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Modelling sparse generalized longitudinal observations with latent Gaussian processes

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  • Peter Hall
  • Hans‐Georg Müller
  • Fang Yao

Abstract

Summary. In longitudinal data analysis one frequently encounters non‐Gaussian data that are repeatedly collected for a sample of individuals over time. The repeated observations could be binomial, Poisson or of another discrete type or could be continuous. The timings of the repeated measurements are often sparse and irregular. We introduce a latent Gaussian process model for such data, establishing a connection to functional data analysis. The functional methods proposed are non‐parametric and computationally straightforward as they do not involve a likelihood. We develop functional principal components analysis for this situation and demonstrate the prediction of individual trajectories from sparse observations. This method can handle missing data and leads to predictions of the functional principal component scores which serve as random effects in this model. These scores can then be used for further statistical analysis, such as inference, regression, discriminant analysis or clustering. We illustrate these non‐parametric methods with longitudinal data on primary biliary cirrhosis and show in simulations that they are competitive in comparisons with generalized estimating equations and generalized linear mixed models.

Suggested Citation

  • Peter Hall & Hans‐Georg Müller & Fang Yao, 2008. "Modelling sparse generalized longitudinal observations with latent Gaussian processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 703-723, September.
  • Handle: RePEc:bla:jorssb:v:70:y:2008:i:4:p:703-723
    DOI: 10.1111/j.1467-9868.2008.00656.x
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    References listed on IDEAS

    as
    1. Fang Yao & Hans-Georg Müller & Andrew J. Clifford & Steven R. Dueker & Jennifer Follett & Yumei Lin & Bruce A. Buchholz & John S. Vogel, 2003. "Shrinkage Estimation for Functional Principal Component Scores with Application to the Population Kinetics of Plasma Folate," Biometrics, The International Biometric Society, vol. 59(3), pages 676-685, September.
    2. Cécile Proust & Hélène Jacqmin-Gadda & Jeremy M. G. Taylor & Julien Ganiayre & Daniel Commenges, 2006. "A Nonlinear Model with Latent Process for Cognitive Evolution Using Multivariate Longitudinal Data," Biometrics, The International Biometric Society, vol. 62(4), pages 1014-1024, December.
    3. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    4. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    5. Patrick J. Heagerty, 1999. "Marginally Specified Logistic-Normal Models for Longitudinal Binary Data," Biometrics, The International Biometric Society, vol. 55(3), pages 688-698, September.
    6. Vandna Jowaheer, 2002. "Analysing longitudinal count data with overdispersion," Biometrika, Biometrika Trust, vol. 89(2), pages 389-399, June.
    7. Jeng‐Min Chiou & Hans‐Georg Müller, 2005. "Estimated estimating equations: semiparametric inference for clustered and longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 531-553, September.
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