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


  • van den Hout, Ardo
  • Muniz-Terrera, Graciela
  • Matthews, Fiona E.


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.

Suggested Citation

  • van den Hout, Ardo & Muniz-Terrera, Graciela & Matthews, Fiona E., 2013. "Change point models for cognitive tests using semi-parametric maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 684-698.
  • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:684-698
    DOI: 10.1016/j.csda.2012.07.024

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    References listed on IDEAS

    1. Bauwens, Luc & Rombouts, Jeroen V.K., 2012. "On marginal likelihood computation in change-point models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3415-3429.
    2. Daniel Rudoy & Shelten G. Yuen & Robert D. Howe & Patrick J. Wolfe, 2010. "Bayesian change-point analysis for atomic force microscopy and soft material indentation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(4), pages 573-593.
    3. Sonja Greven & Thomas Kneib, 2010. "On the behaviour of marginal and conditional AIC in linear mixed models," Biometrika, Biometrika Trust, vol. 97(4), pages 773-789.
    4. Chiu, Grace & Lockhart, Richard & Routledge, Richard, 2006. "Bent-Cable Regression Theory and Applications," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 542-553, June.
    5. G. Muniz Terrera & A. van den Hout & F. E. Matthews, 2011. "Random change point models: investigating cognitive decline in the presence of missing data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(4), pages 705-716, November.
    6. Stasinopoulos, D. M. & Rigby, R. A., 1992. "Detecting break points in generalised linear models," Computational Statistics & Data Analysis, Elsevier, vol. 13(4), pages 461-471, May.
    7. Hall, Charles B. & Ying, Jun & Kuo, Lynn & Lipton, Richard B., 2003. "Bayesian and profile likelihood change point methods for modeling cognitive function over time," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 91-109, February.
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