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

Author

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

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.

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

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    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. Murray Aitkin, 1999. "A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 55(1), pages 117-128, March.
    3. 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, August.
    4. 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.
    5. Bartolucci, Al & Bae, Sejong & Singh, Karan & Griffith, H. Randall, 2009. "An examination of Bayesian statistical approaches to modeling change in cognitive decline in an Alzheimer's disease population," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 561-571.
    6. 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.
    7. 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.
    8. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    9. 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.
    10. 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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    2. Chenghao Chu & Ying Zhang & Wanzhu Tu, 2020. "Stochastic functional estimates in longitudinal models with interval‐censored anchoring events," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 638-661, September.

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