title: Change point models for cognitive tests using semi-parametric maximum likelihood.
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.
authors.affiliation: Department of Statistical Science, University College London, 1-19 Torrington Place, London WC1E 7HB, UK.
authors.forename: Ardo
authors.initials: A
authors.lastname: van den Hout
authors.forename: Graciela
authors.initials: G
authors.lastname: Muniz-Terrera
authors.forename: Fiona E
authors.initials: FE
authors.lastname: Matthews
keywords: Beta-binomial distribution; Latent class model; Mini-mental state examination; Random-effects model