distinct disease stages can be considered. However, parameter estimation in such models is complex, especially due to their highly nonlinear structure and the presence of unobserved states. Moreover, existing inference algorithms are extremely time consuming when the model includes several random effects. New inference procedures are proposed for estimating population parameters, individual parameters and sequences of hidden states in mixed hidden Markov models. The main contribution consists of a specific version of the stochastic approximation EM algorithm coupled with the Baum–Welch algorithm for estimating population parameters. The properties of this algorithm are investigated via a Monte-Carlo simulation study, and an application of mixed hidden Markov models to the description of daily seizure counts in epileptic patients is presented.

Suggested Citation

  • Delattre, M. & Lavielle, M., 2012. "Maximum likelihood estimation in discrete mixed hidden Markov models using the SAEM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2073-2085.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:2073-2085
    DOI: 10.1016/j.csda.2011.12.017
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    References listed on IDEAS

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    1. 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.
    2. Frank Rijmen & Edward H. Ip & Stephen Rapp & Edward G. Shaw, 2008. "Qualitative longitudinal analysis of symptoms in patients with primary and metastatic brain tumours," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(3), pages 739-753, June.
    3. Kuhn, E. & Lavielle, M., 2005. "Maximum likelihood estimation in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1020-1038, June.
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    1. Antonello Maruotti, 2015. "Handling non-ignorable dropouts in longitudinal data: a conditional model based on a latent Markov heterogeneity structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 84-109, March.

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