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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
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    References listed on IDEAS

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    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.
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