IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i4p622-d346729.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/4/622/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/4/622/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Wai-Yin Poon & Hai-Bin Wang, 2010. "Bayesian Analysis of Multivariate Probit Models with Surrogate Outcome Data," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 498-520, September.
    3. Jackson, Christopher, 2011. "Multi-State Models for Panel Data: The msm Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i08).
    4. Smith, Brian J., 2007. "boa: An R Package for MCMC Output Convergence Assessment and Posterior Inference," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i11).
    5. Rosychuk, Rhonda J. & Shofiqul Islam, 2009. "Parameter estimation in a model for misclassified Markov data -- a Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3805-3816, September.
    6. John M. Neuhaus, 2002. "Analysis of Clustered and Longitudinal Binary Data Subject to Response Misclassification," Biometrics, The International Biometric Society, vol. 58(3), pages 675-683, September.
    7. 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.
    8. C. Y. Wang & Yijian Huang & Edward C. Chao & Marjorie K. Jeffcoat, 2008. "Expected Estimating Equations for Missing Data, Measurement Error, and Misclassification, with Application to Longitudinal Nonignorable Missing Data," Biometrics, The International Biometric Society, vol. 64(1), pages 85-95, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Surupa Roy & Kalyan Das & Angshuman Sarkar, 2013. "Analysis of binary data with the possibility of wrong ascertainment," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(3), pages 293-310, August.
    2. Qiu, Qinjing & Kawai, Reiichiro, 2022. "A decoupling principle for Markov-modulated chains," Statistics & Probability Letters, Elsevier, vol. 182(C).
    3. Vernon T. Farewell & Li Su & Christopher Jackson, 2019. "Partially hidden multi-state modelling of a prolonged disease state defined by a composite outcome," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 696-711, October.
    4. Gaffney, Edward & McCann, Fergal, 2019. "The cyclicality in SICR: mortgage modelling under IFRS 9," ESRB Working Paper Series 92, European Systemic Risk Board.
    5. Biagini, Francesca & Groll, Andreas & Widenmann, Jan, 2013. "Intensity-based premium evaluation for unemployment insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 302-316.
    6. Sharples, Linda D., 2018. "The role of statistics in the era of big data: Electronic health records for healthcare research," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 105-110.
    7. Alex Bottle & Chiara Maria Ventura & Kumar Dharmarajan & Paul Aylin & Francesca Ieva & Anna Maria Paganoni, 2018. "Regional variation in hospitalisation and mortality in heart failure: comparison of England and Lombardy using multistate modelling," Health Care Management Science, Springer, vol. 21(2), pages 292-304, June.
    8. Wildhaber, Mark L. & Albers, Janice L. & Green, Nicholas S. & Moran, Edward H., 2017. "A fully-stochasticized, age-structured population model for population viability analysis of fish: Lower Missouri River endangered pallid sturgeon example," Ecological Modelling, Elsevier, vol. 359(C), pages 434-448.
    9. Ralf van der Lans & Bram Van den Bergh & Evelien Dieleman, 2014. "Partner Selection in Brand Alliances: An Empirical Investigation of the Drivers of Brand Fit," Marketing Science, INFORMS, vol. 33(4), pages 551-566, July.
    10. Brajendra C. Sutradhar, 2022. "Fixed versus Mixed Effects Based Marginal Models for Clustered Correlated Binary Data: an Overview on Advances and Challenges," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 259-302, May.
    11. Slaets, Leen & Claeskens, Gerda & Silverman, Bernard W., 2013. "Warping Functional Data in R and C via a Bayesian Multiresolution Approach," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i03).
    12. Frederic Ouedraogo & B. Wade Brorsen, 2018. "Hierarchical Bayesian Estimation of a Stochastic Plateau Response Function: Determining Optimal Levels of Nitrogen Fertilization," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 66(1), pages 87-102, March.
    13. Budhi Surya, 2021. "A new class of conditional Markov jump processes with regime switching and path dependence: properties and maximum likelihood estimation," Papers 2107.07026, arXiv.org.
    14. Tsiropoulos, Vasilis, 2018. "A Vulnerability Analysis for Mortgaged Irish Households," Financial Stability Notes 02-18, Central Bank of Ireland.
    15. João Costa Freitas & Alberto Adrego Pinto & Óscar Felgueiras, 2024. "Game Theory for Predicting Stocks’ Closing Prices," Mathematics, MDPI, vol. 12(17), pages 1-49, August.
    16. Firouzeh Noghrehchi & Jakub Stoklosa & Spiridon Penev, 2020. "Multiple imputation and functional methods in the presence of measurement error and missingness in explanatory variables," Computational Statistics, Springer, vol. 35(3), pages 1291-1317, September.
    17. Liu, Feng & Zhao, Shaoqiong & Li, Yang, 2017. "How many, how often, and how new? A multivariate profiling of mobile app users," Journal of Retailing and Consumer Services, Elsevier, vol. 38(C), pages 71-80.
    18. Sarrias, Mauricio, 2021. "A two recursive equation model to correct for endogeneity in latent class binary probit models," Journal of choice modelling, Elsevier, vol. 40(C).
    19. Emanuel Krebs & Jeong E. Min & Elizabeth Evans & Libo Li & Lei Liu & David Huang & Darren Urada & Thomas Kerr & Yih-Ing Hser & Bohdan Nosyk, 2017. "Estimating State Transitions for Opioid Use Disorders," Medical Decision Making, , vol. 37(5), pages 483-497, July.
    20. Guglielmo D'Amico & Stefania Scocchera & Loriano Storchi, 2021. "Randentropy: a software to measure inequality in random systems," Papers 2103.09107, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:622-:d:346729. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.