## Abstract

Random-effects change point models are formulated for longitudinal data obtained from cognitive tests. The conditional distribution of the response variable in a change point model is often assumed to be normal even if the response variable is discrete and shows ceiling effects. For the sum score of a cognitive test, the binomial and the beta-binomial distributions are presented as alternatives to the normal distribution. Smooth shapes for the change point models are imposed. Estimation is by marginal maximum likelihood where a parametric population distribution for the random change point is combined with a non-parametric mixing distribution for other random effects. An extension to latent class modelling is possible in case some individuals do not experience a change in cognitive ability. The approach is illustrated using data from a longitudinal study of Swedish octogenarians and nonagenarians that began in 1991. Change point models are applied to investigate cognitive change in the years before death.

Original language | English |
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Pages (from-to) | 684-698 |

Number of pages | 15 |

Journal | Computational statistics & data analysis |

Volume | 57 |

Issue number | 1 |

Early online date | 3 Aug 2012 |

DOIs | |

Publication status | E-pub ahead of print - 3 Aug 2012 |

## Keywords

- Beta-binomial distribution
- Latent class model
- Mini-mental state examination
- Random-effects model