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A Hidden Markov Model to Address Measurement Errors in Ordinal Response Scale and Non-Decreasing Process

Author

Listed:
  • Lizbeth Naranjo

    (Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 Ciudad de México, Mexico)

  • Luz Judith R. Esparza

    (Departamento de Matemáticas y Física, Cátedra CONACyT, Universidad Autónoma de Aguascalientes, 20130 Aguascalientes, Mexico)

  • Carlos J. Pérez

    (Departamento de Matemáticas, Facultad de Veterinaria, Universidad de Extremadura, 10003 Cáceres, Spain)

Abstract

A Bayesian approach was developed, tested, and applied to model ordinal response data in monotone non-decreasing processes with measurement errors. An inhomogeneous hidden Markov model with continuous state-space was considered to incorporate measurement errors in the categorical response at the same time that the non-decreasing patterns were kept. The computational difficulties were avoided by including latent variables that allowed implementing an efficient Markov chain Monte Carlo method. A simulation-based analysis was carried out to validate the approach, whereas the proposed approach was applied to analyze aortic aneurysm progression data.

Suggested Citation

  • Lizbeth Naranjo & Luz Judith R. Esparza & Carlos J. Pérez, 2020. "A Hidden Markov Model to Address Measurement Errors in Ordinal Response Scale and Non-Decreasing Process," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:622-:d:346729
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    References listed on IDEAS

    as
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    3. Lizbeth Naranjo & Carlos J. Pérez & Jacinto Martín & Timothy Mutsvari & Emmanuel Lesaffre, 2019. "A Bayesian approach for misclassified ordinal response data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(12), pages 2198-2215, September.
    4. María José García-Zattera & Alejandro Jara & Emmanuel Lesaffre & Guillermo Marshall, 2012. "Modeling of Multivariate Monotone Disease Processes in the Presence of Misclassification," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 976-989, September.
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