## 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 |
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Pages (from-to) | 304-321 |

Number of pages | 18 |

Journal | Statistica Neerlandica |

Volume | 77 |

Issue number | 3 |

DOIs | |

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 |
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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