Change point models for cognitive tests using semi-parametric maximum likelihood
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.
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- 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.
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- Luc Bauwens & Jeroen V.K. Rombouts, 2009.
"On Marginal Likelihood Computation in Change-point Models,"
Cahiers de recherche
- 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.
- BAUWENS, Luc & ROMBOUTS, Jeroen VK, . "On marginal likelihood computation in change-point models," CORE Discussion Papers RP -2403, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- BAUWENS, Luc & ROMBOUTS, Jeroen, 2009. "On marginal likelihood computation in change-point models," CORE Discussion Papers 2009061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- 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.
- 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.
- 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.
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