Change point models for cognitive tests using semi-parametric maximum likelihood

Ardo Van Den Hout*, Graciela Muniz-Terrera, Fiona E. Matthews

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)684-698
Number of pages15
JournalComputational statistics & data analysis
Issue number1
Early online date3 Aug 2012
Publication statusE-pub ahead of print - 3 Aug 2012


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


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