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Variable Selection for Hidden Markov Models with Continuous Variables and Missing Data

Author

Listed:
  • Fulvia Pennoni

    (University of Milano-Bicocca)

  • Francesco Bartolucci

    (University of Perugia)

  • Silvia Pandolfi

    (University of Perugia)

Abstract

We propose a variable selection method for multivariate hidden Markov models with continuous responses that are partially or completely missing at a given time occasion. Through this procedure, we achieve a dimensionality reduction by selecting the subset of the most informative responses for clustering individuals and simultaneously choosing the optimal number of these clusters corresponding to latent states. The approach is based on comparing different model specifications in terms of the subset of responses assumed to be dependent on the latent states, and it relies on a greedy search algorithm based on the Bayesian information criterion seen as an approximation of the Bayes factor. A suitable expectation-maximization algorithm is employed to obtain maximum likelihood estimates of the model parameters under the missing-at-random assumption. The proposal is illustrated via Monte Carlo simulation and an application where development indicators collected over eighteen years are selected, and countries are clustered into groups to evaluate their growth over time.

Suggested Citation

  • Fulvia Pennoni & Francesco Bartolucci & Silvia Pandolfi, 2024. "Variable Selection for Hidden Markov Models with Continuous Variables and Missing Data," Journal of Classification, Springer;The Classification Society, vol. 41(3), pages 568-589, November.
    • Handle: RePEc:spr:jclass:v:41:y:2024:i:3:d:10.1007_s00357-023-09457-9
    DOI: 10.1007/s00357-023-09457-9
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    References listed on IDEAS

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    1. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    2. Abby Flynt & Nema Dean, 2019. "Growth Mixture Modeling with Measurement Selection," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 3-25, April.
    3. Gilles Celeux & Jean-Baptiste Durand, 2008. "Selecting hidden Markov model state number with cross-validated likelihood," Computational Statistics, Springer, vol. 23(4), pages 541-564, October.
    4. Fulvia Pennoni & Beata Bal-Domańska, 2022. "NEETs and Youth Unemployment: A Longitudinal Comparison Across European Countries," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 162(2), pages 739-761, July.
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    7. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Rejoinder 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 484-486, September.
    8. 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.
    9. Cathy Maugis & Gilles Celeux & Marie-Laure Martin-Magniette, 2009. "Variable Selection for Clustering with Gaussian Mixture Models," Biometrics, The International Biometric Society, vol. 65(3), pages 701-709, September.
    10. Zallé, Oumarou, 2019. "Natural resources and economic growth in Africa: The role of institutional quality and human capital," Resources Policy, Elsevier, vol. 62(C), pages 616-624.
    11. Raftery, Adrian E. & Dean, Nema, 2006. "Variable Selection for Model-Based Clustering," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 168-178, March.
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