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

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

doi:10.1111/stan.12286

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

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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	304-321
Number of pages	18
Journal	Statistica Neerlandica
Volume	77
Issue number	3
DOIs	https://doi.org/10.1111/stan.12286
State	Published - Aug 2023

Bibliographical note

Publisher Copyright:
© 2023 Netherlands Society for Statistics and Operations Research.

Funding

This research was partially supported by grant UL11 TR001998 from the National Center for Advancing Translational Sciences and grants AG0386561, AG072946, and AG057191 from the National Institute on Aging.

Funders	Funder number
National Institute on Aging
National Center for Advancing Translational Sciences (NCATS)	AG072946, UL11 TR001998, AG057191, AG0386561
National Center for Advancing Translational Sciences (NCATS)

Keywords

Markov chains
cognitive assessments
h-likelihood
marginal likelihood
multinomial logistic regression
random effect

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1111/stan.12286

Cite this

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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.",

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doi = "10.1111/stan.12286",

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volume = "77",

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AU - Wang, Pei

AU - Abner, Erin L.

AU - Liu, Changrui

AU - Fardo, David W.

AU - Schmitt, Frederick A.

AU - Jicha, Gregory A.

AU - Van Eldik, Linda J.

AU - Kryscio, Richard J.

PY - 2023/8

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N2 - 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.

AB - 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.

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

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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