IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v77y2023i3p304-321.html
   My bibliography  Save this article

Estimating random effects in a finite Markov chain with absorbing states: Application to cognitive data

Author

Listed:
  • Pei Wang
  • Erin L. Abner
  • Changrui Liu
  • David W. Fardo
  • Frederick A. Schmitt
  • Gregory A. Jicha
  • Linda J. Van Eldik
  • Richard J. Kryscio

Abstract

Finite Markov chains with absorbing states are popular tools for analyzing longitudinal data with categorical responses. The one step transition probabilities can be defined in terms of fixed and random effects but it is difficult to estimate these effects due to many unknown parameters. In this article we propose a three‐step estimation method. In the first step the fixed effects are estimated by using a marginal likelihood function, in the second step the random effects are estimated after substituting the estimated fixed effects into a joint likelihood function defined as a h‐likelihood, and in the third step the covariance matrix for the vector of random effects is estimated using the Hessian matrix for this likelihood function. An application involving an analysis of longitudinal cognitive data is used to illustrate the method.

Suggested Citation

  • Pei Wang & Erin L. Abner & Changrui Liu & David W. Fardo & Frederick A. Schmitt & Gregory A. Jicha & Linda J. Van Eldik & Richard J. Kryscio, 2023. "Estimating random effects in a finite Markov chain with absorbing states: Application to cognitive data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(3), pages 304-321, August.
    • Handle: RePEc:bla:stanee:v:77:y:2023:i:3:p:304-321
    DOI: 10.1111/stan.12286
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/stan.12286
    Download Restriction: no
    File URL: https://libkey.io/10.1111/stan.12286?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Francesco Bartolucci & Silvia Bacci & Fulvia Pennoni, 2014. "Longitudinal analysis of self-reported health status by mixture latent auto-regressive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(2), pages 267-288, February.
    2. Yun, Sungcheol & Lee, Youngjo, 2004. "Comparison of hierarchical and marginal likelihood estimators for binary outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 639-650, April.
    3. Paul S. Albert & Dean A. Follmann, 2003. "A Random Effects Transition Model For Longitudinal Binary Data With Informative Missingness," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(1), pages 100-111, February.
    4. Alonso, Ariel & Litière, Saskia & Laenen, Annouschka, 2010. "A Note on the Indeterminacy of the Random-Effects Distribution in Hierarchical Models," The American Statistician, American Statistical Association, vol. 64(4), pages 318-324.
    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. William H. Greene & Mark N. Harris & Rachel J. Knott & Nigel Rice, 2021. "Specification and testing of hierarchical ordered response models with anchoring vignettes," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 31-64, January.
    2. Silvia Bianconcini, 2014. "Comments 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 466-468, September.
    3. Masoura Melpomeni & Malefaki Sonia, 2023. "Evolution of the Digital Economy and Society Index in the European Union: Α Socioeconomic Perspective," TalTech Journal of European Studies, Sciendo, vol. 13(2), pages 177-203, December.
    4. Cibele M. Russo & Gilberto A. Paula & Francisco Jos� A. Cysneiros & Reiko Aoki, 2012. "Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1049-1067, October.
    5. Ardo Van Den Hout & Fiona E. Matthews, 2010. "Estimating stroke‐free and total life expectancy in the presence of non‐ignorable missing values," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(2), pages 331-349, April.
    6. Francesco BARTOLUCCI & Silvia BACCI & Claudia PIGINI, 2015. "A Misspecification Test for Finite-Mixture Logistic Models for Clustered Binary and Ordered Responses," Working Papers 410, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    7. Xia, Ye-Mao & Tang, Nian-Sheng & Gou, Jian-Wei, 2016. "Generalized linear latent models for multivariate longitudinal measurements mixed with hidden Markov models," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 259-275.
    8. Joan Gil & Paolo Li Donni & Eugenio Zucchelli, 2019. "Uncontrolled diabetes and health care utilisation: A bivariate latent Markov model approach," Health Economics, John Wiley & Sons, Ltd., vol. 28(11), pages 1262-1276, November.
    9. Francesco Bartolucci & Valentina Nigro & Claudia Pigini, 2018. "Testing for state dependence in binary panel data with individual covariates by a modified quadratic exponential model," Econometric Reviews, Taylor & Francis Journals, vol. 37(1), pages 61-88, January.
    10. Wu, Jianmin & Bentler, Peter M., 2013. "Limited information estimation in binary factor analysis: A review and extension," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 392-403.
    11. Francesca Bassi, 2016. "Dynamic segmentation with growth mixture models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(2), pages 263-279, June.
    12. Sarah Brown & Pulak Ghosh & Karl Taylor, 2012. "The Existence and Persistence of Household Financial Hardship," Working Papers 2012022, The University of Sheffield, Department of Economics.
    13. Leonardo Grilli & Carla Rampichini, 2015. "Specification of random effects in multilevel models: a review," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 967-976, May.
    14. Wei, Shaoceng & Xu, Liou & Kryscio, Richard J., 2014. "Markov transition model to dementia with death as a competing event," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 78-88.
    15. Noh, Maengseok & Lee, Youngjo, 2007. "REML estimation for binary data in GLMMs," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 896-915, May.
    16. Pennoni, Fulvia & Romeo, Isabella, 2016. "Latent Markov and growth mixture models for ordinal individual responses with covariates: a comparison," MPRA Paper 72939, University Library of Munich, Germany.
    17. Giovanni Piumatti, 2020. "Longitudinal Trends in Self-Rated Health During Times of Economic Uncertainty in Italy," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 148(2), pages 599-633, April.
    18. Silvia Cagnone & Francesco Bartolucci, 2017. "Adaptive Quadrature for Maximum Likelihood Estimation of a Class of Dynamic Latent Variable Models," Computational Economics, Springer;Society for Computational Economics, vol. 49(4), pages 599-622, April.
    19. Giorgio E. Montanari & Marco Doretti, 2019. "Ranking Nursing Homes’ Performances Through a Latent Markov Model with Fixed and Random Effects," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 307-326, November.
    20. Reza Drikvandi & Geert Verbeke & Geert Molenberghs, 2017. "Diagnosing misspecification of the random-effects distribution in mixed models," Biometrics, The International Biometric Society, vol. 73(1), pages 63-71, March.

    More about this item

    Statistics

    Access and download statistics

    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:bla:stanee:v:77:y:2023:i:3:p:304-321. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    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.